PRODUCTION AND OPERATIONS MANAGEMENT POMSywang195/assets/pdf/Wang2011.pdf · MFA [Multiﬁbre...

Regulatory Trade Risk and Supply Chain Strategy

Yimin WangWP Carey School of Business Arizona State University Tempe Arizona 85287-4706 USA yimin_wangasuedu

Wendell GillandKenan-Flagler Business School The University of North Carolina at Chapel Hill Chapel Hill

North Carolina 27599-3490 USA wendell_gillanduncedu

Brian TomlinTuck School of Business Dartmouth College Hanover New Hampshire 03755-9000 USA BrianTTomlintuckdartmouthedu

Trade regulations are an important driver of supply chain strategy in many industries For example the textile paperchemical and steel industries grapple with significant levels of non-tariff barriers (NTBs) such as safeguard controls and

countervailing duties We explore three often observed supply chain strategies in industries subject to NTBs direct procurementsplit procurement and outward processing arrangements (OPAs) We characterize the optimal procurement quantities for each ofthese three strategies and examine how industry and country characteristics influence the firmrsquos strategy preference Forexample we establish that the direct and split strategy profits increase in the NTB price variance but decrease in the mean priceThese effects are sufficiently large that NTB price characteristics can dictate which supply chain strategy is preferred Both thecost disadvantage and lead-time advantage of domestic production are also significant influencers of the preferred strategy as isthe domestic-country mandated production constraint associated with the OPA strategy

Key words regulatory trade risk non-tariff barrier dual sourcing supply chainHistory Received August 2008 Accepted March 2010 by Eric Johnson after 2 revisions

1 IntroductionAs firms increasingly rely on foreign countries to pro-duce goods for their domestic market internationaltrade regulations become an important determinant ofsupply chain strategy While tariffs (pre-determinedduties levied on imported goods) have been falling inthe past two decades from an average of 63 in 1995to 38 in 2000 according to the World Trade Organi-zation (WTO) there has been a concomitant increase inso-called non-tariff barriers (NTBs) eg safeguardcontrols antidumping rules countervailing duties andvoluntary export restraints (World Economic Situationand Prospects WTO 2006) Blonigen and Prusa (2001)report that lsquolsquosince 1980 more AD [antidumping]duties are now levied in any one year worldwide thanwere levied in the entire period of 1947ndash1970rsquorsquo Someunderlying causes of the rise of NTBs include foreigninterests (Hillman and Ursprung 1988) asymmetricinformation (Feenstra and Lewis 1991) the politicalpower balance between domestic interest groups(Rosendorff 1996) the increased importance of politi-cal contributions (Yu 2000) and the pressure to reducetariffs (Anderson and Schmitt 2003)

Historically the textile industry was subject to acomplex system of bilateral quotas but the nature oftrade barriers has been evolving lsquolsquoIn 1995 the Agree-

ment on Textiles and Clothing (ATC) replaced theMFA [Multifibre Arrangement] starting a 10-yearprocess of eliminating quotas for international tradein clothing and textilesrsquorsquo (Martin 2007 p 2) Howeversoon after the expiration of the ATC the EuropeanUnion (EU) and the United States implemented safe-guard controls (temporary quotas in this case) untilthe end of 2008 Post-2008 numerous countries haveimplemented antidumping measures (Martin 2007)and there has been an increase in US companies seek-ing countervailing duties on imported textile products(Reichard 2009) Looking beyond the textile industrytwo recent US examples are the 35 safeguard controlplaced on Chinese tires and the November 5 2009decision to impose a preliminary countervailing dutyon imports of Chinese oil pipes an industry withUS$26 billion of Chinese imports in 2008 (PalmerReuters November 5 2009) The countervailing dutyon oil pipes is quite variable (from 3653 to 9914depending on the exporting company) and uncertain(the duty will be collected first if the preliminarydetermination is not upheld next year the duty will bereturned) In another example from November 2009the United States imposed preliminary countervailingduties ranging from 202 to 43773 on imports ofsteel wire decking from China

522

PRODUCTION AND OPERATIONS MANAGEMENTVol 20 No 4 JulyndashAugust 2011 pp 522ndash540ISSN 1059-1478|EISSN 1937-5956|11|2004|0522

POMSDOI 101111J1937-5956201001167X

r 2010 Production and Operations Management Society

Many industries such as textiles footwear paperchemicals steel and agriculture face significant levelsof NTBs NTBs such as the EU initiated safeguardNTB are designed to protect domestic industries Theyare typically targeted at low cost countries (LCCs) andemerging economies that have a distinct cost advantagein the protected industry For example the EU safe-guard NTB limits the total annual quantity of thecontrolled product that can be imported into the EUfrom a targeted country In what follows we describethree common supply chain strategies seen in manydifferent industries that face NTB risks To be concretewe use the EU-initiated safeguard NTB as an illustra-tive example and focus on a EU firm that is interestedin sourcing finished product from some LCC that issubject to safeguard controls However these threestrategies are also used for other types of NTBs and alsoby other non-EU countries

1 Direct procurement The firm sources exclusivelyfrom an LCC that is subject to safeguard controlsBecause of its sourcing cost advantage direct pro-curement is a potentially high reward strategybut it is a high risk strategy because it passivelyaccepts safeguard controls

2 Split procurement Concerned about safeguardrisk the firm sources from two different countriesIn particular the firm sources only a fraction ofits needs from LCC and sources the rest from amedium cost country (MCC) that is not subject tosafeguard controls The split procurement strategytakes advantage of the lower production cost inLCC but partially protects the firm in the eventthat the finished product from LCC cannot beimported into the EU Because of its higher sourc-ing cost split procurement is a medium rewardstrategy and because it has lower safeguard riskexposure it is a medium risk strategy

3 Outward processing arrangement (OPA) To com-pletely avoid safeguard controls the firm canadopt an OPA strategy Many economic entitiesincluding the United States the EU and HongKong have OPAs with other countries1 An OPAallows the firm to perform certain productionactivities domestically and let suppliers in asafeguard-controlled country perform additionalor full processing The finished product subjectto specific regulations is not subject to safeguardcontrol or full tariffs2 To qualify for OPA thefirm must (1) maintain a full domestic productionline for the finished product (2) domestically pro-duce a quantity that exceeds a certain fraction ofthe firmrsquos total (domestically produced plus im-ported) quantity and (3) use domestically sourcedraw materials (see DTI 2006) For instance knittedcotton shirts sourced from China are subject to

safeguard control if imported to the EU Howevera firm based in Poland for example can avoid thesafeguard control by doing the following sourcethe fabric in the EU ship it to China for processingand import the finished product back to the EUand also produce in Poland a quantity of shirtsthat satisfies the EU mandated minimum produc-tion level OPA has no safeguard risk but becauseof its higher domestic production cost it is a lowreward strategy

In summary the direct procurement strategy hasthe highest NTB risk exposure but the lowest (aver-age) procurement cost The split procurement strategyreduces but does not eliminate NTB risk The OPAcompletely removes NTB risk but the firm mustmaintain a certain level of domestic productionwhich implies a higher procurement cost but a shorterlead time3

In this paper we fully characterize the three strat-egies and explore how certain industry and countrycharacteristics influence a firmrsquos strategy preferenceOur investigation leads to a number of interestingmanagerial and policy implications For examplewe establish that the direct and split strategyprofits increase in the NTB price variance but de-crease in the mean price These effects are sufficientlylarge that NTB price characteristics can dictatewhich supply chain strategy is preferred Both thecost disadvantage and lead-time advantage of do-mestic production are also significant influencersof the preferred strategy as is the domestic-countrymandated production constraint associated withthe OPA strategy We find that policy makerrsquosshould pay careful attention to industry and countrycharacteristics (such as NTB price and demandvolatility) when setting the mandated domestic pro-duction fraction in the OPA strategy lest theyunwittingly induce firms to abandon OPA and moveall production overseas

The rest of this paper is organized as follows Wediscuss the relevant literature in section 2 Section 3introduces model preliminaries We further developand characterize the three strategies in section 4 Man-agerial and policy implications are discussed in section5 Concluding remarks are presented in section 6 Allproofs are contained in the Appendix Some additionalresults are contained in the supporting information

2 LiteratureThere has been extensive research on NTBs in theeconomics political economy and international lawliteratures The economics literature focuses mainlyon the welfare effect of NTBs eg Magee et al (1972)and the underlying causes of NTBs eg Yu (2000)

Wang Gilland and Tomlin Regulatory Trade Risk and Supply Chain StrategyProduction and Operations Management 20(4) pp 522ndash540 r 2010 Production and Operations Management Society 523

The political economy literature focuses primarily onthe influence of the political process (eg lobbying) ontrade policy eg Jones (1984) The international lawliterature has a diverse focus from the equitabletreatment of domestic and foreign firms (so-calledlsquolsquonational treatmentrsquorsquo) in relation to NTBs eg Jackson(1989) to the legal interpretation of specific NTBs egPope amp Talbot Inc v Canada (2000) Most of the aboveresearch in economics and international law dealswith policy issues from an international trade perspec-tive In the operations management literature researchon the implications of trade barriers on a firmrsquos sourc-ing strategy is relatively sparse There exists however astream of literature on global operations where specificissues such as global transportation foreign exchangerate and tariffs are explicitly modeled eg Arntzenet al (1995) Kouvelis et al (2004) and Lu and VanMieghem (2009) We note that Meixell and Gargeya(2005) provide an excellent review of the relevant lit-erature in global supply chain design

Arntzen et al (1995) study global supply chain man-agement issues at Digital Equipment Corporation Theydevelop a large-scale mixed-integer program (thatincorporates tariff rules) to solve the facility locationand transportation problem In a similar vein Munsonand Rosenblatt (1997) also use a mixed-integer linearprogramming approach to solve a global sourcingproblem when a local content rule must be satisfiedMoving beyond local content rules Kouvelis et al(2004) provide a comprehensive treatment of the globalplant location problem incorporating globallocation-related constraints such as government sub-sidy tarifftax and local content rules Using amathematical programming model they explore howthese global location-related constraints influence theoptimal plant locations A recent paper by Li et al(2007) studies a raw material sourcing problem in thepresence of local content rules as well as value-addedrequirements All of these four papers use deterministicmodels and their intent is the development of decisionsupport systems In contrast the purpose of this paperis to explore different supply chain strategies seen inindustries subject to stochastic NTBs and to developmanagerial insights by analyzing and comparing thestrategies Lu and Van Mieghem (2009) explore com-monality strategies in a multi-market facility designproblem and include deterministic tariffsduties in theprocurement costs

Because many NTBs can be modeled as stochasticprice export permits (see section 41) our researchis somewhat related to stochastic price (cost) modelsin the operations literature Kalymon (1971) studies amulti-period purchasing problem where the futurepurchasing prices are Markovian and proves that astate-dependent (s S) policy is optimal Other researchthat incorporates a stochastic purchasing costprice

includes Ozekici and Parlar (1999) and Berling andRosling (2005) All of these papers investigate theform of the optimal purchasing policy for a givenprocurement configuration but do not contrast differ-ent supply chain configurations

The OPA strategy involves two production modesan early procurement decision with a longer lead timeand a postponed domestic production decision with ashorter lead time As such our research is related tothe quick-response literature eg Fisher and Raman(1996) Iyer and Bergen (1997) Kim (2003) and refer-ences therein which has its roots in the earlier researchon forecast updating eg Graves et al (1986) Similarto this stream of literature we also allow for forecastupdating in our work

Finally we note that regulatory trade concerns can beviewed as one element of supply chain risk As such ourwork relates to the broad stream of literature on man-aging supply chain risk eg Bakshi and Kleindorfer(2009) Kleindorfer and Saad (2005) Tomlin (2006) andreferences therein Split procurement is a dual sourcingstrategy in which the firm sources from two countriesThe use of dual sourcing to manage other types of sup-ply risk has been explored by Agrawal and Nahmias(1997) Dada et al (2007) and others

3 Model PreliminariesWe adopt a newsvendor type of model ie there is asingle selling season and only one ordering opportunity(unless otherwise stated) This is a reasonable assump-tion for certain industries eg textile and clothing butmay not be appropriate for other industries eg tiresand oil pipes In what follows we first describe thesupply aspects of our model and then describe the de-mand aspects The firm may source the finishedproduct either domestically (DOM) or overseas froman LCC or an MCC We adopt the convention that LCCis subject to NTB control for importing the product toDOM but MCC is not (unless otherwise stated) Let q0q1 and q2 denote the firmrsquos procurement quantities inLCC MCC and DOM respectively (The procurementquantity q2 in DOM is actually produced by the firmbut for consistency we use the term procurement) Thefirm does not have to import all it procures in LCC andMCC and we therefore use y0 and y1 to denote thefirmrsquos shipment ie import quantities from LCC andMCC respectively The firm cannot import more than itprocures ie yi qi i 5 0 1

Let c0 c1 and c2 denote the unit procurement costfrom LCC MCC and DOM respectively We modelthe common practice that the firmrsquos purchasing con-tract is denominated in its domestic currency andtherefore exchange rates can be ignored There areseveral prevailing types of purchasing contracts ininternational trade FOB (Free On Board) CNF (Cost

Wang Gilland and Tomlin Regulatory Trade Risk and Supply Chain Strategy524 Production and Operations Management 20(4) pp 522ndash540 r 2010 Production and Operations Management Society

and Freight) and CIF (Cost Insurance and Freight)We adopt the often-used CNF type of contract Forour purposes there are two important attributesof a CNF contract worth noting (i) the lsquolsquoprocurementrsquorsquocost includes both purchasing and transportationcosts and (2) the procurement cost is effectivelyincurred upfront as the firm must reserve the funds(to secure a bankrsquos letter of credit to the supplier)when the contract is signed If the firm later imports lessthan it agreed to purchase the payment terms areamended to reflect the avoidance of a portion of thetransportation costs By definition of the countriesit follows that the unit procurement costs satisfyc0 c1 c2 reflecting the relative cost advantages inLCC and MCC Units that are produced but not shippedfrom LCC (MCC) are salvaged at s0 (s1) Units left overin DOM are salvaged at s2 Note that s1 s0 becausec1 c0 but s2 s1 does not necessarily hold as the sal-vage values s0 and s1 include savings from avoidingtransportation to DOM (because the firm pays for pro-duction and transportation when the procurementdecision from LCCMCC is made) For reasons ofspace we restrict attention to s2 s1 but relax this in thenumerical study The analysis for s2os1 can be found inthe supporting information Appendix S1

The procurement lead time for LCCMCC is LP1LTwhere LP is the production time and LT is the trans-portation time to DOM We assume that LCC andMCC have identical production times and identicaltransportation times Because DOM procurement re-quires no transportation the procurement lead time issimply the domestic production lead time which wedenote by LD For reasons of space we restrict atten-tion to LT LD LP1LT The analysis for LDoLT andLD4LP1LT is contained in the supporting informa-tion Appendix S2 Note that we allow for LDoLT inour numerical study

Let r and p denote the unit revenue and penalty costfor unsatisfied demand respectively Let F( ) and f ( )denote the distribution and density function of thefirmrsquos initial forecast of demand X In addition we usem and s to denote the mean and the standard devi-ation of the initial forecast In each of the threestrategies certain decisions eg the LCCMCC pro-curement decisions are made at an earlier point intime than other decisions eg the LCCMCC ship-ping decisions andor the DOM production decisionWe therefore allow for the possibility that the firmupdates its demand forecast over time If between aninitial and a later decision the firm obtains additionalmarket information y the firmrsquos updated demanddistribution is Fy( ) If y completely resolves marketuncertainty then the updated demand distribution issimply the realized demand x

In this paper E[ ] denotes the expectation operatorand if F( ) represents the distribution function then

FethTHORN frac14 1 FethTHORN We use the terms lsquolsquoincreasingrsquorsquo andlsquolsquodecreasingrsquorsquo in the weak sense

4 Modeling and CharacterizationIn this section we first describe and characterize thedirect and split procurement strategies and thenthe OPA strategy Both direct and split strategies arespecial cases of a more general model in which thefirm sources from two countries each of which maybe subject to NTB controls4 In what follows thereforewe first characterize this more general diversificationstrategy and then explore directsplit procurementstrategies as special cases of this general model Beforecharacterizing the diversification strategy we need firstto operationalize the concept of NTBs

41 Modeling NTBsIn general NTBs can either be quantity based egsafeguards and voluntary export restraints or pricebased eg antidumping and countervailing duties5

A quantity-based NTB sets an upper limit on the totalamount of the restricted product that can be importedfrom the targeted exporting country for a fixed periodof time Typically the quantity-based NTB is managedby the targeted country and monitored by the import-ing country A price-based NTB collects a punitive dutyon each unit of the targeted product from the exportingcountry depending on the outcome of the NTB inves-tigation The key distinction between a price-basedNTB and a standard tariff is that a tariff is a predictableduty whereas the price-based NTB is an uncertain duty

Both types of NTBs are uncertain for the importingfirm when procurement decisions are made Forquantity-based NTBs the availability of export per-mits depends on uncertain exports by other firms Forprice-based NTBs the initiation process can belengthy (6ndash12 months) and the outcome of the puni-tive duty decision is highly uncertain For either NTBit is therefore difficult at the time of procurement (iebefore production is launched) for the importing firmto predict the future status of the NTB A quantity-based NTB can be viewed from the importing firmrsquosperspective as equivalent to a price-based NTB Tosee this consider a particular quantity-based NTB thesafeguard between the EU and China the authoritiesin China usually assign a fraction of the availablequantity permits (as specified by the safeguard) toestablished large enterprises at a negotiated price andthen auction off the remaining permits on the marketTo avoid permit speculation however a suppliercannot purchase safeguard permits until it has fin-ished production The permits once allocated can betraded among suppliers (subject to the verification ofproduction completion) Therefore the importingfirm can theoretically obtain a sufficient quantity of


safeguard permits if it is willing to pay the prevail-ing price Because quantity-based NTB permits canbe traded both quantity and price-based NTBs canbe modeled as a stochastic price permit that must beobtained at the time of shipment If the prevailingprice is too high the firm can choose not to exportthe product and instead salvage it in the local pro-ducing country

Hereafter we refer to an NTB price with the under-standing that the price might refer to a (per-unit)permit price in the context of quantity-based NTBsor the per-unit duty in price-based NTBs We letG0( ) and g0( ) denote the distribution and densityfunction of the NTB price Z0 in LCC In the casesfor which we allow MCC to also be subject to NTBs(eg in diversification strategy) we let G1( ) and g1( )denote the distribution and density function of theNTB price Z1 in MCC6 We assume that the firmrsquosprocurement quantities are not so large as to influencethe NTB prices

42 Diversification StrategyIn the diversification strategy the firm first decides itsLCC and MCC procurement quantities q0 and q1and then later decides its LCC and MCC shipmentquantities y0 and y1 to DOM We count the timebackwards and adopt the convention that the sellingseason occurs at time 0 Recall that we assume LCCand MCC have the same lead time and therefore thefirm makes its LCCMCC procurement decisionssimultaneously at time LP1LT The same is true forthe shipment decisions at time LT We have a three-stage stochastic decision problem and the sequenceis as follows In the first stage at time LP1LT pro-curement quantities q0 and q1 are set In the secondstage at time LT after NTB prices and demand infor-mation gain y have been realized the shipmentquantities y0 and y1 are set In the third stage at time0 the remaining demand uncertainty is resolved andthe firm uses its available inventory to fill as muchdemand as it can (see Figure 1)

In what follows we first characterize the firmrsquossecond-stage shipment problem (the third stage is

trivial) and then characterize its first-stage procure-ment problem In the second stage the firm observesthe realized NTB prices z0 and z1 and the informationgain y The firmrsquos problem is to determine the ship-ment quantities y0 and y1 from LCC and MCC LetHyethyTHORNfrac14 r

R y0 xdFyethxTHORNthorn

R1y ydFyethxTHORN

pR1

y ethxyTHORNdFyethxTHORNthorns2

R y0 ethy xTHORNdFyethxTHORN The second-stage expected profit

function is

pethy0 y1jq0 q1 z0 z1 yTHORN frac14Hyethy0 thorn y1THORN thorn s0ethq0 y0THORN

thorn s1ethq1 y1THORN z0y0 z1y1

eth1THORN

where recall that q0 and q1 are the firmrsquos first-stageprocurement decisions The optimal shipment policy(See Lemma A1 in the Appendix) is either full orpartial shipment If the realized NTB price in LCC(MCC) is low then it is advantageous to ship all fin-ished product from LCC (MCC) because of the highersalvage value in DOM relative to LCC (MCC) On theother hand if the realized NTB price is high then it isnot economical to ship any finished product The firmmakes a partial shipment only when the realized NTBprice is moderate

We are now in a position to characterize the firmrsquosfirst-stage problem Let Pethq0 q1jyTHORN denote the firmrsquosfirst-stage expected profit function conditional onthe realized information y Substituting the optimalshipment decisions y0 and y1 from Lemma A1 in theAppendix into (1) and taking the expectation over z0

and z1 we have

Pethq0 q1jyTHORN frac14 c0q0 c1q1

thorn Ez0z1frac12pethy0 y1jq0 q1 z0 z1 yTHORN

eth2THORN

THEOREM 1 (a) The firmrsquos first-stage conditional expectedprofit function Pethq0 q1jyTHORN is jointly concave in q0 and q1(b) The firmrsquos first-stage expected profit functionPethq0 q1THORN frac14 Ey frac12pethq0 q1jyTHORN is jointly concave in q0 and q1

Because the expected profit function is well be-haved the firmrsquos first-stage production quantity can

0

bullInitial demand forecast F (x )

bullUncertain NTB prices

bullDecide LCCMCC procurement

bullUpdate demand forecast F (x )

bullObserve realized NTB prices

bullDecide LCCMCC shipment

LCCMCC Production Lead Time LP

bullSatisfy realized demand

Transit Time LT

1 2 3

LTLP + LT

Figure 1 Decision Time Line for the Diversification Strategy


be uniquely determined Closed form solutions how-ever will not typically exist

Having partially characterized the general diversifica-tion model we now analyze the direct and splitstrategies To allow further characterization for the re-mainder of this subsection (section 42) we assumethat the firm observes the realized market demand byshipment time ie y completely resolves demand un-certainty This approximates the situation where thetransportation time is short relative to the productionlead time a situation which can sometimes arise in theclothing industry While the ratio of the production leadtime to the transportation time for menrsquos jeans sourcedfrom coastal China is approximately 21 (Abernathy et al2005) the ratio for other textile products and other Asiancountries can be 31 (Nuruzzaman 2009) and even ashigh as 91 (Volpe 2005)

421 Split Procurement In the split procurementstrategy the firm procures from two countries LCCand MCC where LCC is subject to NTBs but MCC isnot This model can be obtained by setting z1 0indicating there is no NTB risk associated with MCCSubstituting z1 0 into (1) we obtain the second-stage profit as pethy0 y1jq0 q1 z0 xTHORN frac14 Hxethy0 thorn y1THORNthorns0ethq0 y0THORN thorn s1ethq1 y1THORN z0y0 The optimal shipmentquantity is obtained as a special case of Lemma A1 inthe Appendix

y1frac14q1 y0frac14

q0 z0 s2 s0

minfq0 ethx y1THORNthorng s2 s0oz0rthornps0

0 z04rthorn p s0

8gtgtltgtgt

eth3THORN

Equation (3) implies that the firm always makes a fullshipment from MCC regardless of the realizeddemandmdasheven when the realized NTB price forLCC is very low Substituting (3) and z1 0 into (2)(and taking the expectation over X) we have

Pethq0 q1THORN

frac14Z s2s0

0

Z q0thornq1

0

ethrxthorn s2ethq0 thorn q1 xTHORN z0q0THORNdFethxTHORNdG0ethz0THORN

thornZ rthornps0

0

Z 1q0thornq1

rethq0 thorn q1THORN pethx q0 q1THORNeth z0q0THORNdFethxTHORNdG0ethz0THORN

thornZ 1

s2s0

Z q1

0

ethrxthorn s2ethq1 xTHORN thorn s0q0THORNdFethxTHORNdG0ethz0THORN

thornZ rthornps0

s2s0

Z q0thornq1

q1

rxthorn s0ethq0 thorn q1 xTHORN z0ethx q1THORNeth dFethxTHORNdG0ethz0THORN

thorn G0ethrthorn p s0THORNZ 1

q1

rq1 pethx q1THORN thorn s0q0THORNeth dFethxTHORN c0q0 c1q1

eth4THORN

By Theorem 1 (4) is jointly concave The followingcorollary characterizes the optimal solution

COROLLARY 1 In the split procurement strategy q0 and q1either equal zero or jointly satisfy the following twoequations

Fethq0 thorn q1THORNZ rthornps0

0

ethrthorn p s0 z0THORNdG0ethz0THORN

thorn Fethq0 thorn q1THORNZ s2s0

0

eths2 s0 z0THORNdG0ethz0THORN frac14 c0 s0

ethrthorn pTHORNFethq1THORN thorn Fethq0 thorn q1THORN Fethq1THORN

Z rthornps0

0


thorn ethFethq0 thorn q1THORN Fethq1THORNTHORNZ s2s0

0

eths2 s0 z0THORNdG0ethz0THORN

frac14 c1 s2

422 Direct Procurement In the direct procurementstrategy the firm single sources from LCC which issubject to NTBs This model can be obtained from thegeneral diversification model by setting z1 1 whichmakes MCC an infinite cost country Substitutingz1 1 into (1) we have y1 1 and the firmrsquossecond-stage profit is pethy0jq0 z0 xTHORN frac14 Hxethy0THORN z0y0thorns0ethq0 y0THORN where HxethyTHORN frac14 r minethy xTHORN pethx yTHORNthornthorns2ethy xTHORNthorn reflecting the fact that y completelyresolves demand uncertainty The optimal solution tothe direct procurementrsquos second-stage (shipment)problem is obtained as a special case of Lemma A1 inthe Appendix

y0 frac14q0 z0 s2 s0

minfx q0g s2 s0oz0 rthorn p s0

0 z04rthorn p s0

8gtltgt eth5THORN

In this case regardless of the size of the realizeddemand the firm ships the finished product if andonly if z0 r1p s0 ie the realized NTB price isless than the unit profit foregone by not shippingSubstituting (5) and z1 1 into (2) (and taking theexpectation over X) we have

Pethq0THORN frac14Z s2s0

0

Z q0

0

rxthorn s2ethq0 xTHORN z0q0eth THORNdFethxTHORNdG0ethz0THORN

thornZ rthornps0

0

Z 1q0

rq0 pethx q0THORN z0q0eth THORNdFethxTHORNdG0ethz0THORN

thornZ 1

rthornps0

s0q0 pEfrac12xeth THORNdG0ethz0THORN

thornZ rthornps0

s2s0

Z q0

0

rxthorn s0ethq0 xTHORN z0xeth THORN

dFethxTHORNdG0ethz0THORN c0q0

eth6THORN


By Theorem 1 (6) is concave The following corollarycharacterizes the optimal solution

COROLLARY 2 In the direct procurement strategy thefirmrsquos optimal procurement quantity is given by q0 frac14 F1

G0ethrthornps0THORNethrthornpc0THORNG0ethrthornps0THORNethc0s0THORNR rthornps0

0z0dG0ethz0THORN

G0ethrthornps0THORNethrthornps0THORNR s2s0

0eths2s0z0THORNdG0ethz0THORN

R rthornps0

0z0dG0ethz0THORN

If the NTB price is equal to zero with probability 1

then q0 frac14 F1 rthornpc0

rthornps0

which is the familiar news-

vendor quantity This needs to be appropriatelyadjusted (as specified in Corollary 2) to accountfor the stochastic NTB price and the fact that thedecision to ship or not is made after demand isrealized The following corollary establishes somebasic sensitivity results for both the direct procure-ment and split procurement strategies

COROLLARY 3 For both the direct procurement and splitprocurement strategies the firmrsquos optimal expected profitis decreasing in the unit procurement cost c0 (and c1) andthe unit penalty cost p and increasing in the unit salvagevalues s0 and s2 and the unit revenue r

The above corollary characterizes the directionalimpact of basic system parameters on the firmrsquosoptimal expected profit These sensitivity results arequite intuitive

43 Outward Processing ArrangementIn the OPA strategy the firm procures a fraction of theproduct domestically and procures the rest from anLCC The OPA strategy completely removes NTBcontrols but the firm must maintain a certain level ofdomestic production to qualify That is domestic(DOM) procurement must exceed a certain fraction ofthe total (DOM and LCC imported) procurement Theseverity of the domestic procurement constraintie the minimum fraction is a policy decision made

by the competent authorities eg the Department ofTrade and Industry in the firmrsquos domestic country(see EEC Regulation No 291392 eg)7

Recall that we use q2 to denote the firmrsquos DOM pro-curement quantity and y0 to denote the quantityimported from LCC Let 0 a 1 denote the compe-tent-authority imposed fraction of total (DOM plusLCC) procurement that the firmrsquos domestic procure-ment must satisfy That is the firmrsquos domesticprocurement quantity q2 must satisfy q2=ethy0 thorn q2THORN aThe fraction a is a policy-level decision that reflects thecompetent authoritiesrsquo desire to maintain domestic em-ployment opportunities and production capabilitiesFor the rest of this section we let yD denote informationgained by LD ie the time at which the DOM procure-ment is decided Let FyD

ethTHORN denote the updated demanddistribution at time LD

The firm faces a four-stage stochastic decision prob-lem and the sequence of events is as follows In thefirst stage at time LP1LT LCC procurement decisionq0 is set In the second stage at time LD (recall thatLT LD LP1LT) DOM procurement q2 is deter-mined based on the updated demand distributionIn the third stage at time LT LCC import quantity y0 isdetermined8 In the last stage the firm fulfills as muchdemand as possible after demand uncertainty is re-solved (See Figure 2)9

In what follows we first consider the firmrsquos third-stage problem (the last stage is trivial) To satisfy thedomestic procurement constraint the firmrsquos LCC importquantity y0 must satisfy 0 y0 (1a 1)q2 Becauses2 s0 we must have y0 frac14 minfq0 eth1=a 1THORNq2g re-gardless of the updated demand forecast at time LTSince q2 is determined at time LD the firm can equiv-alently determine y0 at time LD The firmrsquos second-stageexpected profit function is therefore

pethy0 q2jq0 yDTHORN frac14 c2q2 thorn s0ethq0 y0THORN thornHyDethy0 thorn q2THORN eth7THORN

where the shipment decision must satisfy y0 min q0

1aa q2

0


bullDecide LCC procurement

bullUpdate demand forecast F (x)

bullDecide DOM production

LCC Production Lead Time LP

bullUpdate demand forecast

bullDecide LCC shipment

Transit Time LT

1

2 4

ΔL DOM Production Lead Time LD

LTLP + LT LD

3


Figure 2 Decision Time Line for the Outward Processing Arrangement Strategy


THEOREM 2(a) The firmrsquos second-stage optimal expected profit func-

tion is concave in q0(b) For any given LCC procurement quantity q0 the

firmrsquos second stage optimal shipment and DOMprocurement decisions are given by the following

y0 frac14q0 q0 eth1 aTHORNkH

eth1 aTHORNkH q04eth1 aTHORNkH

(

q2 frac14

kL q0 q0 eth1 aTHORNkL

a1 a

q0 eth1 aTHORNkLoq0 eth1 aTHORNkH

akH q04eth1 aTHORNkH

8gtgtgtltgtgtgt

where kL frac14 F1yD

rthornpc2

rthornps2

and kH frac14 F1

yD

rthornpac2eth1aTHORNs0

rthornps2

(c) The firmrsquos second-stage expected profit is given by

pethy0 q2jq0 yDTHORN

frac14

c2q0 thorn ethrthorn p s2THORNR kL

0 xdFyDethxTHORN p EyD

frac12x q0 eth1 aTHORNkL

ethrthorn p ac2THORN q0

1athorn ethrthorn p s2THORNR q0

1a0 xdFyD

ethxTHORN eth1 aTHORNkLoq0

ethrthorn p s2THORN q0

1a FyD

q0

1a

pEyDfrac12x eth1 aTHORNkH

s0q0 thorn ethrthorn p s2THORNR kH

0 xdFyDethxTHORN pEyD

frac12x q04eth1 aTHORNkH

8gtgtgtgtgtgtgtgtgtgtltgtgtgtgtgtgtgtgtgtgt

eth8THORN

For a given LCC quantity q0 the total inventorymade available (imported plus domestically pro-duced) is kL q0(1 a) or kH depending on theupdated demand distribution at time LD In the lat-ter two cases the domestic fraction constraint a isbinding but it is not in the kL case Now kL is thenewsvendor produce-up-to level for DOM indicatingthat the firm produces the optimal domestic quantitywithout having to adjust for the domestic constraintIn contrast kH is the newsvendor produce-up-to levelfor a marginal cost of ac21(1 a)s0 To understandthis produce-up-to level consider that an additionalunit of inventory is created (subject to the bindingdomestic constraint) by producing a domestically andimporting (rather than salvaging) 1 a from LCCthus the effective marginal cost is ac21(1 a)s0

Given the characterization of the firmrsquos second-stage problem the firmrsquos first-stage problem can beexpressed as Pethq0THORN frac14 c0q0 thorn EyD


THEOREM 3 In the OPA strategy P(q0) the firmrsquos first-stage expected profit function is concave in the LCC pro-curement quantity q0

Therefore there exists a unique q0 that maximizesthe firmrsquos first-stage expected profit We note thatthis characterization is very general with respect tothe forecast evolution process the result holds as longas the information gained is non-decreasing overtime10

5 Managerial and Policy ImplicationsWe now explore how the firmrsquos strategy preference(direct split or OPA) is influenced by certain industryand country characteristics We ignore any fixed costsassociated with a strategy eg a fixed cost associatedwith locating in a particular country as the directionaleffects of fixed costs are clear We first describe thenumerical study used to augment some of our lateranalytical findings The study comprises 1102500problem instances (described in Table 1) We kept theDOM cost at c2 5 1 and so the other cost and revenueparameters are essentially scaled relative to the DOMcost Because we adopt a CNF type of contract inwhich the LCC and MCC procurement costs c0 and c1include transportation we explicitly call out the trans-portation cost in our numerical study and denote it asct This allows us to vary the percentage of cost as-sociated with transportation and also to relax theassumption that s2 s1 We use a Weibull distributionfor the NTB price in our numerical study because ithas a non-negative support and can assume variousshapes We also assume a normal distribution forsome of analytic results in this section One keydifference between the Weibull and the normal dis-tribution is that the former is not symmetric whereasthe latter is11 At the start of the planning horizon ieat time LP1LT the firm faces an identical demanddistribution regardless of which strategy the firm

Table 1 Numerical Study

Variable Value Variable Value Variable Value

c0 frac14 c0 thorn ct 020085 (005) ct 002010 (004) Demand mean 100

s0 20c0 thorn ct r 1228 (04) Demand coefficient of variation (CV) 0105 (01)

c1 frac14 c1 thorn ct 090 p 0 Non-tariff barrier (NTB) mean 005035 (005)

s1 20c1 thorn ct LP 4 NTB CV 0212 (02)

c2 100 LT 2 Outward processing arrangement policy a 0105 (01)

S2 20c2 LD 15 (1)

minmax (step size)


uses We adopt a linear martingale process for thedemand forecast evolution ie forecast revisionsare independent identical and normally distributedFor each of the 1102500 problem instances we com-puted the optimal profit for each strategy using a gridsearch technique When applicable the search tookadvantage of the concavity results established in thispaper by using a bisection search Let PDIR PSPL andPOPA denote the optimal profit for the direct splitand OPA strategies respectively

51 Managerial ImplicationsIn what follows we explore the impact (directionand magnitude) of changes in the level and predict-ability of NTB prices the LCC cost and transportationcost percentage the domestic lead time and OPA pro-duction constraint and the demand uncertainty andunit revenue

511 Level and Predictability of NTB Prices SomeNTBs are highly uncertain due to their allocationstructure eg safeguard measures and voluntaryexport restraints whereas other NTBs may be highbut with little uncertainty eg when an industry-levelantidumping duty has been determined and isexpected to last for a number of years We firstconsider stochastic rankings of NTB prices and thenexplore the impact of changes in the mean andvariance of NTB prices

A random variable Za is (first-order) stochasticallydominated by another random variable Zb if for anygiven value of z Ga(z) Gb(z) where Ga( ) andGb( ) are the distribution functions of Za and Zb re-spectively We say that Zb is stochastically larger thanZa and denote this by Zb Za

THEOREM 4 Let Zb0 Za

0 denote two possible NTB pricesin LCC All else equal PDIR under Z0

b is less than thatunder Z0

a and PSPL under Z0b is less than that under Z0

a

Therefore a stochastically larger NTB price hurtsthe DIR and SPL strategies12 Interestingly howevera higher NTB price variance can benefit the DIR andSPL strategies

THEOREM 5 If the NTB price is normally distributed withparameters N(m s) then all else being equal PDIR andPSPL decrease in m and increase in s

The standard deviation (or equivalently variance)result can be explained as follows The firmrsquos down-side exposure to a very high NTB price is boundedby the firmrsquos postponement option of not shippingthe finished product (in which case the firm avoidspaying the high NTB price but incurs the penaltycost for unfilled demand) However the upside

advantage of a very low NTB price is significantThis asymmetry between the bounded downsidedisadvantage and the upside advantage benefits thefirm as the NTB price variance increases

Turning to our numerical study Figure 3 illustratesthe impact of the NTB price mean and coeffi-cient of variation (CV) on the relative profit differ-ences between the three strategies For each meanCV pair Figure 3a shows the relative profit differ-ence between the DIR and SPL strategies wherethe number reported is the average of all prob-lem instances with that meanCV pair13 Figures 3band 3c show the relative profit difference be-tween OPA and DIR and between OPA and SPLrespectively In Figures 3b and 3c we see thatboth DIR and SPL become less attractive relativeto OPA as the mean (CV) NTB price increases(decreases) Because the OPA strategy is unaffectedby the NTB characteristics this observation indi-cates that both the DIR and SPL profits decrease(increase) in the mean (CV) of the NTB price Asimilar finding to Theorem 5 therefore holds evenwhen the NTB price has a Weibull rather than anormal distribution

While the directional result is important it isinteresting to observe the magnitude of the effect ofthe NTB mean and CV Consider the oil pipe exam-ple mentioned in section 1 some firms were hitwith a (provisional) 3653 countervailing dutywhile others were hit with a (provisional) 9914duty or equivalently the expected levy was 27 timeshigher for some firms than for others Looking atFigure 3b we see that an increase in the meanNTB price from 01 to 027 (ie by a factor of27)14 drives the relative profit difference betweenOPA and DIR from approximately 3 to 13 for aCV of 02 In other words OPA goes from beingsomewhat worse than DIR to being very signifi-cantly better15 So differences in the mean NTB pricethat are reasonable (given observations from prac-tice) can have a profound impact on strategy TheNTB price CV also has a material impact withchanges at higher CVs eg from 10 to 12 beingmore significant than changes at lower CVs egfrom 02 to 04

Finally we note that if the NTB price mean (CV) islow (high) the SPL strategy sources almost exclu-sively from LCC and so its profit is only slightlybetter than DIR (see Figure 3a)

512 LCC Cost and Transportation Cost While anincrease in the LCC procurement cost hurts allstrategies it is not immediately obvious howchanges in the LCC cost will influence the relativeranking of the strategies We address this through ournumerical study Figure 4 shows the impact of the


LCC procurement cost c0 and transportation cost ct onthe relative profit differences

Focusing first on the LCC cost c0 DIR becomes lessattractive compared with SPL or OPA as c0 increasesAt low values of c0 SPL is not concerned about theNTB price risk and sources exclusively from LCCand so DIR and SPL have the same profit (see Figure4a) As c0 increases the NTB price risk becomes alarger concern as the NTB adds to the effective LCCcost therefore SPL sources a larger fraction from

MCC to hedge against the NTB price DIR cannothedge and so SPL is increasingly favored over DIRas c0 increases Comparing DIR and OPA (Figure 4b)DIR becomes less attractive as c0 increases becauseOPA has the option of sourcing more domesticallyand the domestic cost disadvantage decreases as c0

increases This finding can be proven under certaintechnical conditions (details available upon request)Observe that the relative profit difference is very sen-sitive to the LCC cost indicating that small changes to

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20

LCC unit procurement cost c0

(Π D

IRminus

Π S

PL)

Π S

PL

Rel profit diff betweenDIR and SPL (SPL preferred

below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR

Rel profit diff betweenOPA and DIR (DIR preferred

below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL

Rel profit diff betweenOPA and SPL (SPL preferred

below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)

Figure 4 Impact of Low Cost Country Procurement Cost and Transportation Cost

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)

NTB CV increasesfrom 02 to 12

NTB CV increasesfrom 02 to 12 NTB CV increases

from 02 to 12

(a) (b) (c)

Figure 3 Impact of Non-Tariff Barriers Price Mean and Coefficient of Variation


the LCC cost may significantly impact strategy pref-erence even when fixed costs are considered16

Comparing SPL and OPA (Figure 4c) the relativeprofit difference is not monotonic in c0 indicatingthat an increase in the LCC cost may benefit orhurt OPA (relative to SPL) depending on the currentLCC cost When c0 is low an increase hurts SPLbecause SPL sources a large fraction from LCCbut OPArsquos LCC production is constrained by the do-mestic production constraint When c0 is veryhigh (ie close to the MCC cost) an increase hurtsOPA because SPL sources almost exclusively fromMCC while OPA still sources some portion fromLCC

Turning now to the transportation cost ct wesee from Figure 4 that it has a negligible impact onthe relative profit differences Recall that the LCCand MCC costs ie c0 and c1 include the trans-portation cost as we adopt the CNF-type contractand so varying ct for a fixed c0 and c1 does notchange the total procurement cost but does changethe portion spent on transportation Because thestrategies can choose not to ship product afterdemand is realized the transportation cost does in-fluence profit somewhat but it does not have a largeimpact on the relative profits (for the values chosenin the numeric study)

513 Domestic Lead Time and OPA ProductionConstraint The OPA strategy engages in some domes-tic production and we next explore the impact of thedomestic lead time LD and the competent-authority

imposed domestic production constraint a Because ashorter domestic lead time and less severe domesticconstraint allows OPA to more precisely fine tuneinventory based on updated demand information thefollowing theorem formalizes what one might expectie OPA benefits from shorter domestic lead times andlower domestic production constraints

THEOREM 6 All else being equal POPA decreases in thedomestic lead time LD and production constraint a

Because both DIR and SPL are unaffected by LD

and a OPA becomes relatively more attractive as LD

and a decrease (see Figure 5)17 Observe that both thelead-time and the production constraint have a sig-nificant impact While not shown in the figure theeffect of the domestic lead time is much more pro-nounced at higher initial demand CVs than at lowerinitial demand CVs18 This derives from the fact thatthe value of delaying domestic production (until abetter demand forecast is obtained) is higher wheninitial demand uncertainty is higher

514 Demand Uncertainty and Unit Revenue Wenow consider market and product characteristicsfocusing in particular on the demand uncertaintyand product revenue Figure 6 presents the relativeprofit differences as a function of the demand CV andthe revenue r The demand CV has a reasonablysignificant impact on the relative attractiveness ofOPA compared with DIR and SPL with OPA beingincreasingly preferred as the CV increases (see Figures

1 2 3 4 5minus10

minus5

0

5

10

15

20

Domestic lead time LD

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

DIR and SPL areindependent of LD and α

OPA α increasesfrom 01 to 05 OPA α increases

from 01 to 05

(a) (b) (c)

Figure 5 Impact of Domestic Procurement Lead Time and Outward Processing Arrangement Policy a


6b and 6c) It is not always true however that ahigher demand uncertainty favors OPA increasingdemand CV can favor SPL and DIR if the DOM leadtime is high and the mean NTB price is low (see thesupporting information Appendix S3) The demandCV has only a small impact on the relative profitdifference between DIR and SPL whereas the unitrevenue r has a moderate impact (see Figure 6a) Therelative profit difference between OPA and either DIRor SPL decreases in r quite significantly in the case ofDIR However one needs to interpret the directionaleffects of r in Figure 6 with some caution While therelative profit difference between OPA and either DIRor SPL decreases in r the actual profit differenceincreases Likewise the actual profit differencebetween DIR and SPL decreases although therelative profit difference increases (For all otherparameters explored in this study the relative andactual profit differences exhibited the same behavior) Asstrategy choice will be determined by the actual profitdifference OPA is favored as the revenue r increasesbecause the domestic cost disadvantage is lesspronounced if the unit revenue is high

52 Policy ImplicationsThe firm must maintain a certain level of domesticproduction to qualify for an OPA strategy The min-imum DOM procurement fraction a is a policydecision made by the competent authorities in thefirmrsquos domestic country (see EEC Regulation No291392 eg) The mandated minimum fractionwhich can vary from one product category to anotherreflects a desire to promote domestic employment but

is often influenced by the lobbying efforts of firmsFrom a policy perspective it is of interest to under-stand whether (i) a higher value of the mandatedfraction does lead to a higher domestic productionlevel and (ii) how much emphasis authorities shouldplace on industry characteristics (beyond firmsrsquo lob-bying capabilities) in setting the mandated fraction

As to question (i) our numerical study found thatif the firm is committed to the OPA strategy a higherdomestic constraint a does result in a higher expecteddomestic procurement quantity although the totalLCC plus DOM procurement quantity decreasesHowever if the firm is not committed to the OPAstrategy then an increase in a may induce the firm toswitch to a different strategy thereby eliminating do-mestic production entirely Such a switch defeats thecompetent-authorityrsquos intent of setting a to promotedomestic production We define the switching fractiona as the value of a at which the firm switches from theOPA to the SPL strategy (recall that SPL weakly dom-inates DIR) Using the numerical study described inTable 1 we calculated the switching fraction a for eachinstance by searching for the a value that resulted inthe OPA profit being equal to the SPL profit Figure 7shows that a is quite sensitive to both NTB price un-certainty (Figure 7a) and demand volatility (Figure 7band c) unless the domestic lead time is long or theunit revenue is low This suggests that when settingthe mandated OPA domestic procurement fractionthe competent authorities should pay attention to in-dustry characteristics (demand and profitability) andNTB characteristics (mean and CV) and not just lob-bying efforts or they run the risk of unwittingly

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

Demand CV increasesfrom 01 to 05



(a) (b) (c)

Figure 6 Impact of Demand Coefficient of Variation and Unit Revenue


driving firms to abandon domestic production alto-gether defeating the very intent of the OPA programIn particular the competent authorities should man-date a lower a for industries with a stable market orlonger domestic procurement time or lower averageNTB price In contrast a higher a can be imposed forindustries with a volatile market and a shorter do-mestic lead-time advantage over the LCC

6 ConclusionIn this paper we explore three supply chain strategiesused in industries subject to NTBs namely directprocurement split procurement and OPAs We char-acterize the optimal procurement decisions in thesestrategies and provide managerial and policy insightsAmong other findings we establish that direct and splitstrategies benefit from NTB volatility (as measured bythe variance of the NTB price) but suffer from increasedNTB mean prices Both the cost disadvantage and lead-time advantage of domestic production are also signifi-cant influencers of the preferred strategy as is thedomestic-country mandated production constraint as-sociated with the OPA strategy Policy makers seekingto maintain domestic production should account forthese drivers when setting the mandated domestic pro-duction fraction for OPA qualification

There are two situations in which our model ofa single selling season coupled with a single-orderopportunity for LCC and MCC would not be appro-priate The first situation is where the LCC and MCClead times are short enough to allow multiple orders

even with one annual selling season In our settingOPA is the only strategy that can fine tune inventorywith a second order This advantage would be damp-ened if the LCC and MCC lead times allowed multipleorders Analyzing this situation would requireamong other things careful thought about how tomodel the NTB price evolution It is an open and in-teresting question as to if and how our findings wouldchange in such a setting The second situation that ourmodel does not capture is that of a functional product(Fisher 1997) ie a product with a long life cycleCertain functional products are prone to tradedisputes eg tires and oil pipes in our introductionand it would be of interest to explore NTB riskfor functional products An infinite-horizon modelwould be more applicable to such a setting Againthe modeling of the NTB price would require carefulthought Stochastic price models eg Kalymon(1971) might offer some pointers Both of these set-tings merit exploration

In closing we discuss other directions for futureresearch The supply chain strategies studied spancountries and because the firmrsquos purchasing contractmay not always be written in its domestic currency itmight be fruitful to explore how exchange rate riskinfluences strategy preferences It would also be in-teresting to explore the strategic interactions betweenthe supplier and the buyer For example in the directprocurement and the split procurement strategies afirm can sometimes negotiate with its supplier tojointly share the NTB risk While many of our findingson firm preferences are supported by anecdotal

010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α

Switching α in mean NTB price(for different values of NTB CV)

1 2 3 4 5025

030

035

040

045

050

055

060

065

070


Switching α in domestic lead time(for different values of demand CV)

12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r

Switching α in unit revenue(for different values of demand CV)




(a) (b) (c)

Figure 7 Switching Fraction a


evidence from the textile industry there might be op-portunities for empirical research to shed further lighton what influences a firmrsquos strategy choice

AcknowledgmentsThe authors would like to thank the associate editor and thetwo referees for their comments and suggestions whichsignificantly improved this paper

Appendix ProofsLEMMA A1 In the diversification strategy the optimalsolution to the firmrsquos shipment decision is given by the

following O1 y0 frac14 q0 y1 frac14 q1 O2 y0 frac14 q0 y

1 frac14 F1

y

rthornps1z1

rthornps2

q0 O3 y0 frac14 q0 y

1 frac14 0 O4 y0 frac14 F1

y

rthornps0z0

rthornps2

q1 y1 frac14 q1 O5 y0 frac14 F1

yrthornps0z0

rthornps2

y1 frac14

0 O6 y0 frac14 0 y1 frac14 q1 O7 y0 frac14 0 y1 frac14 F1y

rthornps1z1

rthornps2

O8 y0 frac14 0 y1 frac14 0 where the regions O1 to O8 are definedas follows O1 0 z0 Myeths0 q0 thorn q1THORN and 0 z1 Myeths1 q0 thorn q1THORN O2 Myeths1 q0 thorn q1THORN z1 My eths1 q0THORNand 0 z0 z1 thorn eths1 s0THORN O3 0 z0 Myeths0 q0THORNand z14Myeths1 q0THORN O4 Myeths0 q0 thorn q1THORN z0 Myeths0 q1

THORN and 0 z1 z0 eths1 s0THORN O5 Myeths0 q0THORN z0 My

eths0 0THORN and z14z0 eths1 s0THORN O6 z04Myeths0 q1THORN and 0 z1 Myeths1 q1THORN O7 Myeths1 q1THORN z1 Myeths1 0THORN andz04z1 thorn eths1 s0THORN O8 z04Myeths0 0THORN and z14Myeths1 0THORN

where Myethu vTHORN frac14 eths2 uTHORNthorn ethrthorn p s2THORN FyethvTHORN

PROOF OF LEMMA A1 The firmrsquos optimal shipment

decision can be obtained by marginal analysis indifferent regions of the realized NTB prices Details ofthe proof available upon request amp

Figure A1 is a schematic representation for the casein which the firmrsquos first-stage procurement decisionsatisfies q1 q0 The case of q1oq0 can be similarlyrepresentedPROOF OF THEOREM 1 For part (a) we prove that theassociated hessian matrix is symmetric negative anddiagonally dominant Using (2) we can derive thesecond-order derivatives

2Pethq0q1jyTHORNq2

0

frac14Z Myeths0q0thornq1THORN

0

Z Myeths1q0thornq1THORN

0

H00yethq0 thorn q1THORNdG1ethz1THORNdG0ethz0THORN

thornZ Myeths0q0THORN

0

Z 1Myeths1q0THORN

H00yethq0THORNdG1ethz1THORNdG0ethz0THORN

2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0

H00yethq1THORN dG1ethz1THORNdG0ethz0THORN

2Pethq0q1jyTHORNq0q1


0


0


Because H00yethTHORNo0 the hessian matrix is negative It isalso clear from the above expressions that the hessianis symmetric and diagonal dominant For part (b) theproblem structure meets the condition in Lemma 5-5A1 in p 237 of Talluri and Ryzin (2004) ie thefirmrsquos expected profit function Pethq0 q1jyTHORN is jointlyconcave for any realization of y The proof for part (b)

Figure A1 Second Stage Optimal Shipment Decision


therefore follows analogously to the proof of Lemma5-5A1 amp

PROOF OF COROLLARY 1 Using (4) we have

q0Pethq0 q1THORN frac14 Fethq0 thorn q1THORN

Z rthornps0

0


thorn Fethq0thornq1THORNZ s2s0

0

eths2s0z0THORNdG0ethz0THORNethc0s0THORN

and

q1Pethq0 q1THORN frac14 ethrthorn pTHORNFethq1THORN thorn ethFethq0 thorn q1THORN Fethq1THORNTHORN

Z rthornps0

0


thorn ethFethq0 thorn q1THORN Fethq1THORNTHORN

Z s2s0

0

eths2 s0 z0THORNdG0ethz0THORN ethc1 s2THORN

By Theorem 1 the firmrsquos revenue function is jointlyconcave in q0 and q1 Therefore the optimal pro-curement quantity q0 and q1 can be obtained by settingthe above two expressions equal to zero amp


P0ethq0THORN frac14 c0 thorn Fethq0THORNZ s2s0

0

eths2 z0THORNdG0ethz0THORN thorn s0Fethq0THORNZ rthornps0

s2s0

dG0ethz0THORN thorn Fethq0THORNZ rthornps0

0

ethrthorn p z0THORN

dG0ethz0THORN thorn s0 G0ethrthorn p s0THORN

By Theorem 1 the firmrsquos revenue function is concaveTherefore the optimal procurement quantity q0 can beobtained by setting the above expression equal tozero amp

PROOF OF COROLLARY 3 First consider the directprocurement strategy The proposition statementscan be obtained by applying the envelope theoremto (6) The sensitivity effect of unit procurement isstraightforward For unit penalty cost we havepPethq0THORN frac14 G0ethrthorn p s0THORN

R q0

0 xdFethxTHORN Efrac12xo0 For unitsalvage value note that (6) can be rewritten as

Pethq0THORN frac14q0

Z rthornps0

0


ethc0 s0THORNq0 pEfrac12x Z q0

0

ethq0 xTHORN

dFethxTHORNZ rthornps0

0


Z s2s0

0


It follows that s0Pethq0THORN frac14 q0 G0ethrthorn p s0THORN

R q0

0 ethq0 xTHORN dFethxTHORNethG0ethrthorn p s0THORN thorn G0eths2 s0THORNTHORN 0 and s2

P

ethq0THORN frac14R q

0ethq

0xTHORNdFethxTHORN

0 G0eths2 s0THORN 0 Finally for unit

revenue we have rPethq0THORN frac14 G0ethrthorn p s0THORNethq0 R q

00

ethq0 xTHORNdFethxTHORNTHORN40 For the split procurement strategythe result can be analogously obtained by applyingthe envelope theorem to (4) amp

PROOF OF THEOREM 2 We first prove part (a) of thetheorem statement Parts (b) and (c) follow directlyfrom the proof of part (a) Note that (7) can berewritten as

Pethy0 q2jq0 yDTHORN frac14 c2q2 thorn ethrthorn p s2THORNZ y0thornq2

0

xdFyDethxTHORN thorn ethy0 thorn q2THORN FyD

ethy0 thorn q2THORN thorn s0ethq0 y0THORN thorn s2ethy0 thorn q2THORN p EyD

frac12xethA1THORN

Because (A1) is increasing in y0 we prove part (a) bycomparing the upper bounds of y0 iey0 min 1a

a q2 q0

For any given y0 (A1) is concave

in q2 and we have

q2ethy0THORN frac14 F1yD

rthorn p c2

rthorn p s2

y0

thorn ethA2THORN

Incorporating the constraint y0 min 1aa q2 q0

(A2)

holds if and only if q0 eth1 aTHORNkL where kL frac14F1yD

rthornpc2

rthornps2

It follows that if q0 eth1 aTHORNkL then y0 frac14

q0 and q2 frac14 kL y0 We now turn attention to the caseof q04eth1 aTHORNkL Because (A1) is increasing in y0 theoptimal solution must be bounded either by q0 or1aa q2 First consider the case of y0 5 q0 Because

q04eth1 aTHORNkL we must have q2ethy0THORN frac14 a1ay0 Substitut-

ing y0 5 q0 and q2ethy0THORN frac14 a1ay0 into (A1) we can prove

that (A1) is concave in q0 Next consider the case of

y0 frac14 1aa q2 Substituting y0 frac14 1a

a q2 into (A1) we can

prove that (A1) is concave in q2 and q2 frac14 akH where

kH frac14 F1yD


rthornps2

It follows that y0 frac14 eth1 aTHORNkH

But this implies q0 eth1 aTHORNkH It is straightforward toprove that (A1) is linearly increasing in q0 forq0 eth1 aTHORNkH Because (A1) is concave in q2 foreth1 aTHORNkL q0 eth1 aTHORNkH and (A1) is continuous atboth (1 a)kL and (1 a)kH we have (A1) concave inq0 Parts (b) and (c) of theorem statement thenfollows amp

PROOF OF THEOREM 3 From the proof of Theorem 2P(q0|y) is continuous in q0 Furthermore P(q0|y) islinear in q0 for q0 eth1 aTHORNkL and q04eth1 aTHORNkH Foreth1 aTHORNkHoq0 eth1 aTHORN kH p(q0|y) is concave in q0Because the upper and lower limit at q0 frac14 eth1 aTHORNkL

are identical and equal to c2 and the upper and lowerlimit at q0 frac14 eth1 aTHORNkH are also identical and equal tos0 the theorem statement then follows amp


PROOF OF THEOREM 4 First consider direct procurementstrategy Using (6) we can rewrite the firmrsquos revenuefunction as

Pethq0THORN frac14Z rthornps0

0


Z q0

0

xdFethxTHORN thorn q0Fethq0THORN

thornZ q0

0

ethq0 xTHORNdFethxTHORNZ s2s0

0


ethc0 s0THORNq0 pEfrac12xethA3THORN

To prove the theorem statement it is suffice to provethat given two distribution function G1( ) G2( )then PethyjG1ethTHORNTHORN PethyjG2ethTHORNTHORN holds Note that

Z rthornps0

0

ethrthorn p s0 z0THORNdG0ethz0THORN frac14 ethrthorn p s0 z0THORN

G0ethz0THORNjrthornps00

Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0

It follows that if G1( ) G2( ) then

Z rthornps0

0


Z rthornps0

0

ethrthorn p s0 z0THORN

dG2ethz0THORN ) Pethy0jG1ethTHORNTHORN Pethy0jG2ethTHORNTHORN

Note that in the above derivation the integrating termR s2s0

0 eths2 s0 z0THORNdG0ethz0THORN can be similarly incorpo-rated when s24s0

We now turn attention to the split procurementstrategy From the proof of the direct procurementstrategy we know that for any given two randomvariables Z1 st Z2

Z A

0

ethA z1THORNdG1ethz1THORN Z A

0

ethA z2THORNdG1ethz2THORN ethA4THORN

Note that (4) can be simplified as

Pethq0 q1THORN frac14Z s2s0

0

eths2 s0 z0THORNdG0ethz0THORNq0Fethq0THORN

thornZ rthornps0

s2s0


Z q0thornq1

q1

ethx q1THORNdFethxTHORN

ethrthorn p s2THORNG0ethrthorn p s0THORN

Z q0thornq1

q1

ethx q1THORNdFethxTHORN thorn q0Fethq0 thorn q1THORNZ rthornps0

0

ethrthorn p z0THORNdG0ethz0THORN

thorn s0q0Fethq0 thorn q1THORNG0ethrthorn p s0THORN

thornZ q0thornq1

0

ethr s2THORNxthorn s0q0 thorn s2q1eth THORNdFethxTHORN

thornZ q0thornq1

q1


thornZ 1

q0thornq1

rq1 pethx q1THORNeth THORNdFethxTHORN X1

ifrac140

ciqi

Therefore to prove the theorem statement it issufficient to prove that

q0Fethq0 thorn q1THORNZ rthornps0

0


thorn s0q0Fethq0 thorn q1THORNG0ethrthorn p s0THORNethA5THORN

satisfies (A4) But (A5) can be simplified as


0


thorn s0q0Fethq0 thorn q1THORN s0q0Fethq0 thorn q1THORNG0ethrthorn p s0THORN

frac14 q0Fethq0 thorn q1THORNZ rthornps0

0


thorn s0q0Fethq0 thorn q1THORN

which clearly satisfies condition (A4) The theoremstatement follows directly amp

PROOF OF THEOREM 5 It follows directly from Theorem4 that PDIR and PSPL decrease in m so we only need toconsider the effect of s First consider the directprocurement strategy By (A3) in the proof of Theorem4 the firmrsquos expected profit function depends on thevariance of the NTB price only through the following

term V frac14R rthornps0

0 ethrthorn p s0 z0THORNdG0ethz0THORN When G( ) is

a normal distribution with parameters (ms) we have

V frac14R rthornps0

1 ethrthorn p s0 z0THORN 1sffiffiffiffi2pp e

z0mffiffi2p

s

2

dz0 The

above equation can be simplified as V frac14 sffiffiffiffi2pp

e rthornps0mffiffi

2p

s

2

thorn 12ethrthorn p s0 mTHORN 1thorn erf rthornps0mffiffi

2p

s

where erf( ) is the standard error function Thereforewe have

sV frac14 1ffiffiffiffiffiffi2pp e

rthornps0mffiffi

2p

s

2

thorn 1ffiffiffiffiffiffi2pp rthorn p s0 m

s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms

2 2ffiffiffiffiffiffi2pp e

rthornps0mffiffi

2p

s

2

frac14 1ffiffiffiffiffiffi2pp e

rthornps0mffiffi

2p

s

2

40


The theorem statement then follows directly by theenvelope theorem We note that the integration termR s2s0

0 eths2 s0 z0THORNdG0ethz0THORN can be similarly incorpo-

rated when s24s0 The case of split procurementstrategy can be analogously proved amp

PROOF OF THEOREM 6 First consider LD Note thatPDIRLD

frac14 0 andPSPLLDfrac14 0 The theorem statement is true if

POPA

LD 0 But

POPA

LD40 cannot hold because for any

given LD4LD the firmrsquos information set at time LD

weakly dominates the firmrsquos information set at time

LD In other words a DOM procurement lead time LD

is a relaxation to the firmrsquos optimization problem thefirm can always make an identical DOM procurementdecision to that associated with the earlier informationset obtained at time LD and achieves at least the samelevel of expected profit Thus the firmrsquos optimalexpected profit cannot increase as the DOM lead timeLD increases Next consider a The theorem statementfollows from the fact that reducing a relaxes theconstrained optimization problem (7) amp

Notes1See eg Council Regulation (EEC) No 291392 and

Commission Regulation 245493

2The product under OPA may be subject to additionalquantity-based controls but such controls are normally sat-isfied before the product undergoes OPA processing

3A firm may also eliminate NTB risk by leveraging third-party OPA programs For example a firm based in Europemay take advantage of the existing OPA programs betweenHong Kong and China by procuring from Hong Kong in-stead of procuring from China directly This indirectapproach avoids the NTB control imposed on exports fromChina to Europe We omit the treatment of this strategy forreasons of space Details are available on request

4While we adopt the convention that MCC is not subject toNTBs for the sake of characterizing a more general modelwe allow for NTB in MCC for the diversification strategy

5While the 1996 Uruguay Round Agreement aims to phaseout voluntary export restraints exceptions can be granted incertain industry sectors For example in agriculture sectorlsquolsquoThe Agreement allows their [quota] conversion into tariff-rate quotas (TRQs) which function like quotasrsquorsquo (see Skully2001 USDA Technical Bulletin No TB1893)

6Although the purchasing contract is denominated in thefirmrsquos home currency the NTB price may be denominated inforeign currencies Hence we assume that G0( ) and G1( )incorporate exchange rate uncertainty when the NTB priceis denominated in foreign currencies

7The term lsquolsquocompetent authoritiesrsquorsquo is standard terminologyfor the entities that govern a countryrsquos trade rules eg theDepartment for Business Enterprise and Regulatory Reformin the United Kingdom

8While in theory the firm can choose an import quantitythat violates the policy constraint a in practice this rarelyoccurs because it will jeopardize the firmrsquos future OPAapplication The allocation of the available OPA amountto a firm is contingent on the firmrsquos previous yearrsquos actualproduction and import quantities (see eg (12a iii) and(12b ii) in DTI 2006)

9We do not consider the lead time to ship raw materialfrom the home country to the LCC for further processingbecause firms often procure raw materials from overseasregardless of which of the three strategies the firm adopts

10The forecasting process can be operationalized using anadditive Martingale forecast revision process (see Graveset al 1986) This allows a further characterization of the OPAstrategy Details available on request

11To the best of our knowledge there is no established con-sensus as to what price distribution is most appropriate Wenote that the literature in agriculture quota management(eg Bose 2004) suggests that the quota price evolution maynot be symmetric However in a somewhat related field theeconomics literature on environmental tradable permits(eg Maeda 2004) suggests that the uncertainties that influ-ence the permit price may be normally distributed

12Theorem 4 can be generalized to second-order stochasticdominance (SSD) and its special case mean-preserving SSDThe proof follows from applying the definition of SSD lsquolsquoZb

dominates Za under SSD ifR x1 GbethzTHORNdz

R x1 GaethzTHORNdz for

every xrsquorsquo to the proof of Theorem 4

13Because fixed costs are ignored SPL weakly dominates DIRas the SPL strategy can single source from LCC if it choosesTherefore the curves are all below the 0 line in Figure 3a

14With the average value of c0 in our study being 0525 amean of 01 (027) is equivalent to an average percentage of19 (514) but the actual percentages vary across probleminstances as c0 varies

15The effect on the difference between OPA and SPL is sub-stantial but somewhat lower (see Figure 3c) because the SPLstrategy is less sensitive to NTB changes as it does not relyexclusively on LCC

16The fact that DIR is preferred to OPA at lower LCC costsreflects the evolution of textile supply chain in EuropeGerman firms pioneered the use of the OPA strategy (asopposed to 100 domestic production) in the 1960s and1970s primarily using Eastern European countries as theirLCC (Snyder 2000) As Asia became a viable LCC optionwith even lower procurement costs than Eastern Europemany German firms abandoned their OPA strategies andadopted the direct procurement strategy using Asian coun-tries as the LCC Interestingly Eastern European countries


such as Poland have more firms using OPA than WesternEuropean firms because the cost advantage of LCCcompared with DOM is less significant This and later tex-tile-industry anecdotes are based on conversations withmanagers from one of the largest textile firms in China Thecompany has over 40 years of experience in the textileindustry and the management liaise frequently with over300 firms in Europe and North America

17Examining the textile industry we note that some firms inItaly and Spain still use the OPA strategy while many othersuse the DIR strategy The firms that use OPA are those thathave a significantly lower domestic lead time comparedwith the potential domestic lead time of those that use DIRWhile part of the reason for their maintaining domesticproduction is to maintain production capabilities the valueof the short DOM lead time is also a factor

18For example (at a5 04) reducing LD from 50 to 10 in-creases POPA PDIR

=PDIR from 23 to 40 if the

demand CV is 05 but only from 06 to 05 if the de-mand CV is 01

References

Abernathy F H A Volpe D Weil 2005 The future of the appareland textile industries Prospects and choices for public andprivate actors Technical Report Harvard Center for Textile andApparel Research Boston MA

Agrawal N S Nahmias 1997 Rationalization of the supplier basein the presence of yield uncertainty Prod Oper Manag 6(3)291ndash308

Anderson S P N Schmitt 2003 Non-tariff barriers and trade lib-eralization Econ Inquiry 41(1) 80ndash97

Arntzen B C G G Brown T P Harrison L L Trafton 1995Global supply chain management at digital equipment corpo-ration Interfaces 25(1) 69ndash93

Bakshi N P R Kleindorfer 2009 Coopetition and investment forsupply-chain resilience Prod Oper Manag 18(6) 583ndash603

Berling P K Rosling 2005 The effects of financial risks on inven-tory policy Manage Sci 51(12) 1804ndash1815

Blonigen B A T J Prusa 2001 Antidumping NBER Workingpaper series University of Oregon Eugene OR

Bose S 2004 Price volatility of south-east fisheryrsquos quota speciesAn empirical analysis Int Econ J 18(3) 283ndash297

Dada M N C Petruzzi L B Schwarz 2007 A newsvendorrsquosprocurement problem when suppliers are unreliable ManufServ Oper Manage 9(1) 9ndash32

DTI 2006 Notice to importers 2735 Outward processing trade fortextiles (OPT)mdashyear 2007 arrangements for Belarus China andMontenegro Department of Trade and Industry UK (Renamedto Department for Business Enterprise and Regulatory Reformin 2008)

Feenstra R C T R Lewis 1991 Negotiated trade restrictions withprivate political pressure Q J Econ 106(4) 1287ndash1307

Fisher M A Raman 1996 Reducing the cost of demand uncertaintythrough accurate response to early sales Oper Res 44(1) 87ndash99

Fisher M L 1997 What is the right supply chain for your productHarv Bus Rev 75(2) 105ndash116

Graves S C H C Meal S Dasu Y Qui 1986 Two-Stage ProductionPlanning in a Dynamic Environment Chapter Multi-Stage ProductionPlanning and Inventory Control Springer-Verlag Berlin 9ndash43

Hillman A L H W Ursprung 1988 Domestic politics foreigninterests and international trade policy Am Econ Rev 78(4)729ndash745

Iyer A V M E Bergen 1997 Quick response in manufacturer-retailer channel Manage Sci 43(4) 559ndash570

Jackson J H 1989 National treatment obligations and non-tariffbarriers Michigan J Int Law 10(1) 207ndash224

Jones K 1984 The political economy of voluntary export restraintagreements Kyklos 37(1) 82ndash101

Kalymon B A 1971 Stochastic prices in a single-item inventorypurchasing model Oper Res 19(6) 1434ndash1458

Kim H-S 2003 A Bayesian analysis on the effect of multiple supplyoptions in a quick response environment Nav Res Logist 50(8)937ndash952

Kleindorfer P R G H Saad 2005 Managing disruption risks insupply chains Prod Oper Manag 14(1) 53ndash68

Kouvelis P M J Rosenblatt C L Munson 2004 A mathematicalprogramming model for global plant location problems Anal-ysis and insights IIE Trans 36(2) 127ndash144

Li Y A Lim B Rodrigues 2007 Global sourcing using local con-tent tariff rules IIE Trans 39(5) 425ndash437

Lu L X J A Van Mieghem 2009 Multi-market facility networkdesign with offshoring applications Manuf Serv Oper Manage11(1) 90ndash108

Maeda A 2004 Impact of banking and forward contracts on trad-able permit markets Int Econ J 6(2) 81ndash102

Magee S P C F Bergsten L Krause 1972 The welfare effects ofrestrictions on US trade Brookings Papers on Economic Activity1972(3) 645ndash707

Martin M F 2007 US clothing and textile trade with China andthe world Trends since the end of quotas Technical ReportCongressional Research Service Report RL34106 WashingtonDC

Meixell M J V B Gargeya 2005 Global supply chain designA literature review and critique Transp Res Part E 41(6)531ndash550

Munson C L M J Rosenblatt 1997 The impact of local contentrules on global sourcing decisions Prod Oper Manag 6(3) 277ndash290

Nuruzzaman A H 2009 Lead time management in the garmentsector of Bangladesh An avenues for survival and growth EurJ Sci Res 33(4) 617ndash629

Ozekici S M Parlar 1999 Inventory models with unreliable sup-pliers in a random environment Ann Oper Res 91(0) 123ndash136

Palmer D 2009 US sets more duties on China pipe in record caseReuters November 5

Pope amp Talbot Inc v Government of Canada 2000 httpwwwstategovslc3747htm (accessed date November 182009)

Reichard R S 2009 Textiles 2009 Some late bottoming out but nomiracles Available at httpwwwtextile worldcomArticles2009FebruaryFeaturesTextiles_2009html (accessed dateJanuary 20 2010)

Rosendorff B P 1996 Voluntary export restraints antidump-ing procedure and domestic politics Am Econ Rev 86(3)544ndash561

Skully D W 2001 Economics of Tariff-Rate Quota AdministrationTechnical Bulletin No 1893 Market and Trade EconomicsDivision Economic Research Service US Departments ofAgriculture

Snyder F 2000 The Europeanisation of Law European Law Series HartPublishing Oxford

Talluri K T G J V Ryzin 2004 The Theory and Practice of RevenueManagement Springer New York


Tomlin B 2006 On the value of mitigation and contingency strat-egies for managing supply-chain disruption risks Manage Sci52(5) 639ndash657

Volpe A P 2005 Modeling flexible supply options for risk-adjustedperformance evaluation PhD thesis Harvard University Bos-ton MA

World Economics Situation and Prospects 2006 United NationsNew York

Yu Z 2000 A model of substitution of non-tariff barriers for tariffsCan J Econ 33(4) 1069ndash1090

Supporting Information

Additional supporting information may be found in the

online version of this article

Appendix S1 Salvage Value

Appendix S2 Domestic Production Lead Time

Appendix S3 Effect of Domestic Leadtime and Demand CV

Please note Wiley-Blackwell is not responsible for the

content or functionality of any supporting materials sup-

plied by the authors Any queries (other than missing

material) should be directed to the corresponding author for

the article


Many industries such as textiles footwear paperchemicals steel and agriculture face significant levelsof NTBs NTBs such as the EU initiated safeguardNTB are designed to protect domestic industries Theyare typically targeted at low cost countries (LCCs) andemerging economies that have a distinct cost advantagein the protected industry For example the EU safe-guard NTB limits the total annual quantity of thecontrolled product that can be imported into the EUfrom a targeted country In what follows we describethree common supply chain strategies seen in manydifferent industries that face NTB risks To be concretewe use the EU-initiated safeguard NTB as an illustra-tive example and focus on a EU firm that is interestedin sourcing finished product from some LCC that issubject to safeguard controls However these threestrategies are also used for other types of NTBs and alsoby other non-EU countries

1 Direct procurement The firm sources exclusivelyfrom an LCC that is subject to safeguard controlsBecause of its sourcing cost advantage direct pro-curement is a potentially high reward strategybut it is a high risk strategy because it passivelyaccepts safeguard controls

2 Split procurement Concerned about safeguardrisk the firm sources from two different countriesIn particular the firm sources only a fraction ofits needs from LCC and sources the rest from amedium cost country (MCC) that is not subject tosafeguard controls The split procurement strategytakes advantage of the lower production cost inLCC but partially protects the firm in the eventthat the finished product from LCC cannot beimported into the EU Because of its higher sourc-ing cost split procurement is a medium rewardstrategy and because it has lower safeguard riskexposure it is a medium risk strategy

3 Outward processing arrangement (OPA) To com-pletely avoid safeguard controls the firm canadopt an OPA strategy Many economic entitiesincluding the United States the EU and HongKong have OPAs with other countries1 An OPAallows the firm to perform certain productionactivities domestically and let suppliers in asafeguard-controlled country perform additionalor full processing The finished product subjectto specific regulations is not subject to safeguardcontrol or full tariffs2 To qualify for OPA thefirm must (1) maintain a full domestic productionline for the finished product (2) domestically pro-duce a quantity that exceeds a certain fraction ofthe firmrsquos total (domestically produced plus im-ported) quantity and (3) use domestically sourcedraw materials (see DTI 2006) For instance knittedcotton shirts sourced from China are subject to

safeguard control if imported to the EU Howevera firm based in Poland for example can avoid thesafeguard control by doing the following sourcethe fabric in the EU ship it to China for processingand import the finished product back to the EUand also produce in Poland a quantity of shirtsthat satisfies the EU mandated minimum produc-tion level OPA has no safeguard risk but becauseof its higher domestic production cost it is a lowreward strategy

In summary the direct procurement strategy hasthe highest NTB risk exposure but the lowest (aver-age) procurement cost The split procurement strategyreduces but does not eliminate NTB risk The OPAcompletely removes NTB risk but the firm mustmaintain a certain level of domestic productionwhich implies a higher procurement cost but a shorterlead time3

In this paper we fully characterize the three strat-egies and explore how certain industry and countrycharacteristics influence a firmrsquos strategy preferenceOur investigation leads to a number of interestingmanagerial and policy implications For examplewe establish that the direct and split strategyprofits increase in the NTB price variance but de-crease in the mean price These effects are sufficientlylarge that NTB price characteristics can dictatewhich supply chain strategy is preferred Both thecost disadvantage and lead-time advantage of do-mestic production are also significant influencersof the preferred strategy as is the domestic-countrymandated production constraint associated withthe OPA strategy We find that policy makerrsquosshould pay careful attention to industry and countrycharacteristics (such as NTB price and demandvolatility) when setting the mandated domestic pro-duction fraction in the OPA strategy lest theyunwittingly induce firms to abandon OPA and moveall production overseas

The rest of this paper is organized as follows Wediscuss the relevant literature in section 2 Section 3introduces model preliminaries We further developand characterize the three strategies in section 4 Man-agerial and policy implications are discussed in section5 Concluding remarks are presented in section 6 Allproofs are contained in the Appendix Some additionalresults are contained in the supporting information

2 LiteratureThere has been extensive research on NTBs in theeconomics political economy and international lawliteratures The economics literature focuses mainlyon the welfare effect of NTBs eg Magee et al (1972)and the underlying causes of NTBs eg Yu (2000)



























R1y ydFyethxTHORN

pR1



function is



eth1THORN



and z1 we have



eth2THORN



0









Transit Time LT

1 2 3

LTLP + LT






y1frac14q1 y0frac14

q0 z0 s2 s0


0 z04rthorn p s0

8gtgtltgtgt

eth3THORN


Pethq0 q1THORN

frac14Z s2s0

0

Z q0thornq1

0


thornZ rthornps0

0

Z 1q0thornq1


thornZ 1

s2s0

Z q1

0


thornZ rthornps0

s2s0

Z q0thornq1

q1



q1


eth4THORN




0



0



Z rthornps0

0



0


frac14 c1 s2




0 z04rthorn p s0

8gtltgt eth5THORN



0

Z q0

0


thornZ rthornps0

0

Z 1q0


thornZ 1

rthornps0


thornZ rthornps0

s2s0

Z q0

0



eth6THORN





0z0dG0ethz0THORN



R rthornps0

0z0dG0ethz0THORN



rthornps0













1aa q2

0








Transit Time LT

1

2 4


LTLP + LT LD

3









(

q2 frac14


a1 a



8gtgtgtltgtgtgt


rthornpc2

rthornps2

and kH frac14 F1

yD


rthornps2



frac14






1a0 xdFyD



1a FyD

q0

1a






eth8THORN














S2 20c2 LD 15 (1)

minmax (step size)










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article



























R1y ydFyethxTHORN

pR1



function is



eth1THORN



and z1 we have



eth2THORN



0









Transit Time LT

1 2 3

LTLP + LT






y1frac14q1 y0frac14

q0 z0 s2 s0


0 z04rthorn p s0

8gtgtltgtgt

eth3THORN


Pethq0 q1THORN

frac14Z s2s0

0

Z q0thornq1

0


thornZ rthornps0

0

Z 1q0thornq1


thornZ 1

s2s0

Z q1

0


thornZ rthornps0

s2s0

Z q0thornq1

q1



q1


eth4THORN




0



0



Z rthornps0

0



0


frac14 c1 s2




0 z04rthorn p s0

8gtltgt eth5THORN



0

Z q0

0


thornZ rthornps0

0

Z 1q0


thornZ 1

rthornps0


thornZ rthornps0

s2s0

Z q0

0



eth6THORN





0z0dG0ethz0THORN



R rthornps0

0z0dG0ethz0THORN



rthornps0













1aa q2

0








Transit Time LT

1

2 4


LTLP + LT LD

3









(

q2 frac14


a1 a



8gtgtgtltgtgtgt


rthornpc2

rthornps2

and kH frac14 F1

yD


rthornps2



frac14






1a0 xdFyD



1a FyD

q0

1a






eth8THORN














S2 20c2 LD 15 (1)

minmax (step size)










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article





y1frac14q1 y0frac14

q0 z0 s2 s0


0 z04rthorn p s0

8gtgtltgtgt

eth3THORN


Pethq0 q1THORN

frac14Z s2s0

0

Z q0thornq1

0


thornZ rthornps0

0

Z 1q0thornq1


thornZ 1

s2s0

Z q1

0


thornZ rthornps0

s2s0

Z q0thornq1

q1



q1


eth4THORN




0



0



Z rthornps0

0



0


frac14 c1 s2




0 z04rthorn p s0

8gtltgt eth5THORN



0

Z q0

0


thornZ rthornps0

0

Z 1q0


thornZ 1

rthornps0


thornZ rthornps0

s2s0

Z q0

0



eth6THORN





0z0dG0ethz0THORN



R rthornps0

0z0dG0ethz0THORN



rthornps0













1aa q2

0








Transit Time LT

1

2 4


LTLP + LT LD

3









(

q2 frac14


a1 a



8gtgtgtltgtgtgt


rthornpc2

rthornps2

and kH frac14 F1

yD


rthornps2



frac14






1a0 xdFyD



1a FyD

q0

1a






eth8THORN














S2 20c2 LD 15 (1)

minmax (step size)










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article





0z0dG0ethz0THORN



R rthornps0

0z0dG0ethz0THORN



rthornps0













1aa q2

0








Transit Time LT

1

2 4


LTLP + LT LD

3









(

q2 frac14


a1 a



8gtgtgtltgtgtgt


rthornpc2

rthornps2

and kH frac14 F1

yD


rthornps2



frac14






1a0 xdFyD



1a FyD

q0

1a






eth8THORN














S2 20c2 LD 15 (1)

minmax (step size)










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article







(

q2 frac14


a1 a



8gtgtgtltgtgtgt


rthornpc2

rthornps2

and kH frac14 F1

yD


rthornps2



frac14






1a0 xdFyD



1a FyD

q0

1a






eth8THORN














S2 20c2 LD 15 (1)

minmax (step size)










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article










a














020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article






020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

020 036 053 069 085minus15

minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)

ct=002ct=006ct=010

ct=002

ct=006ct=010

ct=002ct=006ct=010

(a) (b) (c)


005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠD

IRminus

ΠS

PL)

ΠS

PL


below 0 DIR above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠD

IR)

ΠD

IR


below 0 OPA above)

005 010 015 020 025 030 035minus10

minus5

0

5

10

15

20

25

Mean NTB price

(ΠO

PAminus

ΠS

PL)

ΠS

PL


below 0 OPA above)



from 02 to 12

(a) (b) (c)













1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article












1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

1 2 3 4 5minus10

minus5

0

5

10

15

20


(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)



from 01 to 05

(a) (b) (c)







12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article






12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π D

IRminus

Π S

PL)

Π S

PL


below 0 DIR above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π D

IR)

Π D

IR


below 0 OPA above)

12 16 20 24 28minus50

minus25

0

25

50

75

100

Unit revenue r

(Π O

PAminus

Π S

PL)

Π S

PL


below 0 OPA above)




(a) (b) (c)








010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article







010 015 020 025 030 035025

030

035

040

045

050

055

060

065

070

Mean NTB price

Sw

itchi

ng α


1 2 3 4 5025

030

035

040

045

050

055

060

065

070



12 16 20 24 28025

030

035

040

045

050

055

060

065

070

Unit revenue r





(a) (b) (c)







1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article






1 frac14 F1

y

rthornps1z1

rthornps2



y

rthornps0z0

rthornps2


yrthornps0z0

rthornps2

y1 frac14


rthornps1z1

rthornps2








2Pethq0q1jyTHORNq2

0


0


0



0

Z 1Myeths1q0THORN


2Pethq0q1jyTHORNq2

1


0


0


thornZ 1

Myeths0q1THORN

Z Myeths1q1THORN

0




0


0








Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article





Z rthornps0

0



0


and


Z rthornps0

0



Z s2s0

0





0


s2s0


0

ethrthorn p z0THORN




R q0



Z rthornps0

0



0

ethq0 xTHORN


0


Z s2s0

0



R q0


P


0ethq

0xTHORNdFethxTHORN



00




0



frac12xethA1THORN


a q2 q0


in q2 and we have


rthorn p c2

rthorn p s2

y0

thorn ethA2THORN


(A2)


rthornpc2

rthornps2









kH frac14 F1yD


rthornps2








0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article




0


Z q0

0


thornZ q0

0


0




Z rthornps0

0



Z rthornps0

0

G0ethz0THORNdz0

frac14Z rthornps0

0

G0ethz0THORNdz0


Z rthornps0

0


Z rthornps0

0






Z A

0


0




0


thornZ rthornps0

s2s0


Z q0thornq1

q1



Z q0thornq1

q1


0



thornZ q0thornq1

0


thornZ q0thornq1

q1


thornZ 1

q0thornq1


ifrac140

ciqi



0





0




0








V frac14R rthornps0


z0mffiffi2p

s

2

dz0 The


e rthornps0mffiffi

2p

s

2


2p

s



rthornps0mffiffi

2p

s

2


s

2

e

rthornps0mffiffi2p

s

2

1

2

rthorn p s0 ms


rthornps0mffiffi

2p

s

2


rthornps0mffiffi

2p

s

2

40







POPA

LD 0 But

POPA
































References






















































the article







POPA

LD 0 But

POPA
































References






















































the article







References






















































the article
















the article


PRODUCTION AND OPERATIONS MANAGEMENT POMSywang195/assets/pdf/Wang2011.pdf · MFA [Multiﬁbre...

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