A System Dynamics Modeling Framework for the Strategic 2004
Transcript of A System Dynamics Modeling Framework for the Strategic 2004
www.elsevier.com/locate/jfoodeng
Journal of Food Engineering 70 (2005) 351–364
A system dynamics modeling framework for the strategicsupply chain management of food chains
Patroklos Georgiadis *, Dimitrios Vlachos, Eleftherios Iakovou
Department of Mechanical Engineering, Aristotle University of Thessaloniki, Division of Industrial Management,
P.O. Box 461, Thessaloniki 541 24, Greece
Received 3 October 2003; received in revised form 22 December 2003; accepted 23 June 2004
Available online 25 November 2004
Abstract
The need for holistic modeling efforts that capture the extended supply chain enterprise at a strategic level has been clearly rec-
ognized first by industry and recently by academia. Strategic decision-makers need comprehensive models to guide them in efficient
decision-making that increases the profitability of the entire chain. The determination of optimal network configuration, inventory
management policies, supply contracts, distribution strategies, supply chain integration, outsourcing and procurement strategies,
product design, and information technology are prime examples of strategic decision-making that affect the long-term profitability
of the entire supply chain. In this work, we adopt the system dynamics methodology as a modeling and analysis tool to tackle stra-
tegic issues for food supply chains. We present guidelines for the methodology and present its development for the strategic mod-
eling of single and multi-echelon supply chains. Consequently, we analyze in depth a key issue of strategic supply chain
management, that of long-term capacity planning. Specifically, we examine capacity planning policies for a food supply chain with
transient flows due to market parameters/constraints. Finally, we demonstrate the applicability of the developed methodology on a
multi-echelon network of a major Greek fast food chain.
� 2004 Elsevier Ltd. All rights reserved.
Keywords: System dynamics; Supply chain management; Food logistics; Capacity planning
1. Introduction
Supply chain management (SCM) has been met with
increased recognition during the last decade both by
academicians as well as practitioners. However, despite
its significant advances and dramatic improvements in
information technology (IT), the discipline of SCM re-
mains incapable of addressing satisfactorily many prac-
tical real-world challenges. One key reason for thisinadequacy is the interdependencies among various
operations and the autonomous partners across the
chain, which renders all traditional myopic models inva-
0260-8774/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2004.06.030
* Corresponding author. Tel.: +30 2310 996046; fax: +30 2310
996018.
E-mail address: [email protected] (P. Georgiadis).
lid (Iakovou, 2001; Tayur, Ganeshan, & Magazine,1999). Rather, strategic decision-makers need compre-
hensive models to guide them in the decision-making
process so as to increase the total profitability of the
chain.
A critical shortcoming of most of the existing strate-
gic models is their inability to take into account the im-
pact of regulatory legislation within today�s already
volatile environment. This is particularly important forfood supply chains because of their unique characteris-
tics, stemming among others from product storage and
transportation specifications (Hobbs & Young, 2000;
Van der Vorst, Beulens, De Wit, & Van Beek, 1998).
For example, product perishability creates uncertainty
for the buyer with respect to product quality, safety
and reliability (i.e. quantity) of supply. It creates
352 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
uncertainty for the seller in locating a buyer, as perish-
able products must be moved promptly to the market-
place to avoid deterioration, leaving sellers unable to
store the products awaiting favorable market condi-
tions. This further leads to the need for frequent deliver-
ies, through dedicated modes of transportation (e.g.refrigerators). Moreover, food products usually exhibit
high seasonality in raw materials availability and in
end-products demand, and therefore they need effi-
ciently designed storage facilities to further ensure their
quality. In addition, food safety issues have profound
ramifications on the design of the supply chain. For in-
stance, proper monitoring and response to food safety
problems requires the ability to trace back small lots,from retailer to processor or even back to the supplying
farm. Another feature of food chains is that few prod-
ucts are transformed from commodity to differentiated
branded foods, while others undergo packaging but re-
main essentially intact in character. All these character-
istics along with the dynamically evolving legislative
framework further hinder the task of managing effi-
ciently food supply chains.The motivation behind this research is (i) to facilitate
the decision-making process for capacity planning of
multi-echelon supply chains in such uncertain environ-
ments by studying the long-term behavior of supply
chains and (ii) to further offer a generic methodological
framework that could address a wider spectrum of stra-
tegic SCM related problems.
Most of the standard methodologies for the analysisof supply chains study the steady state of the system,
i.e. they assume that all transient phenomena have been
diminished. This assumption may be valid in several
supply chains, where product demand exhibits a smooth
pattern, i.e. demand has a low coefficient of variation
(functional items, in (Fisher, 1997)). However, there is
an increasingly important family of products with short-
er life cycles and larger demand variability, for which theutilization of the traditional methodologies may lead to
considerable errors (innovative items, in (Fisher, 1997)).
While focusing on the latter, we employ the system
dynamics (SD) methodology, well known and proven
in strategic decision-making, as the major modeling
and analysis tool in this research.
Forrester (1961) introduced SD in the early 60s as a
modeling and simulation methodology for the analysisand long-term decision-making of dynamic industrial
management problems. Since then, SD has been applied
to various business policy and strategy problems (Ster-
man, 2000). The version of the well-known Beer Distri-
bution Game, an experiential educational game
presented in (Sterman, 1989), is a role playing SD model
of a supply chain originally developed by Forrester. To-
will (1995) uses SD in supply chain redesign to gainadded insights into SD behavior and particularly into
its underlying casual relationships. The outputs of the
proposed model are industrial dynamics models of sup-
ply chains. Minegishi and Thiel (2000) use SD to im-
prove the understanding of the complex logistic
behavior of an integrated food industry. They present
a generic model and then provide practical simulation
results applied to the field of poultry production andprocessing. Sterman (2000) presents two case studies
where the SD methodology is used to model reverse
logistics problems. Georgiadis and Vlachos (2004) use
the SD methodology to estimate stocks and flows in a
reverse supply chain providing specific mechanisms with
a fixed remanufacturing capacity change per year.
Sterman (2000) introduced a generic SD model of the
stock management structure which is used to explain thesources of oscillation, amplification and phase lag ob-
served in supply chains. Haffez, Griffiths, Griffiths, and
Nairn (1996) describe the analysis and modeling of a
two-echelon industry supply chain encountered in the
construction industry, using an integrated system
dynamics framework. Simulation results are further
used to compare various re-engineering strategies.
In this work we develop an SD-based holistic model ofthe entire supply chain, which may be used as decision-
making aid tool, mainly for strategic decision-making.
More specifically, we design generic single-echelon
inventory systems that incorporate all state variables
(stocks on-hand and on order) and policies for both
inventory control and capacity planning. Using this sin-
gle-echelon model as a basic module we demonstrate
how generic multi-echelon supply chain models can beconstructed. Although such an analysis may differ from
one product (or stock keeping unit, SKU) to another,
we keep the proposed model as generic as possible to
facilitate its implementation on a wide spectrum of
real-world cases.
The next section presents the problem under study
and the modeling approach along with the major under-
lying assumptions. In Section 3 we demonstrate theapplicability of the developed model on a multi-echelon
network of a major Greek fast food chain. Finally, we
wrap-up with summary and conclusions in Section 4.
2. Problem and model description
Strategic supply chain management deals with a widespectrum of issues and includes several types of decision-
making problems that affect the long-term development
and operations of a firm, namely the determination of
number, location and capacity of warehouses and man-
ufacturing plants and the flow of material through the
logistics network, inventory management policies, sup-
ply contracts, distribution strategies, supply chain inte-
gration, outsourcing and procurement strategies,product design, decision support systems and informa-
tion technology.
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 353
The methodological approach developed in this
paper, could potentially be used for capturing most of
the above strategic SCM problems. However, since each
of the problems has its unique characteristics, we present
guidelines for the methodology and further analyze in
depth a specific strategic management problem, that oflong-term capacity planning; this is the problem of iden-
tifying dynamically (at strategic time instances), optimal
levels of vendor sourcing, production, warehousing, dis-
tribution and transportation capacity. Our approach
utilizes a well-proven methodological tool for strategic
decision-making, that of SD.
2.1. System dynamics methodology
A supply chain being the ‘‘extended enterprise’’ that
encompasses vendors, manufacturers/producers, distrib-
utors and retailers is characterized by a stock and flow
structure for the acquisition, storage, and conversion
of inputs into outputs and the decision rules governing
these flows (Forrester, 1961; Sterman, 2000). The flows
often create important feedbacks among the partnersof the extended chain, thus making SD a well-suited
modeling and analysis tool for strategic supply chain
management.
The structure of a system in SD methodology is
exhibited by causal loop (influence) diagrams; a causal
loop diagram captures the major feedback mechanisms.
These mechanisms are either negative (balancing) or po-
sitive feedback (reinforcing) loops. A negative feedbackloop exhibits a goal-seeking behavior: after a distur-
bance, the system seeks to return to an equilibrium situ-
ation. In a positive feedback loop an initial disturbance
leads to further change, suggesting the presence of an
unstable equilibrium. Causal loop diagrams play two
important roles in SD. First, during model development,
they serve as preliminary sketches of causal hypotheses
and secondly, they can simplify the representation of amodel. The structure of a dynamic system model
contains stock (state) and flow (rate) variables. Stock
variables are the accumulations (i.e. inventories), within
the system, while flow variables represent the flows
in the system (i.e. order rate), which are the byproduct
of the decision-making process. The model structure
Fig. 1. Causal loop diagram of an open-lo
and the interrelationships among the variables are
represented by stock-flow diagrams. The mathematical
mapping of a SD stock-flow diagram occurs via a system
of differential equations, which is numerically solved via
simulation. Nowadays, high-level graphical simulation
programs (such as i-think�, Stella�, Vensim�, andPowersim�) support the analysis and study of these
systems.
2.2. Single-echelon model
In Fig. 1 we present the stock and flow structure for a
single-echelon inventory system in its corresponding
causal loop diagram. The verbal descriptions coincidewith the variables of the model. The arrows represent
the relations among variables. The direction of the influ-
ence lines displays the direction of the effect. Signs ‘‘+’’
or ‘‘�’’ at the upper end of the influence lines exhibit the
sign of the effect. When the sign is ‘‘+’’, the variables
change in the same direction; otherwise they change in
the opposite one. The structure of the system�s internalenvironment consists of the stock variables Supply Lineand Inventory. Supply Line monitors the accumulation
of unfilled orders, i.e. orders that have been placed but
not received yet, while Inventory monitors the accumula-
tion of products on hand. Orders increase the Supply
Line. The rate of Order Fulfillment is determined by
the Orders after a time delay equal to Lead time. Order
Fulfillment reduces the stock of products in Supply Line
and increases Inventory. The variable Inventory isdepleted by Sales. This process takes time equal to the
Response Time to Customers� Demand.The clear definition of the boundaries between the
system under study and its external environment is an
essential step of SD; thus, the model and its analysis
are kept as simple as possible while capturing all neces-
sary elements for the analysis of the system under study.
In the simplistic model exhibited in Fig. 1, producers(a term used for vendors, suppliers or manufacturers)
and customers represent the external environment of
the system (source and sink in SD nomenclature, respec-
tively); thus, the SD underlying assumption is that pro-
ducers and customers do not affect the behavior of the
system under study. However, in a different model
op single-echelon inventory system.
354 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
producers and/or customers could potentially be in-
cluded in the system boundaries and thus, the effect of
their particular attributes in stock and flows determina-
tion would be captured.
The mathematical equations that describe the stock
and flow structure of the single-echelon inventory sys-tem are the following:
Supply LineðtÞ
¼ Supply Lineðt ¼ 0Þ þZ t
0
½OrdersðtÞ
�Order FullfilmentðtÞ�dt;
InventoryðtÞ
¼ Inventoryðt ¼ 0Þ þZ t
0
½Order FullfilmentðtÞ
� SalesðtÞ�dt;
SalesðtÞ¼ min½InventoryðtÞ=Response Time;
Customers’ DemandðtÞ�;
Order FullfilmentðtÞ ¼ Ordersðt � Lead TimeÞ:
Orders are governed by a decision rule to adjust the
stocks both in Supply Line and the Inventory to the de-
sired values. This decision process converts the open-
loop structure of Fig. 1 into the closed-loop structure
of Fig. 2. Specifically, Orders is defined as the sum oftwo terms, namely:
OrdersðtÞ ¼ Expected DemandðtÞþ Inventory Position AdjustmentðtÞ:
Fig. 2. Causal loop diagram of a closed-lo
The first term is a forecasted value for demand, calcu-
lated from a first order exponential smoothing of the
past values of Customer’s Demand with a smoothing fac-
tor equal to 1/aDL. Hence:
Expected DemandðtÞ
¼ Expected Demandðt � dtÞ þ 1
aDL
½DemandðtÞ
� Expected DemandðtÞ�dt:
The second term is a periodical adjustment, which is
proportional to the difference between Desired Inventory
Position (which is a decision variable) and actual Inven-
tory Position (Inventory Position expresses the sum of
Supply Line and Inventory over time):
Inventory Position AdjustmentðtÞ
¼Desired Inventory PositionðtÞ� Inventory PositionðtÞInventory Position Adjustment Time
;
where Inventory Position Adjustment Time represents
how quickly the firm tries to correct the discrepancy
above and bring the inventory position in line with its
goal. Such a policy for Orders determination is an an-
chor and adjustment policy that is standard in modelingspecifically inventory systems in the SD literature (Ster-
man, 2000). Naturally, Orders are limited by the inven-
tory level of the producers, which is considered adequate
as in this model it is an external variable.
The closed-loop structure of Fig. 2 restricts the end-
less accumulation of inventory (that occurs in the model
of Fig. 1) whatever the demand level may be. This oc-
curs due to two negative feedback loops displayed inFig. 2. Loop #1 is defined by the sequence of the vari-
ables Orders—Order Fulfillment—Inventory—Inventory
op single-echelon inventory system.
TimeP
Demandforecast
Capacityleading
matching
trailing
2P
Fig. 4. Alternative capacity expansion strategies.
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 355
Position—Inventory Position Adjustment, while Loop #2
is defined by the variables Orders—Supply line—Inven-
tory Position—Inventory Position Adjustment. To ex-
plain the negative feedback mechanism, we follow the
route around Loop #1. An increase in Orders will in-
crease the Order Fulfillment and thus, Inventory andInventory Position will also increase. This causes Inven-
tory Position Adjustment to decrease, since the Desired
Inventory Position changes slowly and it can be assumed
to be constant for the next time step. Finally, the de-
crease in Inventory Position Adjustment restricts Orders.
Therefore, Orders will stabilize at a finite level and even-
tually the system will reach an equilibrium (steady) state.
2.3. Multi-echelon supply chain model
A supply chain being the total ‘‘extended enterprise’’
that captures all partners including vendors, manufac-
turers, producers, distributors and retailers, extends
over multiple echelons. Each partner of the chain typi-
cally manages his/her own inventory (operating as an
autonomous linkage of the chain), which is replenishedfrom the upstream echelon, while using a control policy
to determine the frequency and magnitude of the orders.
We can design generic multi-echelon food supply chains
that fit real-world cases by linking the appropriate num-
ber of single-echelon inventory models. For example,
Fig. 3 depicts a supply chain with three echelons, where
the causal loop diagram of each actor at each echelon is
equivalent to the causal loop diagrams shown in Fig. 2.Using the SD approach we can expand these generic
multi-echelon supply chains adding strategic supply
chain management issues. Capacity planning and man-
power planning are examples of such issues with the for-
mer being the focus of the rest of the paper.
Capacity may refer to all operations of a supply
chain, e.g. stock space, manpower, production facilities,
transportation means, etc. In the remainder of thispaper we concentrate on transportation capacity and
we examine efficient ways to dynamically determine their
levels. Generally, capacity determination is quite simple
Fig. 3. Generic causal loop diagram o
in a steady-state situation; however, in a evolving envi-
ronment, as in the case under study, it is important to
consider a dynamic capacity planning policy. To develop
a decision-making system for capacity planning, a firm
needs to carefully balance the tradeoff between customer
service maximization and maximization of capacity uti-lization. This is done by either leading capacity strate-
gies, where excess capacity is used so that the firm can
absorb sudden demand surges, or trailing capacity strat-
egies, where capacity lags the demand and therefore
capacity is fully utilized (Martinich, 1997). A third form
of capacity planning is the matching capacity strategy,
which attempts to match demand capacity and demand
closely over time. The three strategies are depicted inFig. 4. In all three cases the firm is making decisions
to acquire new capacity or not, at equally spaced time
intervals with length equal to the review period.
It appears that a decision-maker could determine
capacities for all these operations once in the beginning
of the planning horizon, and that this could be done
using a standard management technique that incorpo-
rates steady-state conditions. However, this is not thecase in the environment under study since product flows
can change dramatically for several reasons; for example
f a three-echelon supply chain.
356 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
promotion activities or price variation strategies of the
competitors. Although, such demand shifts take time
to materialize, they have to be considered for the devel-
opment of efficient capacity planning policies. Thus, it is
evident that an appropriate modeling methodology
needs to be able to capture the transient effects of flowsin a food supply chain. SD has this capacity and more-
over, it easily describes the diffusion effects related to
market behavior.
In addition, an operation may be performed using
either owned capacity or additional leased capacity.
The problem of determining the optimal ratio of owned
to leased capacity units (‘‘buy or lease’’ problem) is also
typical for supply chain operations. The causal loop dia-gram of Fig. 5 illustrates the generic single-echelon sys-
tem embellished with a dynamic loop that expresses a
capacity planning decision-making mechanism. Specifi-
cally, we assume that an operation may be performed
using owned and leased (if needed) capacity units. This
control mechanism is modeled as a negative feedback
loop.
More specifically, Capacity Needed is determined by avariable of the supply chain model. For example, if we
study the capacity of the transportation system, this var-
iable may be the Orders, while if we study the necessary
warehouse space this variable may be the on hand Inven-
tory. Capacity Needed is compared with the Actual
Capacity. In case there is a Capacity Shortage, capacity
is then leased to achieve the Desired Service Level.
Capacity Expansion Rate determines the rate ofchange of capacity towards the desired value. We as-
Fig. 5. Capacity planning dec
sume that capacity is reviewed periodically (every P
time units) and then a decision is made whether or
not to invest on capacity expansion and to what extent.
We have found this policy typical for most of the food
supply chains we have encountered, including the one
we discuss in the next Section. Capacity Expansion Rateis modeled by pulse functions, which may be positive
for times that are integer multiples of P. The pulse mag-
nitude is proportional to the Smoothed Capacity Short-
age (obtained from Capacity Shortage using first order
exponential smoothing to avoid unnecessary oscilla-
tions) multiplied by a control variable K. The variable
K represents alternative capacity expansion strategies.
Values of K < 1 represent trailing capacity expansionstrategies, values of K > 1 represent leading strategies,
and values close to 1 represent matching strategies. Nat-
urally, a serious lead time elapses between a decision
epoch of increasing capacity and the actual operation
of the corresponding capacity units. The Capacity
Acquisition Rate captures this time and is determined
by delaying the values of the Capacity Expansion Rate.
Moreover, Actual Capacity has a useful life time(Capacity Life-Time), which regulates the Capacity Dis-
posal Rate.
A decision-maker and/or regulator could further em-
ploy the developed model to capture the impact of var-
ious policies using various levels of the above
parameters; in other words, the model can be used for
the conduct of various ‘‘what-if’’ analyses. For example,
the impact of different leading strategies on the new orunexpected demand satisfaction and the capacity
ision-making structure.
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 357
utilization subject to a given capacity review period P
can be evaluated. On the other side, a decision maker
could investigate the impact of different values of capac-
ity review periods for a given capacity expansion policy.
More advanced ‘‘what-if’’ analyses may be further con-
ducted to develop a long-term capacity planning stra-tegy with the optimal values of P and K. In the
following Section we demonstrate how the above gene-
ric single-echelon supply chain model with capacity
planning can be used to model a real-world food supply
chain.
3. An illustrative real-world case study
3.1. A fast-food supply chain
We applied the research approach and modeling
methodology in the food supply chain of a major fast-
food restaurants chain in Greece. The supply chain of
the form is comprised of a central producer and ware-
house (CW) located in Thessaloniki, which then suppliesdirectly sixty restaurants in northern Greece (NR). The
firm also owns a distribution centre (DC) in Athens,
which supplies sixty nine restaurants located in the
southern and coastal Greece (SR). These organizations
maintain a chain partnership (based on franchising con-
tracts) to improve business performance via responsive
operations combined with better utilization of resources.
The franchising contracts cover various issues such asquality, customer service levels, etc. A major component
of the replenishment contracts is related to food distri-
bution (inventory replenishment policies, lead times, re-
quired storing space and conditions, delivery times,
etc.). The specific characteristics of the system are the
following:
• The desired fill rate of the restaurants is 100%. Tomaintain this goal the safety stocks at CW and the
restaurants are considerable, even though the lead
times are short. For the same reason both the inven-
tory and the production capacity of CW in Thessalo-
niki is practically infinite.
• The demand for each restaurant is generally high and
further fits to a normal distribution, the parameters
of which are estimated applying standard statisticaltechniques on real data (fitting the sample mean
and variance to the unknown parameters l and r2
of the distribution).
• The DC in Athens and each restaurant employ an
(R,S, s) policy for inventory replenishment. Thus,
inventory is inspected every R periods. If it is found
to be at a level less than or equal to s then an order
‘‘up to the desired inventory level, S’’ is placed. Thispolicy is formulated as an anchoring and adjustment
process (described in Section 2.2). The review period
R is set to 1 day. The optimal parameters S and s for
each restaurant are determined using classical
inventory management techniques (see Nahmias,
2001).
• The maximum acceptable lead time for an order is
24h. This implies that the central warehouse CW,or the distribution center DC, must adjust their deliv-
ery schedules to satisfy all orders within this time win-
dow. Deliveries may occur any time during day or
night.
• Both the CW and DC maintain two independent
fleets of trucks.
• When the number of the company-owned trucks is
inadequate to satisfy demand, CW and DC currentlylease third party trucks (usually trucks of a 3PL, third
party logistics company) to accommodate increased
demand. There is no additional delay in the acquisi-
tion of leased trucking capacity since the contractual
agreements between the company and the 3PL guar-
antee immediate response for tracks and drivers. Nat-
urally, there are constraints in leased capacity
volume, but based on historical data these limitsnever became active in the past.
In other working environments for which the last
assumption is not valid one would have to tackle the po-
tential delay resulting from leasing capacity and limited
leased-capacity resources and thus, the model would
have to be extended using delays functions to capture
the delayed availability of leased capacity. Such a model,despite its increased complexity, could easily be devel-
oped with the appropriate changes in our Powersim�
code. In our manuscript, we present the simpler in-
stance, since it is actually more reflective of the working
environment that we encountered for the fast food com-
pany that we worked with.
In such a dynamic environment with an absolutely
strict fill rate the company has to simply decide if itshould invest in increasing its fleet size or if should con-
tinue the current practice of using few owned trucks and
leasing 3PL trucks to cover its needs. Thus, the objective
of this case study is the development of efficient deci-
sions regarding the chain�s transportation capacity
(company-owned fleet size), that minimize total trans-
portation cost.
3.2. The simulation model
We first developed the causal loop diagram of the en-
tire chain, taking into consideration the inventory con-
trol policies used by the restaurants and the DC. The
entire diagram, which includes all system variables and
the regulating feedbacks, is exhibited in Fig. 6.
To develop the causal loop diagram, we used the fol-lowing assumptions, the validity of which was thor-
oughly checked with the CW and the restaurants:
Northern Greece Restaurants
Southern Greece RestaurantsDistribution Center
Supply lineNR
Sales
Inventory CW
OrdersNR
Lead TimeNR
Order FulfillmentNR
Demand NR
InventoryNR+- -
+delay
+
+
Inventory position NR
+ +
InventoryPosition
AdjustmentNR
-
Desired Inventory Position
NR
Inventory Position
Adjustment Time NR
-
+
+
+
+
-
SNR
sNR
+
+
Supply Line SR
Sales SROrdersSR
Lead timeSR
Order FulfillmentSR
Demand SRInventory
SR+- -
+
delay
+
+
Inventory Position SR
++
Inventory Position
AdjustmentSR
-
DesiredInventory
Position SR
Inventory Position
Adjustment Time SR
-
+
+
+ +
-
sSR
SSR
+
+Supply
Line DC
OrdersDC
Lead TimeDC
Order FulfillmentDC
InventoryDC
+-
delay
+
Inventory Position
DC
+
+
Inventory Position
AdjustmentDC
-
DesiredInventory
Position DC
+
+
+
-
SDC
sDC
+
+
Transportation Capacity
Needed NRTransportation
Capacity Shortage NR
Transportation Capacity
Leasing NR
DesiredFill Rate
NR
Smoothed Transportation
Capacity Shortage NR
Transportation Capacity
Expansion Rate NR
Transportation Capacity
Acquisition Rate NR
Transportation Capacity NR
Transportation Capacity
Disposal Rate NR
Capacity Life Cycle
NR
+
+
Smoothing +
+
+
+delay+
-
+
-
-
Transportation Capacity
Needed SRTransportation
Capacity Shortage SR
Transportation Capacity
Leasing SR
DesiredFill Rate
SR
SmoothedTransportation
Capacity Shortage SR
Transportation Capacity
ExpansionRate SR
Transportation Capacity
AcquisitionRate SR
Transportation Capacity
Disposal Rate SR
Capacity Life Cycle
SR+
Smoothing +
+
+
+delay+
-
+
-
ResponseTime NR
-
+
-Transportation Capacity SR
Expected Demand NR
+
+
ExpectedDemand SR
+
+
Expected AggregateOrders SR+
+
-
--
OrderHandling Time NR
-
OrderHandling Time SR
-
OrderHandling Time CW
-
ResponseTime SR
-
Fig. 6. Causal loop diagram of the fast-food chain.
358 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
• No order is greater than the capacity of a single truck.
• Each truck serves one restaurant at a time. This is
generally true for restaurants that are in the vicinity
of the CW facilities. For the other ones each truck
serves two restaurants at a route. Therefore, this
assumption easily makes sense, assuming that thelead time is half of the loading–transportation–
unloading time.
• There are no emergency deliveries.
• There is no collaboration (no lateral movements)
among restaurants.
The next step of the SD methodology involves the
mapping of the causal loop diagram into a dynamicsimulation model using specialized software. We used
the Powersim� 2.5c software for this purpose. The
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 359
embedded mathematical equations are divided into two
main categories: the stock equations and the flow equa-
tions. Stock equations define the accumulations within
the system through the time integrals of the net flow
rates. Another typical form of stock equations is used
to define the smoothed stock variables that are ex-pected values of specific variables usually obtained
from their past values using exponential smoothing
(e.g. the smoothed stock variable Expected Demand
NR in Fig. 6 is obtained from Demand NR using first
order exponential smoothing). Flow equations define
the flows among the stocks as functions of time. Con-
verters and Constants form the fine structure of flow
variables. The holistic model includes 260 state vari-ables and a considerable number of converters and
constants. The mathematical equations for the specific
model, as they are provided by Powersim�, are in-
cluded in Appendix A. It should be noted that the out-
put of Powersim� 2.5c uses the qualifiers ‘‘init’’ for
initial stock (level) equations, ‘‘flow’’ for stock (level)
equations, ‘‘aux’’ for smoothed stock equations and
for flow (rate) equations and converters, ‘‘const’’ forconstants and ‘‘dim’’ for the dimension of vector vari-
ables (single-dimension arrays in Powersim�). The units
of each variable are also included in brackets. Data has
been scaled to respect corporate confidentiality. In the
following subsection we present the results of our sim-
ulation runs.
3.3. Simulation results
The model presented thus far includes a periodically
reviewed capacity planning policy. Therefore, the model
may be used for long-term capacity planning with dy-
namic adjustments occurring at the review points. In
addition, if the length of review period is set to infinity
then the model prescribes optimal truck capacity once,
without the ability of future adjustment.To proceed with the capacity planning process we
need to obtain an understanding of the transportation
demand characteristics. We first estimate the probability
distribution of the transportation demand (Transporta-
0%
2%
4%
6%
8%
10%
12%
14%
10 20 30 40driver-shifts
f(.)
NR
SR
F(
Fig. 7. pdf f(•) and cdf F(•) of transportation d
tion Capacity Needed NR, Transportation Capacity
Needed SR in Fig. 6) measured in vehicle-hours or in
driver shifts. Transportation demand can be calculated
from orders since the busy time of a truck is equal to
two times the lead time (one to deliver and one to return
to the DC) minus the loading and the unloading time(the lead time includes loading, transportation and
unloading times).
Thus, we conducted the simulation experiment using
the model of the previous subsection and then logged
the transportation demand for NR and SR. The proce-
dure was repeated for 1000 times to obtain accurate esti-
mates of the transportation demand distribution. Fig. 7
depicts the probability density function (p.d.f.), f(•), andcumulative distribution function (c.d.f.), F(•), of the
transportation demand in driver shifts per day for both
NR and SR.
The transportation demand pattern fits a normal dis-
tribution. The current numbers of driver shifts per day is
16 for the CW in Thessaloniki and 22 for the DC in Ath-
ens. To determine the optimal fleet size which minimizes
the total system cost, we needed to identify the costsof the alternative strategic decisions (‘‘own’’ or ‘‘lease’’).
The cost of using a company-owned truck for one driver
shift is used as a reference cost and it is set to 100 units.
This cost includes variable costs (cp = 60 monetary
units) which are charged per shift a truck is employed,
and fixed costs (cf = 40 monetary units) which are in-
curred whether the truck is used or not. The cost of leas-
ing a truck is c1 = 180 monetary units per driver shift. Ifx is the demand then the total cost per day, TC, as a
function of capacity A (number of driver shifts per
day) is given by:
TCðAÞ ¼ Acf þ cp
Z A
0
xf ðxÞdxþ cpAZ 1
Af ðxÞdx
þ c1
Z 1
Aðx� AÞf ðxÞdx:
The problem of determining the optimal number ofdriver shifts A* has the form of the well-known news-
vendor problem (Nahmias, 2001) and thus its solution
is given by
0%
20%
40%
60%
80%
100%
10 15 20 25 30 35 40driver shifts
.)
NR
SR
emand for northern and southern Greece.
360 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
A ¼ F �1 c1 � cp � cfc1 � cp
� �:
Hence, the optimal policy, prescribes 21 driver shifts
for the CW in Thessaloniki and 26 for the DC in Athens.
This indicates that the transportation capacity of both
the CW warehouse in Thessaloniki and the DC in Ath-
ens has to be increased by five and four driver shifts
units respectively.Moreover, the model may be used to perform ‘‘what-
if’’ analyses regarding the results and the policy param-
eters. For example, we can use the model to answer the
following questions:
• How should we fine-tune the inventory control policy
parameters ‘‘S’’ and ‘‘s’’ in order for the currently
existing transportation capacity to be optimal?• What is the impact of increasing or decreasing the
inventory control policy parameters ‘‘S’’ and ‘‘s’’ on
the optimum fleet sizes?
Using the model we may address the first question; in
this case the firm decides to fine tune operational param-
eters, so that the current fleet size is optimal. Specifi-
cally, the current transportation capacity turns out tobe optimal if we decrease all the reorder point (s) values
by 25% or the base stocks (S) by 10% for the restaurants
in northern Greece and if we decrease the order point
values by 15% or the base stocks by 6% for the restau-
rants in southern Greece. Naturally, such decisions must
be checked with other problem constraints (e.g. the per-
ishability and the life time of the food products, storage
space, etc.).To address the second question we may vary all reor-
der points parameters (s) of the NR restaurants; for
example, by a specific percentage and then repeat run-
ning the simulator. The results are exhibited in Fig. 8.
We note that the optimal number of driver shifts per
day changes from 21 to 26 when s is increased by 20%
(17 when is decreased by 20%). Moreover, if we repeat
the experimentation with the base stock quantities (S)
13
18
23
28
33
38
-30% -20% -10% 0% 10% 20% 30%% change in parameter value
driv
er s
hift
s pe
r da
y
s
S
Fig. 8. Sensitivity of the optimal capacity while varying operational
parameters.
we notice that the optimal number of driver shifts per
day changes from 21 to 14 when S is increased by 20%
(37 when S is decreased by 20%). Therefore, it is evident
that the optimal capacity is more sensitive to base stock
quantity adjustments.
The above procedure that calculates the optimalcapacity appears to be static since the problem seems
to be reduced to the newsvendor problem based on the
empirically derived distributions of necessary driver-
shifts. First, we should note that simulation is needed
to obtain the distribution of transportation demand to
be used in the closed form solution of the newsvendor
problem. On a second hand, the following question
needs to be answered: why should we employ SD to ob-tain F(•), instead of using the classical discrete event
simulation method? The answer is quite straightforward.
If the customers� demand is stationary, then the trans-
portation demand would also be stationary and the opti-
mal capacity may be obtained using either discrete event
or SD simulation. However, if any input variable or
parameter (e.g. demand, inventory policy parameters,
etc.) evolves with time, then the only appropriate meth-odology is that of the SD, since this dynamic behavior
cannot be captured by discrete event simulation.
To this end we conducted another experimentation
assuming that the mean demand exhibits a 10% increase
per year. In that case we assume that the initial transpor-
tation capacity would be equal to the optimal found in
the previous paragraphs, specifically 21 driver shifts
for the CW in Thessaloniki and 26 for the DC in Athens.The capacity review period is set to half a year. Fig. 9
depicts the optimal expansion of owned capacity mea-
sured in driver shifts for a five year period.
Other possible ‘‘what-if’’ scenarios that could be fur-
ther investigated include among others:
• The impact of sudden demand spikes/valleys on the
system�s transportation capacity. In such a case itwould be interesting to measure the length of the
transient phase of the flows or to measure what is
the impact on total system cost. Moreover, if such a
2628
2930
3233
3435
3738 39
2122
2324
2627
2829
3032
33
20
25
30
35
40
0 1 2 3 4 5 6 7 8 9 10half-years
Ow
ned
driv
er s
hift
s SR
NR
Fig. 9. Transportation capacity planning of owned-trucks if demand
exhibits an annual increase of 10%.
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 361
disturbance occurs frequently, it would be interesting
to investigate a modified capacity planning policy
which allows for emergency capacity reviews (on time
instances different for the multiples of review period)
when the percentage demand variation in a short per-
iod exceeds a specific level (decision variable).• The impact of potential state regulatory interventions
for food storage and distribution on various opera-
tional parameters (inventory control parameters,
transportation capacity). SD is a methodology that
allows for capturing the diffusion effect of regulatory
interventions, since SD can map efficiently the time
necessary for the manifestation of these interventions
in the system.• The merit of alternative inventory management and
control policies. For example, we can employ similar
methodologies to investigate the impact of a continu-
ous review inventory management policy following
the appropriate information technology investments
(such as Electronic Data Interface, EDI or XML)
that allow for real time communication between
CW and all its restaurants.
4. Summary/Conclusions
We presented a system dynamics-based methodolog-
ical approach for mapping and analyzing multi-echelon
food supply chains. The methodology constructs supply
chain models by linking single-echelon models as mod-ules. The holistic model can be used to identify effective
policies and optimal parameters for various strategic
decision-making problems. The methodology has been
implemented for the transportation capacity planning
process of a major Greek fast-food restaurant supply
chain.
The developed model can be further used to analyze
various scenarios (i.e. to conduct various ‘‘what-if’’analyses) and answer questions about the long-term
operation of supply chains using total supply chain
profit as the measure of performance. The model can
further be tailored and used in a wide range of food sup-
ply chains. Thus, it may prove useful to policy-makers/
regulators and decision-makers dealing with a wide
spectrum of strategic food supply chain management
issues.
Appendix A
Stock equations:
init INVENTORY_CW = INFINITY
flow INVENTORY_CW = �dt * Orders_DC � dt * ARRSUM(Orders_NR) [items]
init INVENTORY_DC = 40000
flow INVENTORY_DC = +dt * Order_Fulfillment_DC � dt * ARRSUM(Orders_SR) [items]
dim INVENTORY_NR = (D = 1 .. 60)init INVENTORY_NR = [. . .]flow INVENTORY_NR = �dt * Sales + dt * Order_Fulfillment_NR [items]
dim INVENTORY_SR = (D = 1 .. 69)
init INVENTORY_SR = [. . .]flow INVENTORY_SR = �dt * Sales_SR + dt * Order_Fulfillment_SR [items]
init SUPPLY_LINE_DC = 0
flow SUPPLY_LINE_DC = �dt * Order_Fulfillment_DC + dt * Orders_DC [items]
dim SUPPLY_LINE_NR = (D = 1 .. 60)init SUPPLY_LINE_NR = 0
flow SUPPLY_LINE_NR = + dt * Orders_NR � dt * Order_Fulfillment_NR [items]
dim SUPPLY_LINE_SR = (D = 1 .. 69)
init SUPPLY_LINE_SR = 0
flow SUPPLY_LINE_SR = �dt * Order_Fulfillment_SR + dt * Orders_SR [items]
init Transportation_Capacity_NR = 0
flow Transportation_Capacity_NR = �dt * Trans_Cap_Disposal_NR + dt * Trans_Cap_Acquisition_NR [trucks]
init Transportation_Capacity_SR = 0flow Transportation_Capacity_SR = + dt * Trans_Cap_Acquisition_SR � dt * Trans_Cap_Disposal_SR [trucks]
Flow equations:
aux Order_Fulfillment_DC = DELAYPPL(Orders_DC,Lead_Time_DC,0) [items/hour]
dim Order_Fulfillment_NR = (D = 1 .. 60)
aux Order_Fulfillment_NR = DELAYPPL(Orders_NR(D),Lead_time_NR,0) [items/hour]
362 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
dim Order_Fulfillment_SR = (D = 1 .. 69)
aux Order_Fulfillment_SR = DELAYPPL(Orders_SR(D),Lead_time_SR,0) [items/hour]
aux Orders_DC = IF(Inventory_Position_DC < s_DC,MIN(INVENTORY_CW/Order_Handling_Time_CW,
Expected_Aggregate_Orders_SR + Inventory_Position_Adjustment_DC),0) [items/hour]
dim Orders_NR = (D = 1 .. 60)
aux Orders_NR = IF(Inventory_Position_NR < s_NR,MIN(INVENTORY_CW/Order_Handling_Time_NR,Expected_Demand_NR + Inventory_Position_Adjustment_NR),0) [items/hour]
dim Orders_SR = (D = 1 .. 69)
aux Orders_SR = IF(Inventory_Position_SR < s_SR,MIN(INVENTORY_DC/Order_Handling_Time_SR,
Expected_Demand_SR + Inventory_Position_Adjustment_SR),0) [items/hour]
dim Sales = (D = 1 .. 60)
aux Sales = MIN(INVENTORY_NR/Response_Time_DC, Demand_NR) [items/hour]
dim Sales_SR = (D = 1 .. 69)
aux Sales_SR = MIN(INVENTORY_SR(D)/Response_Time_SR, Demand_SR) [items/hour]aux Trans_Cap_Acquisition_NR = DELAYPPL(Trans_Cap_Expansion_NR,Acquisition_Time_TC_NR,0)
[trucks/hour]
aux Trans_Cap_Acquisition_SR = DELAYPPL(Trans_Cap_Expansion_SR,Acquisition_Time_TC_SR,0)
[trucks/hour]
aux Trans_Cap_Disposal_NR = Transportation_Capacity_ NR/Capacity_Life_Cycle_NR [trucks/hour]
aux Trans_Cap_Disposal_SR=Transportation_Capacity_ SR/Capacity_Life_Cycle_SR [trucks/hour]
Converters:
aux Aggregate_Orders_SR = ARRSUM(Orders_SR)[items/hour]
dim Demand_NR = (D = 1 .. 60)
aux Demand_NR = NORMAL(m_NR,sd_NR)[items/hour]
dim Demand_SR = (D = 1 .. 69)
aux Demand_SR = NORMAL(m_SR,sd_SR)[items/hour]
aux Expected_Aggregate_Orders_SR = DELAYINF(Aggregate_Orders_SR,a_AO_SR,1,Aggregate_Orders_SR)
[items/hour]dim Expected_Demand_NR = (D = 1 .. 60)
aux Expected_Demand_NR = DELAYINF(Demand_NR(D),a_D,1,Demand_NR)[items/hour]
dim Expected_Demand_SR = (D = 1 .. 69)
aux Expected_Demand_SR = DELAYINF(Demand_SR(D),a_D_SR,1,Demand_SR)[items/hour]
aux Inventory_Position_Adjustment_DC = MAX(S_DC-Inventory_Position_DC,0)/Inventory_Position_
Adjustment_Time_DC[items/hour]
dim Inventory_Position_Adjustment_NR = (D = l .. 60)
aux Inventory_Position_Adjustment_NR = MAX(S_NR-Inventory_Position_NR,0)/Inventory_Position_Adjustment_Time_NR[items/hour]
dim Inventory_Position_Adjustment_SR = (D = 1 .. 60)
aux Inventory_Position_Adjustment_SR = MAX(S_SR-Inventory_Position_SR,0)/Inventory_Position_
Adjustment_Time_SR[items/hour]
aux Inventory_Position_DC = INVENTORY_DC + SUPPLY_LINE_DC[items]
dim Inventory_Position_NR = (D = l .. 60)
aux Inventory_Position_NR = INVENTORY_NR + SUPPLY_LINE_NR[items]
dim Inventory_Position_SR = (D = 1 .. 69)aux Inventory_Position_SR = INVENTORY_SR + SUPPLY_LINE_SR[items]
dim Trans_demand_NR = (D = l .. 60)
aux Trans_demand_NR = IF((Orders_NR * TIMESTEP) > 0,(2 * Lead_time_NR * 24-1),0)[hour]
dim Trans_demand_SR = (D = 1 .. 69)
aux Trans_demand_SR = IF((Orders_SR * TIMESTEP) > 0,(2 * Lead_time_SR * 24-1),0)[hour]
aux Smoothed_Tran_Cap_Shortage_NR = DELAYINF(Transportation_Capacity_Shortage_NR,a_TC_NR,1,
Transportation_ Capacity_Shortage_NR)[trucks]
aux Smoothed_Tran_Cap_Shortage_SR = DELAYINF(Transportation_Capacity_Shortage_SR,a_TC_SR,1,Transportation_Capacity_Shortage_SR)[trucks]
aux Total_trans_demand_NR = ARRSUM(Trans_demand_NR)/Hours_per_Shift_NR[driver-shifts]
P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364 363
aux Total_trans_demand_SR = ARRSUM(Trans_demand_SR)/Hours_per_Shift_SR[driver-shifts]
aux Trans_Cap_Expansion_NR = INT(K_NR * (PULSE(Smoothed_Tran_Cap_Shortage_NR,4000,Pr_NR)))
[trucks/hour]
aux Trans_Cap_Expansion_SR = INT(K_SR * (PULSE(Smoothed_Tran_Cap_Shortage_SR,4000,Pr_SR)))
[trucks/hour]
aux Transportation_Capacity_Leasing_NR = Transportation_Capacity_Shortage_NR * Desired_Fill_Rate_NR[trucks]
aux Transportation_Capacity_Leasing_SR = Transportation_Capacity_Shortage_SR * Desired_Fill_Rate_SR
[trucks]
aux Transportation_Capacity_Needed_NR = Total_trans_demand_NR/Driver_Shifts_per_Truck_NR[trucks]
aux Transportation_Capacity_Needed_SR = Total_trans_demand_SR/Driver_Shifts_per_Truck_SR[trucks]
aux Transportation_Capacity_Shortage_NR = MAX(Transportation_Capacity_Needed_NR-
Transportation_Capacity_NR,0)[trucks]
aux Transportation_Capacity_Shortage_SR = MAX(Transportation_Capacity_Needed_SR-Transportation_Capacity_SR,0)[trucks]
Constants:
const a_AO_SR = 12 [hour]
dim a_D = (D = 1 .. 60)
const a_D = 12 [hour]
dim a_D_SR = (D = 1 .. 69)const a_D_SR = 12 [hour]
const a_TC_NR = 12 [hour]
const a_TC_SR = 12 [hour]
const Acquisition_Time_TC_SR = 720 [hour]
const Acquisition_Time_TC_NR = 720 [hour]
const Capacity_Life_Cycle_NR = 40,000 [hour]
const Capacity_Life_Cycle_SR = 40,000 [hour]
const Desired_Fill_Rate_NR = 1 [ ]const Desired_Fill_Rate_SR = 1 [ ]
const Driver_Shifts_per_Truck_NR = 3 [driver-shifts/truck]
const Driver_Shifts_per_Truck_SR = 3 [driver-shifts/truck]
const Hours_per_Shift_NR = 8 [hour/driver-shifts]
const Hours_per_Shift_SR = 8 [hour/driver-shifts]
const Inventory_Position_Adjustment_Time_DC = 1 [hour]
dim Inventory_Position_Adjustment_Time_NR = (D = 1 .. 60)
const Inventory_Position_Adjustment_Time_NR = 1 [hour]dim Inventory_Position_Adjustment_Time_SR = (D = 1 .. 69)
const Inventory_Position_Adjustment_Time_SR = 1 [hour]
const K_NR = 1 [1/hour]
const K_SR = 1 [1/hour]
const Lead_Time_DC = 9 [hour]
dim Lead_time_NR = (D = l .. 60)
const Lead_time_NR = [. . .] [hour]dim Lead_time_SR = (D = 1 .. 69)const Lead_time_SR = [. . .] [hour]dim m_NR = (D = 1 .. 60)
const m_NR = [. . .] [items/hour]
dim m_SR = (D = 1 .. 69)
const m_SR = [. . .] [items/hour]
const Order_Handling_Time_CW = 1 [hour]
const Order_Handling_Time_NR = 1 [hour]
const Order_Handling_Time_SR = 1 [hour]const Pr_NR = 4320 [hour]: NR transportation capacity review period
const Pr_SR = 4320 [hour] : SR transportation capacity review period
364 P. Georgiadis et al. / Journal of Food Engineering 70 (2005) 351–364
dim Response_Time_NR = (D = l .. 60)
const Response_Time_NR = 0.1 [hour]
dim Response_Time_SR = (D = 1 .. 69)
const Response_Time_SR = 0.1 [hour]
const S_DC = . . .[items]
dim S_NR = (D = 1 .. 60)const S_NR = [. . .] [items]
dim S_SR = (D = 1 .. 69)
const S_SR = [. . .] [items]
const s_DC = . . .[items]
dim s_NR = (D = 1 .. 60)
const s_NR = [. . .] [items]
dim s_SR = (D = 1 .. 69)
const s_SR = [. . .] [items]dim sd_NR = (D = 1 .. 60)
const sd_NR = [. . .] [items/hour]
dim sd_SR = (D = 1 .. 69)
const sd_SR = [. . .] [items/hour]
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