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Int. J. Production Economics 111 (2008) 195–208

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Designing and evaluating sustainable logistics networks

J. Quariguasi Frota Neto�, J.M. Bloemhof-Ruwaard,J.A.E.E. van Nunen, E. van Heck

Rotterdam School of Management (RSM), Erasmus University, The Netherlands

Received 13 January 2006; accepted 20 October 2006

Available online 26 May 2007

Abstract

Consumers and legislation have pushed companies to re-design their logistic networks in order to mitigate negative

environmental impacts. The objective in the design of logistic networks has changed, therefore, from cost minimization

only, to cost and environmental impact minimization. The objective of this paper is to develop a framework for the design

and evaluation of sustainable logistic networks, in which profitability and environmental impacts are balanced. In this

paper, we review the main activities affecting environmental performance and cost efficiency in logistic networks, we show

the advantages of using multi-objective programming (MOP) to design sustainable networks, we present the expected

computational difficulties of using the MOP approach in the design of sustainable networks, and we introduce a technique,

based on the commonalities between data envelopment analysis (DEA) and MOP, to evaluate the efficiency of existing

logistic networks. The European pulp and paper industry will be used to illustrate our findings.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Supply chain design; Sustainable supply chain; Eco-efficiency; Multi-objective programming; Data envelopment analysis

1. Introduction

In recent years, consumers and governments havebeen pressing companies to reduce the environ-mental impact of their products and processes(Thierry et al., 1995). The members of the EuropeanUnion (EU), for instance, have committed them-selves to develop, implement and enforce legislationthat makes producers responsible for the collection,treatment, recycling and environmentally safe dis-posal of all electrical and electronic equipment(WEEE/2002/96/EC, 2002).

front matter r 2007 Elsevier B.V. All rights reserved

e.2006.10.014

ng author. Tel.: +3110 408 1781;

9010.

ss: jquariguasi@rsm.nl

rota Neto).

A number of companies have also pro-activelyacted in favor of a more sustainable development.Their assertive approach toward the environmenthas helped them to reap the benefits of anenvironment-friendly image, e.g. to gain or retainenvironment-conscious consumers, to comply withthe sometimes cumbersome and blurry currentlegislation, and to anticipate necessary changes tocope with future legal environmental standards.

Among those, a group of companies has gonefurther and achieved economic gains from theadoption of environment-friendly logistic networks.IBM, for instance, has profited from its programsto receive end-of-use products, promote secondhand items internet auctions and dismantle equip-ment as a source of spare parts (Fleischmann et al.,2003).

.

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208196

The win-win situations experienced by IBM,however, are exceptions. Only a limited number ofinitiatives for environment-friendly production haveproved to be profitable. Literature and practicesuggests that substantial improvement in the en-vironment is often only possible with substantialinvestments that brings none or negative financialreturns (Walley and Whitehead, 1994). As aconsequence, the focus of sustainable logistic net-work research and practice has swung from thesearch for win-win solutions to the search forsolutions smartly compromising business and theenvironment.

This paper aims to contribute to the design ofsustainable logistic networks balancing planet andprofit. In order to provide a first simple frameworkfor sustainable networks design, we start byreviewing, from the literature, the main factorinfluencing sustainability in logistic networks.Furthermore, we discuss how the use of multi-objective programming (MOP) to design sustainablelogistic networks helps to assess the trade-offsbetween the logistic network cost and its environ-mental impact, as well as to calculate efficiency ofexisting logistic networks. We also discuss theexpected CPU-time difficulties regarding an MOPapproach for the design of sustainable logisticnetworks. Finally, we propose our method to assessefficiency of existing logistic networks. We illustrateour approach on the European pulp and papersector.

Fig. 1. Framework for a sustainable logistic n

This paper is divided as follows: In Section 2we review the main activities affecting networksefficiency in terms of environmental costs. We alsopresent a framework for such networks, including anon-articulated multi-objective model. Non-articu-lated models are those in which the user or decisionmaker (DM) do not interact with the model in orderto find most preferable solutions. For moreinformation on non-articulated models see Climacoet al. (1996). A short discussion on computationalresults for this formulation is also carried out. InSection 3 we provide a simple tool to evaluatePareto efficiency, using data envelopment analysis(DEA) techniques and MOP. In Section 4 wepresent an illustrative example of the Europeanpulp and paper sector. Section 5 presents the mainconclusions.

2. Pareto efficiency in logistic networks in terms of

the environment and costs

In a logistic network, a number of actors willinfluence business costs and corresponding environ-mental impact. Suppliers, manufactures, consumers,logistic operators, as well as third parties operatingin testing, refurbishing, recycling and energy pro-duction for the end-of-life products are the mainplayers. These players perform majority of theactivities impacting business and the environment.

In general terms, the activities performed in alogistic network are related to manufacturing,

etwork. Adapted from Sheu et al. (2005).

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208 197

transportation, usage and end-of-life products’destination. Fig. 1 depicts these activities. Thedecisions regarding these activities will, therefore,determine the network costs and environmentalimpact. These decisions are strategic (e.g. locationof factories), tactical (e.g. the destination ofproducts end-of-life) as well as operational (e.g.the choice of suppliers, third parties, etc.).

Furthermore, it is clear that choosing the rightactivities in modeling specific logistic networks iscrucial. The combinatorial and multi-objectivenature of designing sustainable logistic networksrequires, besides smart algorithms, parsimoniousconceptual models in order to keep the problemCPU-time tractable, without losing its explanatorypower. In problems with low inverse flows, like thereverse logistic of cameras, the model might excludethe decision regarding the location of manufactur-ing plants, and leave the location-allocation pro-blem to the end-of-use facilities (Fleischmann,2000). Table 1 presents, in broad terms, the mainactivities influencing the environmental impact andcosts in logistic networks.

Literature into logistic network design is mostlydivided in two approaches: minimizing costs (or

Table 1

Main activities influencing costs and environmental impact in

logistic networks

Type of factor Variables

1. Transportation 1.1. Transport from supplier to

manufacturer and vice versa

1.2. Transport from supplier to

consumers and vice versa

1.3. Transport from supplier to end-of-

life facilities and vice versa

1.3. Transport from manufacturers to

consumers and vice versa

1.4. Transport from manufacturers to

end-of-life facilities and vice versa

1.4. Transport from consumers to end-

of-life facilities and vice versa

2. Manufacturing 2.1. Manufacturing at suppliers

2.2. Manufacturing at manufacturers

3. Product use 3.1. Product use by consumers

4. Testing 4.1. Testing

5. End-of-use

alternatives

5.1. Re-use

5.2. Refurbishing

5.3. Recycling

5.4. Energy production

maximizing profits) and minimizing environmentalimpact. There is little done integrating these twoformulations (Bloemhof-Ruwaard et al., 2004).The drawbacks of such perspectives is straight-forward: they do not capture the trade-offs betweenthe logistics network costs and its respectiveenvironmental footprint. We propose the optimiza-tion of both objectives simultaneously, in order tomake it possible for DM, in logistic networkswith centralized control, to evaluate his choice andselect, out of a number of solutions provided by themodel, the one that best capture his objectives interms of the environment and cost. Anotherimportant application is the definition of an upperbound for networks with multiple agents. Theimportance of defining and efficient frontier isthreefold:

(1)

Evaluation of the current situation in terms ofthe system’s efficiency relative to environmentalimpact and costs. It is possible, for instance, tocalculate efficiency indexes for existing networkconfigurations using DEA techniques. Forfurther description of DEA see the seminalpaper of Charnes et al. (1978).

(2)

Determination of the trade-offs between theresulting environmental impact and costs in alogistic network.

(3)

Evaluation of the necessity of policies andefficiency assessment of different legislations.We also prove general rules for differentlegislations, using the same concept of Paretooptimality.The idea of exploring the best alternatives isbased on Pareto optimality. The Pareto-optimalfrontier is composed of the set of the images ofall efficient solutions of the network regardingtwo objectives: optimize economic and environ-mental goals, like cost minimization and wasteminimization, respectively. An MOP is denotedby (Steuer and Piercy, 2005):

maxfc1x ¼ z1g . . .maxfckx ¼ zkg s:t.

fx 2 RnjAxpb; b 2 Rm;xX0g, (1)

where k is the number of objectives. A solutionx 2 S � Rn is efficient if and only if there is nox 2 S such that: cixXcix for all i, and there is atleast one cix4cix.

In our formulation, c1x represents the environ-mental impact of a certain solution. We assess the

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208198

coefficients of the environment impact function viathe following three steps:

(1)

Fig. 2. Pareto-optimal frontier. Adapted from Huppes and

Ishikawa (2005).

Assessment of the environmental impact in each

activity. For each activity affecting the environ-mental impact of the proposed logistic network(i.e. transportation of 1 kg of wasted paper perkm) we calculate the associated environmentalimpacts, namely: global warming, ecotoxidity,photo-chemical oxidation, acidification,nitrification and solid waste. The coefficients(e.g. global warming potential (GWP) per kilo-gram per kilometer of paper transported) areobtained via life cycle analysis (LCA), astandard technique for evaluating environmen-tal impact.

(2)

Normalization. The scores obtained for eachclass of environmental impact are normalizeddividing them by a reference level. In our studywe take the larger contributor as the referencelevel.

(3)

Weightening. We propose equal weight for eachof the environmental impacts. For more detailson the assessment of the proposed environmental

index see Bloemhof et al. (1996).The assessment of the environmental footprintcan be as well performed with different methods,such as Eco-Indicator99s, for instance.

The second objective function c2x represents therespective total cost ðk ¼ 2Þ. Our objective is toexplore, completely or not, the set of efficient

logistic network configurations. In other words, weare interested in supply chains in which it is notpossible to decrease costs or environmental impactswithout a trade-off between them. Fig. 2 illustratesthe efficient frontier.

The Pareto frontier can be completely defined bya set of all extreme points in an MOP in aformulation with two objectives. Although deter-mining these points is the only task to be performedto obtain the frontier, its accomplishment isextremely CPU-time consuming. The completeexploration of all extreme efficient solutions forlarge networks is intractable, even for linear models.For CPU-time processing details see Steuer (1994)and Steuer and Piercy (2005). For integer (i.e.location-allocation) models, computational effortsare much higher, as expected.

In order to obtain a subset of efficient networkconfigurations, it is possible to formulate the MOP,for the linear case, as several problems with a single

objective. The principle of such heuristics is torationally explore different weights for the objectivefunctions, avoiding weight indifference regions.Despite the term ‘‘heuristic’’ the final subset iscomposed of optimal solutions, only. We apply theterm ‘‘heuristic’’ in this particular case to designatea non-comprehensive exploration of the subsetanalyzed. The cardinality of this subset is definedby model parameters, but is obviously upperbounded by the number of non-dominated solutionsin an MOP formulation. An estimation for the lattercan be found in Steuer and Piercy (2005). Eq. (2)gives the equivalent LP of Eq. (1), for problems withtwo objective functions:

minfc1xl1 þ c2xð1� l1Þg s:t.

fx 2 RnjAxpb; b 2 Rm;xX0g. ð2Þ

For mixed linear and integer problems (e.g. decisionregarding disassembly, location-allocation) notonly with the frontiers will the frontier defined‘‘heuristically’’, but also the points defining thefrontier (or via approximation schemes). It isevident that in case where the single objectiveproblem is NP-complete, the multi-objectiveformulation will never be P; NPaP. The literatureon solving both linear and combinatorial multi-objective problems is relatively scarce if comparedto its single objective pair. For multi-objectivecombinatorial problems, Ehrgott (2000) and Ehr-gott and Gandibleux (2000) present a detailedreview on such methods. A survey on multi-objective meta-heuristics is available in Hansen(1998) and Jones et al. (2002).

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208 199

3. Evaluating Pareto efficiency in logistic networks

Intuitively, we can think of the efficient solutionsexplored in the last section as benchmarks forexisting logistic networks. Comparing the mappedenvironmental impact and costs of the currentconfiguration to the theoretical optimal providesan indicator of efficiency in the existing logisticnetwork. If the actual environmental impact andcosts are close to the frontier, for instance, there willbe no need for configuration changes. Furthermore,it is possible to give a measure of efficiency forexisting networks. In order to do so, we need thefollowing lemmas:

Lemma 1. Each image of an efficient x solution in (1)ðc1x1; . . . ; ckxk

Þ is an efficient Decision Making Unit(DMU) in a DEA problem with DMUs

ðc1x1; . . . ; ckxkÞ for x 2 S � Rn in (1).

Proof. For a problem with a continuous set ofimages of efficient solutions, the linear convexcombinations of these images also map a realsolution in the original problem. In that case, oncethe convex combinations are part of the images ofthe solution set for the problem at question, theposterior addition of such solutions will notdominate any previously existing non-dominatedsolution. Once no convex combination will result ina solution that dominates the original non-domi-nated set, the efficient solutions will map efficientDMUs in a DEA problem. &

Lemma 2. Every image of an efficient x solution in

(1) ðc1x1; . . . ; ckxkÞ is an efficient DMU in a DEA

problem with DMUs ðc1x1; . . . ; ckxkÞ for x 2 S � Rn

in (1), in case we require x 2 S � Zn, iff x is also

supported

Proof. For non-supported solutions, there exists atleast two supported solutions that makes the non-supported solution inefficient in DEA terms. Forsupported solutions, no convex combination ofother supported solutions dominates it. &

For an in-depth discussion of such propertiesof DEA and MOP, see Korhonen et al. (2003). Wefirst formalize our approach, for linear models(allocation) and then extend for mixed-integermodels.

We map every image of the non-dominatedsolutions as an efficient DMU of a DEA formula-tion, using Lemma 1. Once the problem is linear, allefficient solutions are supported, and are, therefore,

efficient in DEA terms (the same does not hold withcombinatorial problems). After this step, we calcu-late efficiency based on the efficient measureproposed by Cooper et al. (1999). We use theprojection of Cooper et al. (1999) due to the factthat it provides a more robust measure whencompared to the traditional radial projection asproposed by Charnes et al. (1978). The projectionwe use avoids projections in Pareto-inefficientparts of the frontier, providing a measure thatassess the inefficiency of all dimensions at analysis(in our case environmental impact and logisticnetwork costs).

It is also possible to explore other projectionsfor such problems, allowing the DM to morefreely explore the efficient frontier. For interactiveand non-articulated methods for finding radialprojections see Halme et al. (1999), Quari-guasi Frota Neto and Angulo-Meza (2007), Tha-nassoulis and Dyson (1992) and Zhu (1996).Furthermore, it is easy to see that every non-radialprojection in the DEA formulation maps a realsolution in the original logistic network. Formixed-integer problems, the set of unsupportedefficient solutions are not efficient in a DEAperspective, as proved in Lemma 2. In this case,we say that the solution is Pareto-efficient iff it isnot dominated by any other solution provided bythe mixed-integer formulation. This can be done,in polynomial time on the number of solutions,via simple pairwise comparison between the solu-tion being tested and all the efficient (supportedand non-supported) solutions of the multi-objectivemixed-integer problem. A measure for ineffi-ciency for combinatorial MOP is, as far as weknow, not available in the literature. The minimaldistance necessary to bring the inefficient pointinto the non-dominated set would be an alternative.We propose the following mixed and non-linearformulation:

min

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid21 þ d22

q;

s:t: ða� d1 � ajÞo0 or

ðb� d2 � bjÞo0 8ðaj ; bj

Þ 2 ND;

(3)

where ða; bÞ is the point at analysis, ND is the set ofall non-dominated points for the mixed-linearformulation, and d1 and d2 are the minimumnecessary reductions in, respectively, environmentalimpact and costs, to eliminate inefficiency. In orderto eliminate the quadratic and logical terms, we

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208200

reformulate as follows:

min y

s:t:

djaða� d1 � ajÞ þ d

jbðb� d2 � bj

Þo0 8ðaj ; bjÞ 2 ND

dja þ d

jb ¼ 1 8ðaj ; bj

Þ 2 ND

d1b� d2a ¼ 0

d1b� y ¼ 0

dja; d

jb 2 f0; 1g 8ðaj ; bj

Þ 2 ND:

(4)

The new variables dja and d

jb are dummies intro-

duced to eliminate the logic constraints. Note thatnow the model search for the minimal necessaryequi-proportional reduction of ða; bÞ for eliminatingdominance. The optimization and evaluation of thesustainable logistic networks, as illustrated in Fig. 3,can be summarized in the following steps:

(1)

Fig.

asse

eval

Explore, partially or completely, non-dominatedpoints of the logistic network. When completelyexploring the extreme efficient solutions in alinear models, it is possible to construct a convexpiecewise linear frontier. For mixed-integermodels, the frontier is likely to be no longerconvex, as presented before, and cannot beexplored via the standard DEA techniques.

3. Steps to calculate the Pareto-efficient frontier and to

ss eco-efficiency in sustainable logistic networks, as well as to

uate environmental legislation.

More precisely, the convex combinations notonly do not provide the efficient frontier inPareto terms, but also do not map real net-works. The concept of frontier may therefore berelaxed and efficiency tested in terms of dom-inance with the solutions of the mixed-linearmulti-objective formulation. In the case of non-exhaustive exploration of the efficient solutions,the frontier is an upper bound of the realefficient frontier, and its closeness to the realtheoretical frontier will depend on the numberof non-dominated vertexes explored.

(2)

Calculate the efficiency of the logistic network.The current situation is bound by the efficientfrontier and is a convex combination of theefficient points or an inefficient DMU in DEAterms. It is possible, furthermore, to evaluate theefficiency of the current situation throughstandard DEA techniques for end-of-use deci-sions and allocation problems. For location-allocation problems we need a new metric, aspresented before, such as the minimal equi-proportional reduction of environmental impactand costs to bring the dominated point into thenon-dominated set.

(3)

Assess the efficiency of a specific mandatorylegislation by its capacity of locking-out envir-onmentally harmful solutions, without deterior-ating the proposed frontier, and evaluate theimpact of a market-based legislation. In somecases, it may be possible to improve the efficientfrontier, providing cheaper and more environ-ment-friendly solutions, as well as locking outharmful environment logistic network con-figurations, through adequate market-basedlegislation.

In the next section we illustrate the use of theproposed methodology to optimize the logisticnetworks in terms of the environment and costs,as well as the efficiency of the current one, and theimpact of mandatory legislation.

4. The European paper and pulp sector case study

In order to illustrate the concepts presented inthe last sections we take the European pulp andpaper industry as a case study. The sector hassignificant impact in both environment and businessfor the EU. For Scandinavian countries, forinstance, it corresponds to a significant part of theindustrial activity and generates a considerable

ARTICLE IN PRESSJ.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208 201

portion of the GDP. In Finland, the forest sectorrepresents 7% of the GDP and approximately one-fifth of industrial production in the country (FFI-Association, 2006). For the environment, theimpacts are also significant and they appear indifferent parts of the life cycle: forest management,pulp production, pulp bleaching, paper consump-tion, waste management and transportation(Bloemhof et al., 1996). The magnitude of wastepaper produced is impressive: in Europe, wastepaper responds for 35% of the total waste byvolume (Buwal, 1991).

We describe the re-organization of the Europeanpulp and paper logistic network as a multi-objectivelinear problem, with the network cost and environ-mental impact objectives to be optimized. Weconsider facility locations as fixed, which lead usto a problem of allocation and end-of-use decision.This formulation can be extended to include facilityallocation decisions. For an operational perspective,however, it is reasonable to assume that the locationof energy generation plants, paper recycling orpaper production will not change in a short periodof time.

The model divides the EU in six regions:Scandinavia, Germany, France, UK, Italy andIberia (Portugal and Spain). These six regions areresponsible for 80% of the paper consumption andproduction in the EU. In order to assess ecologicalimpact we use the environment index proposedproposed in Bloemhof et al. (1996). The index usesLCA, considering the diverse emissions in thesupply chain regarding the pulp and paper sector,namely global warming, human toxicity, ecotoxi-city, photochemical oxidation, acidification, nitrifi-cation and solid waste, and provides a singleweighted measure for environmental impact foreach phase of the supply chain. The economicobjective function is the sum of the cost of thefollowing activities: transportation, production,recycling and incineration. Data from environmen-tal impact is directly taken from Bloemhof et al.(1996). We also use secondary data for the costsfrom production, recycling and incineration ofpaper (FFI-Association, 2006).

The logistic network we describe has multipleagents: producers, consumers, third parties workingon recycling, incineration and energy generation.At a higher level, governments can also beconsidered players, for their role in legislation. Wemodel the system, however, for a centralized controlperspective. This approach allows us to explore

the efficient frontier, and from that, as presented inSection 2:

�

Provide an upper bound for a system from agame theoretical perspective. Modeling environ-mental legislation is an example of a bi-levelgame: the government creates legislation tomitigate environmental impact, without dama-ging the economy, while companies adapt to suchlegislation—working to minimize the associatedadditional costs. For the European Govern-ments, for example, the efficient frontier providesinsights on the best alternatives for the usedpaper. Presently, such decisions are highly biasedby the economic interests of the members, as wellas by the belief that some (supposedly) environ-ment-friendly alternatives should be preferred.Scandinavia advocates that the production ofclean virgin pulp is both environmentally andeconomically preferable over recycling. Francefavors incineration, while Germany goes forrecycling (Bloemhof et al., 1996). An exampleof applications of Game Theory in Legislation isfound in Amouzegar and Moshirvaziri (1999). � Determine the cost of decreasing environmental

impact for the pulp and paper sector. This is keyinformation for DMs in private and publicsectors. For governments, this particular infor-mation is useful as an input for decisionsregarding subsidizing or taxing activities (e.g.incineration, transport or recycling) of thelogistic network, for instance. In cases wherethe environmental improvements come at a lowcost, subsidizing clean logistic networks isrecommended. In cases where decreasing envir-onmental impact comes at a high cost, taxationand investment in other sectors may be moreappealing.

� Determine the efficiency of the sector relative to

the environment and costs. The efficiency will tellus how much the system can be improved withinitiatives integrating and directing the playerswithin the logistic network. This re-design of thelogistic network can happen directly, by a self re-organization of the players (in that case, con-sidering cooperative players), as well as indirectlyvia a leader, from a game theoretical perspective.For example, governments may take the role of aleader—projecting the actual inefficient system tothe frontier via legislation.

� Determine ‘‘optimal’’ configurations for the

European pulp and paper sector. The results

ARTICLE IN PRESS

Table 2

Variables for the European pulp and paper model

Indexesa

i; j; k 2 I ¼ Indices for the six regions

v 2 V ¼ Index for the four virgin pulp types

p 2 P ¼ Index for the seven paper types

Decision variables:

VPiv Virgin pulp production of type v in region i

VTijv Virgin pulp transport type v, from region i to

region j

VDiv Virgin pulp demand in region i of type v

RPi Recycled pulp production in region i

PDi Recycled pulp demand in region i

PTijp Paper transport of paper p, from region i to region j

WTij Waste paper transport, from region i to region j

WIi Waste paper incinerated in region i

WPi Waste paper ‘‘production’’ for recycling in region i

WDi Waste paper demand for recycling in region i

Lip Share of recycled pulp in furnish of paper type p in

region i

Exogenous variables

vsi Virgin pulp wood supply in region i

ppip Paper production of type p in region i

pdip Paper demand for paper type p in region i

wsi Waste paper supply for recycling or incineration to

non EU-countries

peip Paper import from non-EU countries to region i

Other parameters

eviv Environmental impact of virgin pulp production of

type v in region i

eri Environmentalimpact of recycled pulp production

in region i

eii Environmental impact of incineration of waste

paper in region i

etij Environmental impact of transport from region i to

region j

rp Total share of pulp in the inputs of paper type p

J.Quariguasi Frota Neto et al. / Int. J. Production Economics 111 (2008) 195–208202

provide a clear guideline for the configurations ofproduction, transport and end-of-use destinationfor paper.

The multi-objective formulation for the Europeanpulp and paper sector is presented in Tables 2 and 3.

Objective (3) minimizes environmental impact ofvirgin pulp (both in Europe and North America),recycled pulp production, waste paper incineration,and transport. Objective (4) minimizes the costs forthe same activities. Constraints (5) are the capacityconstrains for wood pulp. Constraints (6) and (7)define flow conditions for virgin pulp and recycledpulp. Constraint (8) defines the allowable share ofrecycled pulp in order to satisfy conditions for papertypes. Constraint (9) defines the allowable share ofrecycled pulp in order to satisfy conditions for papertypes. Constraint (10) represents the natural boundon the share of recycled pulp in the overallfurnishing of paper products. Constraint (11)defines flow condition for paper. Constraint (12)defines the destination of collected waste paper to beeither incineration or recycling. Constraint (13)defines flow conditions for waste paper. Constraint(14) considers the yield from waste paper forrecycled pulp. Constraints (4) and (6) allow us torepresent all paper produced in one variable.Constraint (7) uses the same rationale to reducethe number of technologies used for virgin pulpprocessing. Fig. 4 represents the network flow forone European region. For the paper and pulp sectorwe assume that:

(yield of paper from pulp)

mvp Furnish rate of virgin pulp type v wrt to total virgin

� pulp share in paper product p

lmaxp Maximum share of recycled pulp in the furnish of

paper type p

dp Long-term consumption rate for paper type p

The production and consumption of paper isconstant. This implies that the virgin andrecycling pulp demand, as well as the wastegeneration are maintained in the actual levels.

sp Sewage rate of waste paper for paper type p

� yip Collection rate of waste paper originating from

paper type p in region i

w Estimated fiber yield of waste paper

Economic parameters

The production of virgin pulp making is limitedby the capacity installed in each region. Further-more, the formulation does not allow increase ofcapacity.

cviv Production cost of virgin pulp production of type v

� in region i

cri Productioncost of recycled pulp in region i

cii Costs of incineration of waste paper in region i

ctij Transport cost from region i to region j

The proportion of paper produced newsprint14%, printing quality paper 36%, liner 12%,fluting 9%, boxboard 9%, household 5% andothers 15% is fixed.

�

Waste paper supply for either recycling or incineration i is defined as

follows:

wsi ¼P

p2Pð1� lpÞð1� spÞ � yip � pdip

The proportion of virgin pulp production tech-nology (sulphate bleach, sulphate unbleach,sulphite bleach and TMP bleach) used is fixed.

�

aThe set Iþ:¼I [NA relates to the OECD-Europe regions plus

North America.

The proportion between the actual use ofrecycled fiber and its maximum value isequal for each paper. The bigger the maximumof recycled pulp allowed (this is a technical

ARTICLE IN PRESS

Table 3

Mathematical formulation for the European pulp and paper model

minPv2V

evivVPiv þPi2I

eriRPi þPi2I

eiiWIi þP

i2Iþ

Pj2I

etijPv2V

VTijv þPi2I

Pj2J

etijPp2P

PTijp þWTij

!" #(3)

minPv2V

cvivVPiv þPi2I

criRPi þPi2I

ciiWIi þP

i2Iþ

Pj2I

ctijPv2V

VTijv þPi2I

Pj2J

ctijPp2P

PTijp þWTij

!" #(4)

s:t:Pv2V

VPivpvsi; 8i 2 I (5)Piaj2Iþ

VTijv þ VPjv ¼ VDjv þP

iaj2I

VTjkv; 8j 2 I ; v 2 V (6)

RPj ¼ DRj ; 8j 2 IV (7)

VDiv ¼Pp2P

mvpð1� LipÞ � rp � ppip 8i 2 I ; v 2 V (8)

RDi ¼Pp2P

Lip � rp � ppip; 8i 2 I (9)

Lipplmaxp 8i 2 I ; p 2 P (10)

pijp þP

i2I ;iaj

PTijp þ ppjp ¼ pdjp þP

k2I ;kaj

PTjkp þ pejp; 8j 2 I ; p 2 P (11)

wsi ¼WIi þWPi ; 8i 2 I (12)Pi2I ;iaj

WTij þWPj ¼WDj þP

k2I ;kaj

WTjk; 8j 2 I (13)

RPi ¼ w�WDi ; 8i 2 I (14)

Fig. 4. Network flow model for the European pulp and paper model.

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restriction: papers such as printing accept amaximum of 50% recycling pulp), the biggerthe proportion in relation to the overall recycledpulp used.

� The network flow conditions involving virgin and

recycled pulp, paper and waste should berespected. Furthermore, we consider that thereis no transport of recycled pulp.

The decision variables for the problem are there-fore: the transportation of virgin pulp, paper andwaste paper among the six described regions, theimport and export of, respectively, pulp and paperfrom outside EU, and the destination of the end-of-use paper.

We understand that the problem is more complexthan is portrayed in the paper, but as said,

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assumptions presented can be relaxed. The reasonfor such simplification is that we are more interestedin showing an application of the proposed metho-dology than provide results for decision making insuch industry. We believe that the illustrative modelworks properly for that purpose.

5. Results

We first analyze the efficient frontier for theEuropean pulp and paper sector in order todetermine the theoretical trade-offs between envir-onmental impact and costs, as described in Section2. Furthermore, we use the frontier to find ameasure of efficiency for the actual logistic network,as described in Section 3.

The minimization of costs gives a total cost ofapproximately 60% the cost for the configurationwith minimum environmental impact. On the otherhand, the environmental impact for the logisticnetwork with minimum cost is 90% higher than theminimum feasible environmental impact. Note thatthe objective function values, in percentage terms,differ much among the efficient solutions, despitethe impact of transportation, which is simulta-neously optimized for both objectives. Anotherinteresting observation is that the parts of the sideof the frontier which maps the costly solutions, are

Fig. 5. Configuration of the logistic network for minimum en

dominated by virgin pulp production associatedwith incineration. Despite the common belief thatrecycling is always cleaner, solutions with highrecycling proportions are not always more environ-ment-friendly for the particular case of the Eur-opean pulp and paper sector. The positive marginalenvironmental impact of incineration for energygeneration, if compared to fuel fossil energygeneration, as well as the carbon emission fromthe transportation of wasted paper from theconsumption centers to the recycling facilitiesexplains such results. Recycling is, on the otherhand, present in the lower costs configurations.Mandatory recycling quotas, therefore, may bringno positive results for the environment.

Figs. 5–7 show three efficient configurations forthe European pulp and paper sector, and theirrespective environmental impact and costs. Notethat, although they do not differ much in termsof the environment and cost results, they presentquite different configurations. The solution withlowest costs has no incineration, and significantflows of wasted paper, besides the expected flow ofnew paper from the Scandinavian countries to therest of Europe. The solution with the highest cost isa mix between virgin pulp utilization, incinerationand recycling. Also, there is no flow of wastedpaper. An intermediate solution presents both

vironmental impact. Volumes are represented in 1000 t.

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Fig. 7. Configuration of the logistic network with maximum environmental impact. Volumes are represented in 1000 t.

Fig. 6. Configuration of the logistic network compromising environmental impact and costs. Volumes are represented in 1000 t.

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incineration and recycling, but no flow of wastedpaper. There are also flows of paper from Scandi-navia to the rest of Europe and virgin pulp toGermany.

In order to calculate the network efficiency, weuse the measure of inefficiency proportions (MIP)proposed in Cooper et al. (1999). The logisticnetwork measure of inefficiency is equal to 0.24,

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which mean that an weighted average of 24%improvement in the environmental impact and costsin the logistic network is necessary to reachefficiency. Note that we do not use radial projection,despite the easier interpretation of results, due to therisk of projecting in inefficient parts of the frontier.This is a well-known problem in the literature, andoccurs for the data of this specific study case.Furthermore, the model proposed by Cooper et al.(1999) gives a single real value as efficiency measure

Fig. 8. Radial projection for the Eur

Fig. 9. Cooper et al. (1999) projections for t

and incorporates all inefficiencies in the model.Figs. 8 and 9 show, respectively, the two projections.The efficiency calculation and the optimizationphase, are modeled as linear systems, and thereforeperformed in polynomial time. CPU-time is negli-gible for both problems, the assessment of theefficient frontier and the calculation of the efficiencyof the existing logistic network configuration.

We also analyze the impact of legislation on theefficient frontier. We explore four scenarios: in the

opean pulp and paper industry.

he European pulp and paper industry.

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Fig. 10. Pareto-optimal frontier for the European pulp and paper industry with mandatory legislation.

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first scenario we have no mandatory recycling. Thesecond scenario is the 20% mandatory recyclingscenario for the members of the EU. Here wesuppose that the parliament decides to, based on theactual directives for wasted paper, to mandatethis percentage of recycled pulp. We expand ouranalysis for the 50% scenario. We also analyze theresult of 100% mandatory recycling legislation inGermany.

The Pareto optimal configuration, including thescenarios, is presented in Fig. 10. Note thatmandatory policies for recycling may deterioratethe Pareto-optimal frontier. It is also worth tohighlight that environment-friendly scenarios werelocked out, instead of the expected effect to lock outunfriendly ones.

The adoption of mandatory legislation for 20%of recycled pulp does not highly deteriorate thePareto-efficient frontier, but locks-out environment-friendly alternatives. The effect of 50% use ofrecycled pulp in the EU and 100% in Germany issimilar: locking-out environment-friendly alterna-tives and deteriorate the Pareto frontier.

6. Conclusions

The concern of consumers, companies andgovernments with the environment has steadilyincreased in the last years. Cleaner process, re-useof products and components, re-manufacturing and

recycling are examples of initiatives to reduceenvironmental impact in logistic networks. Unfor-tunately, win-win solutions for the environment andbusiness are very elusive in practice.

The adoption of cleaner solutions is generallybounded by an increase in costs. Companies aimingto decrease the environmental impact of theirlogistic networks should, then, look for goodtrade-offs between environmental impact and costs.The game is, therefore, smartly compromising thetwo P’s: Planet and Profit. The same rationale istrue for governments: effective legislation shouldtake into consideration specific trade-offs of thelogistic network in question, as well as the efficiencyof the existing logistic network.

In this paper we review the main family ofactivities influencing the environment and costs inlogistic network, namely: transportation, manufac-turing, product use, testing and end-of-use alter-natives. Furthermore, we present a framework foroptimizing the design of efficient logistic networks,based on multi-objective programming (MOP), interms of the environment and costs. We also discussthe expected computational challenges of suchapproach for the design of sustainable logisticnetworks. Applications and further developmentsof such frontier are also discussed.

In addition, we introduce a new methodology toevaluate efficiency in logistic networks, based on theproperties shared by MOP and data envelopment

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analysis. We also pinpoint the main mathematicalcharacteristics of such an efficiency indicator. Theindicator tells the decision maker, in companies,sectors or governments, about the necessity of bettercoordinating his logistic networks, or better tuningenvironmental legislation.

We use the European pulp and paper sector as abackground for presenting the methodologies pro-posed in this paper. We present the efficient frontierfor such sector, as well as the trade-offs between theenvironment and costs. Furthermore, we show thatmandatory legislation favoring recycling might notlock out bad environmental solutions, and willdeteriorate the efficiency of the sector in terms of theenvironment and business. We also show that theactual system has space for win-win gains. The re-organization of the logistic network as it is now tothe logistic network illustrated in Figs. 5–7 wouldbring environmental impact and logistic networkcosts down as in Fig. 9.

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