bur -- business research volume 6 | issue 2 | november 2013 | … · 2017-08-28 · volume 6 |...

BuR -- Business ResearchOfficial Open Access Journal of VHBGerman Academic Association for Business Research (VHB)Volume 6 | Issue 2 | November 2013 | 215-240

Integrated Strategic Planning of GlobalProduction Networks and Financial Hedgingunder Uncertain Demands and ExchangeRatesAchim Koberstein, Detlef-Huebner-Chair in Logistics and Supply Chain Management, Goethe University Frankfurt, Germany, E-mail:[email protected] Lukas, Chair in Financial Management and Innovation Finance, Otto-von-Guericke University Magdeburg, Germany, E-mail:[email protected] Naumann Decision Support and Operations Research Lab, University of Paderborn, Paderborn, Germany, E-mail: [email protected]

AbstractIn this paper,we present amulti-stage stochastic programmingmodel that integrates financial hedgingdecisions into the planning of strategic production networks under uncertain exchange rates andproduct demands. Thismodel considers the expenses of production plants and the revenues ofmarkets indifferent currency areas. Financial portfolio planning decisions for two types of financial instruments,forward contracts and options, are represented explicitly by multi-period decision variables and amulti-stage scenario tree. Using an illustrative example, we analyze the impact of exchange-rate anddemand volatility, the level of investment expenses and interest rate spreads on capacity locationand dimensioning decisions. In particular, we show that, in the illustrative example, the exchange-rate uncertainty cannot be completely eliminated by financial hedging in the presence of demanduncertainty. In this situation, we find that the integrated model can result in better strategic planningdecisions for a risk-averse decision maker compared to traditional modeling approaches.

JEL classification: C61, M11, G62

Keywords: strategic production network planning, financial hedging, uncertainty, stochastic program-ming

Manuscript received July 9, 2011, accepted by Karl Inderfurth (Operations and Information Systems)June 7, 2013.

1 IntroductionCurrent economic developments, which are char-acterized primarily by the increasing globaliza-tion of markets, global networking by companiesand significantly shorter product life cycles, pro-vide major positioning and growth opportunities,but also significant risks for companies. While theavailability of information has improved steadilydue to modern communication technologies, theuncertainty and volatility of future developmentshas increased. Therefore, companies must con-sider uncertainty in their mid-term (tactical) aswell as their long-term (strategic) planning. Forcompanies that source, manufacture and sell on a

global scale, strategic planning includes the de-sign of an international supply chain network,consisting of suppliers, manufacturing plants ofsemi-finished and finished products, warehouses,transportation routes and sales markets. Strate-gic decisions about the number and the locationof plants and warehouses, product-plant assign-ments, installed capacities and production tech-nologies are often associated with large invest-ments and typically cannot be reversed easily.Consequently, these decisions largely determinea company’s tactical and operational leeway toreact to uncertain future developments.Quantitative strategic supply chain planning mod-els account for the future consequences of strategic

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decisions by incorporating anticipation schemesfor expenses and revenues at the tactical and oper-ational levels, e.g., for transportation, production,inventory and the workforce. Two of the mainsources of risk in global supply network designplanning are uncertain exchange rates and de-mands. In this paper, we integrate an anticipa-tion scheme for financial hedging and portfolioplanning into a stochastic supply chain designmodel of the type described by Santoso, Ahmed,Goetschalckx, and Shapiro (2005) and Bihlmaier,Koberstein, and Obst (2009). We develop a multi-stage stochastic mixed-integer linear program-ming model, which includes discrete strategic de-cisions on facility location, product-plant assign-ment and capacity dimensions on the first timestage and operational production and logistics andfinancial decisions on subsequent time stages un-der uncertain exchange rates and demands. Weanalyze the consequences of the integrated antic-ipation of operational and financial hedging de-cisions for a risk-averse decision maker’s optimalstrategic planning solution in the context of anillustrative example.The remainder of this paper is structured as fol-lows: After reviewing the relevant literature in thefields of strategic production planning, real op-tions valuation and financial hedging, we developa multi-stage stochastic model that integrates fi-nancial hedging decisions into a traditional sup-ply network designmodel. Special consideration isgiven to themodeling of two financial instruments,forward and option contracts, and the discretiza-tion of exchange-rate and demand uncertainty.Next, we present an illustrative example and studythe impact of exchange-rate and demand volatil-ity, investment expenses and interest rate spreadson strategic investment decisions. We conclude bysummarizing our main results and by giving ourperspective on future research.

2 Literature reviewModels and methods for strategic production anddistribution network design have been availablesince the early days of the field of operations re-search, in particular for facility and warehouselocation and capacity dimensioning, taking into ac-count a variety of linear and nonlinear cost factorsassociated with transportation, production and in-ventory (see, e.g., the reviews of Beamon 1998;

Aikens 1985; Vidal and Goetschalckx 1997; Owenand Daskin 1998; Klose and Drexl 2005). Geof-frion and Graves (1974) laid the foundations formany deterministic, network-flow-based strategicnetwork planning models. The goal of their single-period mixed-integer model is to compute a mini-mumcost design of amulti-commodity productionand distribution network using intermediate dis-tribution centers. Computational tractability wasachieved by using a customized solution algorithmbased on Bender’s decomposition principle. Withgrowing computational capabilities of hardwareand standard solution software for mixed integerprogramming problems, more requirements fromindustrial practice could be considered with anincreasing level of detail. A typical example of ahighly-detailed deterministic model is describedin the article of Arntzen, Brown, Harrison, andTraffton (1995). The authors presented a multi-periodmixed-integermodel for global supply chainplanning. Their model includes detailed produc-tion, inventory and transportation planning andstrategic decisions as product allocation with re-lated fixed costs. The objective function includesthe minimization of costs as well as weighted pro-duction and shipping times. A particular featureof the model is the focus on international aspectssuch as duties, import taxes or duty drawbacks.However, uncertainty in exchange rates or de-mands are not considered. The model is appliedto a real-world example of a computer manufac-turer. A second example is the more recent paperof Fleischmann, Ferber, and Henrich (2006), whopresented a detailed multi-period mixed-integermodel based on experiences at BMW (for detailssee Ferber 2005). Strategies for capacity and flex-ibility are optimized simultaneously, while takinginto account a detailed representation of techni-cal capacity stages and an anticipation of tacticalworkforce planning.In the last decade, some researchers proposedstochastic programming models for supply net-work design as well as specially tailored solutionalgorithms and implementations for these kinds ofmodels. MirHassani, Lucas, Mitra, Messina, andPoojari (2000) presented a multi-period, mixed-integer, two-stage stochastic program for capac-ity planning in supply chain design problems.The first stage comprises the opening and clos-ing of plants and sets capacity levels. On the sec-ond stage, optimized decisions about production

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and distribution costs are made. Furthermore, theauthors presented an effective acceleration tech-nique for Bender’s decomposition algorithm anddemonstrated how well this approach can handlehundreds of scenarios for a particular case study.Alonso-Ayuso, Escudero, Garìn, Ortuño, and Pérez(2003) presented a two-stage stochastic programand a corresponding solution method for a simi-lar supply chain design problem. Santoso, Ahmed,Goetschalckx, and Shapiro (2005) presented anaccelerated Benders’ Decomposition method formixed-integer, two-stage stochastic programs forplanning realistically scaled supply chain designnetworks. Utilizing a sampling strategy, they wereable to handle a great number of scenarios. Theirapproach was successfully applied to strategic pro-duction network planning under uncertain de-mands in the automotive industry by Bihlmaier,Koberstein, and Obst (2009).Another stream of literature focusses on the val-uation of different kinds of operational flexibilityin production networks. Jordan and Graves (1995)evaluated product flexibility to hedge against un-certain demands. Their numerical studies showthat linking products and plants in a chain-likefashion is nearly as advantageous as a fully flexiblestrategy. This work provided a basis for a numberof other researchers, e.g., Boyer and Keong Leong(1996), who included diverse setup costs incurredby simultaneous production of several productsin a flexible plant, and Francas, Kremer, Min-ner, and Friese (2009), who evaluated the impactof demand dynamics caused by product life cy-cles. Chandra, Everson, and Grabis (2005) formu-lated amodel for flexibility planning specifically forthe automotive industry. Stochastic programmingmodels have been used as ameans to evaluate flex-ibility in manufacturing systems. Fine and Freund(1990) developed a stochastic programmingmodelfor optimizing product-flexible capacity under afinite number of possible demand realizations.Gupta, Gerchak, and Buzacott (1992) developed asimilar model for finding optimal investment poli-cies in the presence of fixed initial capacities. Chen,Li, and Tirupati (2002) optimized the capacity ofa flexible manufacturing system using stochasticprogramming, where the evolution of stochasticdemand is represented using demand scenarios.None of the above works considers exchange-rateuncertainties.A series of early papers by Jucker and Carl-

son (1976), Hodder (1984), Hodder and Jucker(1985a), Hodder and Jucker (1985b) and Hodderand Dincer (1986) incorporated demand and priceuncertainty, including exchange-rate uncertainty,in the context of an uncapacitated and, in the laterpapers, capacitated plant-location problem. An in-fluential contribution was made by Huchzermeierand Cohen (1996) and Cohen and Huchzermeier(1999), who showed how operational flexibility canbe utilized to hedge against demand and exchange-rate contingencies and demonstrated that the ade-quatemodel-wise anticipationof operational hedg-ing has a major effect on the underlying strategicdecisions. They developed a stochastic dynamicprogramming model to evaluate the expected, dis-counted, after-tax profit for a set of predefinedsupply network configurations (strategy options),which determine the degree of a firm’s manu-facturing flexibility. Exchange rates are modeledas stochastic diffusion processes that take inter-country correlations into account. The authorsdemonstrated that operational hedging can cre-ate an effective hedge in the long term, whilefinancial instruments can be more effective in theshort term. Their approach is similar to ours asit provides a computational tool to analyze real-world supply and production networks of practicaldimensions. However, our model offers severalextensions: First, financial hedging instrumentsare explicitly considered in our model which isnot the case in the dynamic programming ap-proach. Thereby, tradeoffs between financial andoperational hedging can be exploited directly andevaluated by the model. Second, network configu-rations and capacity dimensioning are representedas decision variables in our model, which enablesthe consideration of a much greater combinatorialcomplexity (in their case study, only 16 differentconfigurations are considered). While switchingcosts could in principle be incorporated in ourmodel, we do not consider them in this paper tokeep the computational requirements controllable.Operational hedging practices have also been in-vestigated analytically by several other authors(e.g. Cohen and Mallik 1997; Kouvelis 1999).Kazaz, Dada, and Moskowitz (2005) developeda two-stage stochastic program to evaluate twotypes of operational hedging under exchange-ratefluctuations: production hedging, where a firm de-liberately produces less than the total demand,and allocation hedging, where the firm utilizes

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the option of not serving a certain market due tounfavorable exchange rates. The authors showedthat both strategies are integral features of opti-mal policies. Financial hedging is not consideredin their analysis. In the field of finance, the use offinancial instruments such as forward and optioncontracts hedge against exchange-rate risks hasbeen well known for a long time (cf., e.g., Briysand Solnik 1992; Froot, Scharfstein, and Stein1993; Broll, Wahl, and Zilcha 1999; Chen, Lee,and Shrestha 2003). However, in these works,financial hedging is typically considered as totallyindependent of an underlying global manufactur-ing and distribution network, in spite of the in-tuitively apparent inter-dependencies. Cohen andHuchzermeier (1999) outlined the joint consider-ations of financial and operational hedging in thecontext of strategic supply chain planning as animportant direction for future research. Neverthe-less, this gap in the research literature received agreater amount of attention only recently. Chod,Rudi, andVanMieghem(2010) investigated the re-lationship between financial hedging and productflexibility under uncertain demands. They showedthat product flexibility and financial hedging canbe both complements and substitutes dependingon the prevailing demand correlations. Exchange-rate uncertainty was neglected in their model. Zhuand Kapuscinski (2006) investigated operationalversus financial hedging in a multinational risk-averse newsvendor framework under demand andexchange-rate uncertainty. They developed a dy-namic programming formulation and showed innumerical experiments that operational hedgingdominates financial hedging in terms of savings inmost situations, that financial hedging can changethe relationship between domestic and overseascapacities in some rare situations and that for ashort planning horizon the level of savings heav-ily depends on the relative extent of the differenthedging policies. Aytekin and Birge (2004) stud-ied the use of financial hedging instruments versusthe build-up of foreign production capacities for asimplified single-product firm operating in a homemarket and a foreign market under exchange-rateuncertainty only. They developed an analytic con-tinuous time model to value the additional flex-ibility from building up capacity in foreign mar-kets and deduce upper bounds on the value ofadditional capacities over all potential exchange-rate volatilities. Ding, Dong, and Kouvelis (2007)

showed in a rigorous analysis of stylized cases of upto two currency regions, markets, and productionfacilities, that a firm’s optimal financial hedgingstrategy closely ties to its operational strategy andcan have major effects on strategic supply chaindecisions such as the location and the number ofproduction facilities and the dimensioning of pro-duction capacities. Their work can be seen bothas a theoretical foundation as well as a motivationfor extending the traditional strategic supply chainplanning models.

3 Model description3.1 Overview and notationThe strategic single-period multi-commoditysupply network design model of Santoso, Ahmed,Goetschalckx, and Shapiro (2005) serves as thebasis for our integrated model. In this two-stagestochastic mixed-integer programming model,strategic investment decisions are representedby first-stage variables, and production andtransportation quantities are represented bysecond-stage variables. Uncertainties in costs,demands and production rates are modeled as arandom vector with a known discrete probabilitydistribution. We extend this model with thefollowing features:

• By adding time indices, we transform thesingle-periodmodel into amulti-periodmodel.For a typical strategic planning application, theplanning horizon covers between five and fif-teen years. Due to the strategic setting, wedo not consider inventory balances among thetime periods. We assume that there is no pro-duction during the first period. Strategic de-cisions and financial hedging decisions, whichmust be taken before the actual productionbegins, are assigned to the first time period.

• To consider the exchange-rate uncertainty, webuild separate cash flows for each currencyregion. These cash flows are transformed intoa reference currency and discounted over time.

• We integrate financial portfolio decisions overtime on the purchase and execution of forwardand options contracts on currencies to hedgeagainst exchange-rate uncertainties. We as-sume a perfect financial market without trans-action costs and arbitrage opportunities.

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• We capture uncertain exchange rates and de-mand over time in a scenario tree that is em-bedded in a multi-stage stochastic program-mingmodel. Each timeperiod corresponds to adecision stage of the scenario tree. Investmentand financial hedging decisions, which mustbe made before actual production begins, arerepresented by first-stage decision variables,which must be determined before uncertaintyunfolds over time. Production and transporta-tion quantities as well as the remaining finan-cial hedging decisions are tied to certain nodesof the scenario tree. We state the model in im-plicit deterministic equivalent form. The deci-sion variables are introduced for each scenario(= leaf of the scenario tree) and each time pe-riod, and the structure of a particular scenariotree is captured by adding non-anticipativityconstraints (for an introduction to multi-stagestochastic programming see Birge and Lou-veaux 1997). We state some exemplary non-anticipativity constraints for the illustrativeexample that is analyzed in section 4 in theAppendix.

• The model maximizes a mean-risk objectivefunction consisting of a weighted sum of theexpected net present value of the profits andthe conditional value at risk (CVaR) of the dis-tribution of the scenario dependent net presentvalues in the reference currency. The expectednet present value is the difference betweenthe discounted, scenario-dependent cash flowsand the investment expenses.

In the remainder of the paper, we will use thefollowing notation:

Sets and indicesS = set of scenarios sZ = set of suppliers zL = set of processing facilities l,

including manufacturing centers andmachines, finishing facilities andmachines, and warehouses

M = set of marketsmN = set of nodes i in the supply

network (sometimes also indexed by j),N = Z ∪ L ∪M

A = set of arcs (i, j) in the supplynetwork, A ⊆ N ×N

P = set of products pC = set of currencies cZL = set of tuples (z, c) which associate

currency c with supplier z,ZL ⊆ L × C

LL = set of tuples (l, c) which associatecurrency c with processing facility l,LL ⊆ L × C

ML = set of tuples (m, c) that associatecurrency c with marketm,ML ⊆ M × C

Input parametersT = number of time periodsprobs = probability of scenario scbuildlp = fixed initial investment, if

processing facility l is built forproduct p

coperatelp = fixed operating expenses per timeperiod, if processing facility l has beenbuilt for product p

qijpt = per-unit expenses of processingproduct p at facility i orpurchasing product p fromsupplier i and/ortransporting product p onarc (i, j) ∈ A in period t

supzp = maximal supply of product pprovided by supplier z

caplp = maximal capacity of processingfacility l for product p

dmpts = demand of product p on marketmin time period t and scenario s

pricempt = price of product p on marketmin time period t

MHT = maximum duration of forward andoption contracts

exrcts = exchange rate between the referencecurrency and currency c

[refc

]in time

period t and scenario sirc = interest rate of a riskless investment

in currency c

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irref = interest rate of a risklessinvestment in the referencecurrency

irwacc = company specific interest rateused to compute discounted cashflows (e.g., WACC: weighted averagecost of capital)

fexrctt′s = hedged exchange rate betweenreference currency and currency cfor a forward contract whichis signed in period t and becomeseffective in period t′

qputctt′ = price of a put option between thereference currency and thecurrency c that is purchased intime period t and can beexercised in time period t′

qcallctt′ = price of a call option betweenthe reference currency and thecurrency c that is purchasedin time period t and can beexercised in time period t′

Decision variablesylp = binary variable:

1 if processing facility lis built for product p,0 otherwise

xijpts = flow of product p on arc (i, j)in time period t andscenario s

f revctt′s = amount of revenues incurrency c hedged by aforward contract that issigned in time period tand becomes effectivein time period t′

f expctt′s = amount of expenses incurrency c hedged by aforward contract that issigned in time period tand becomes effective intime period t′

callbctt′s = amount in currency cfor which call optionsare purchased intime period t in scenario s

that can be exercised intime period t′

putbctt′s = amount in currency cfor which put optionsare purchased intime period t in scenario sthat can be exercised intime period t′

callectt′s = amount in currency cfor which call optionsare exercised intime period t′ in scenario sthat were purchased intime period t

putectt′s = amount in currency cfor which put optionsare exercised intime period t′ in scenario sthat were purchased intime period t

expvarits = expenses (for production/

purchasing and transportation)at processing facility / fromsupplier i in timeperiod t and scenario s

expoptionbuyts = amount of expenses in

reference currency for whichoption rights are acquired in period tand scenario s

explinebuildc = total initial investment

in currency cexplineoperate

c = total fixed operating expensesin currency c

revenuemt = revenues on marketm in timeperiod t and scenario s

pcfcts = cash flow of production activitiesin currency c in time period tand scenario s

fcfcts = cash flow of financial hedgingactivities in currency c in timeperiod t and scenario s

fcf refts = financial cash flow in referencecurrency in time period tand scenario s

cf refts = total (production and financial)cash flow in reference currency intime period t and scenario s

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npvs = net present value inreference currency inscenario s

expected_npv = expected net present valuein reference currency

CVaR = conditional value at risk inreference currency for agiven probability α

y0,ys = auxiliary dual variablesneeded in the CVaRformulation

3.2 Basic production network designmodel

The network design portion of our model resem-bles a classical multi-commodity network designformulation on the graph G = (N ,A):∑

i∈N

xilpts −∑j∈N

xljpts = 0 ∀l,p, t, s(1)

∑l∈L

xlmpts ≤ dmpts ∀m,p, t, s(2)

∑l∈L

xzlpts ≤ supzp ∀z,p, t, s(3)

∑i∈N

xilpts ≤ caplp · ylp ∀l,p, t, s(4)

y ∈ Y ⊆ {0,1}L×P(5)

xijpts ≥ 0 ∀i, j,p, t, s(6)

Constraint set (1) assures the flow balance of theincoming and the outgoing product quantities forprocessing facilities. The demand satisfaction foreach market is formulated by constraint set (2).If shortfalls are not permitted, then the constraintcan be modified to equality. However, this modifi-cation can lead to feasibility problems in the pres-ence of scenario-dependent demands. Constraintset (3) requires that the total flow of product pfrom a supplier node z cannot exceed the maximalsupply supzp at that node. The product-dependentcapacity constraints (4) mark a slight differencefrom Santoso’s model, where different productscan share a maximum capacity. While our formu-lation has greater combinatorial complexity dueto its increased number of binary variables, ourmodel more accurately represents a typical plan-ning situation in our favorite application domain,the automotive industry. In this industry, enablinga production facility to simultaneously manufac-

ture different products entails large investments,which must be considered in the objective func-tion. If a certain product p is processed at facility l,then the constraint set (4) requires that the respec-tive indication variable ylp equals 1. If facility l isnot built (ylp = 0), then the constraint will forceall flow variables xilpts = 0. Constraint (5) declaresthat the decision variables ylp are binary. The set Ycan include fixed opening (ylp = 1) or closing(ylp = 0) decisions. Constraint set (6) declares theflow variables as continuous and nonnegative. Thefollowing monetary components are formulatedfor the production-related portion of the model:

expvarits =

∑(i,j)∈A

∑p∈P

qijptxijpts ∀i, t, s(7)

revenuemt =∑p∈P

pricemptdmpt ∀m, t(8)

explinebuildc =

∑(l,c)∈LL

∑p∈P

cbuildlp ylp ∀c(9)

explineoperatec =

∑(l,c)∈LL

∑p∈P

coperatelp ylp ∀c(10)

pcfcts =∑

(m,c)∈ML

revenuemt(11)

−∑

(i,c)∈LL∪ZL

expvarits − explineoperate

c ∀c, t, s

Constraint set (7) determines the expensesincurred by the purchasing, production andtransportation functions for each processingfacility/supplier in each time period andscenario. Likewise, constraint set (8) computesrevenues. Note, that the currency of both sets ofbookkeeping variables is determined implicitlyby the associated supplier, processing facilityand market. In the following, the sets ZL, LLand ML are used to identify which suppliers,processing facilities and markets belong to acertain currency region. The sum of all initialinvestment and operating expenses in a certaincurrency are calculated in constraint sets (9)and (10), respectively. In constraint set (11),cash flows induced by all operational productionactivities (excluding initial investments) in acertain currency region are computed.

3.3 Modeling of financial instrumentsOur representation of financial hedging decisionsis a simplified versionof themodel proposedbyWu

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and Sen (2000). We assume perfect financial mar-kets and do not consider transaction costs. Fur-thermore, wemake the following assumptions thatlargely coincide with those of Wu and Sen (2000):

• We only consider European options, whichcannot be exercised before their due date.

• The financial instruments used in this modelhave amaximum lifetime ofMHT time periodsand a minimum lifetime of one period. Notethat in our strategic model, the time periodsusually span from several months to a year.

• The outcomes of randomvariables are revealedsequentially over time, and their outcomes areobserved only at the end of each time period.

• The purchase and the disposal of financial in-struments can only take place at the beginningof each time period.

• The amounts of the options and forward con-tracts can be traded in fractions of a unit.

• We do not account for taxes in our model.

3.3.1 Forward contractsForward contracts are always signed between acurrency c and the reference currency. The pe-riod in which the forward contract is signed isdenoted by t, and the period in which it takes ef-fect is denoted by t′. The variables f expctt′s are usedto hedge the expenses (incurred by production,transportation and line operations) in currency c.These variables are equal to the amount of cur-rency c that is obtained by exchanging the refer-ence currency in the time period t′ at the hedgedexchange rate fexrctt′s. Likewise, the variables f revctt′sequal the negative amount of currency c that isexchanged into the reference currency to hedgerevenues of currency c. For clarity the revenuesand the expenses are hedged independently in ourmodel. Note that given the above interpretation,decision variables associated with forward con-tracts can only take values greater than zero forcurrencies other than the reference currency. Weassume without loss of generality that the refer-ence currency is denoted by subscript 1 and set thecorresponding variables to zero:

f revctt′s ≤ 0, fexpctt′s ≥ 0 ∀c,0 ≤ t′ − t ≤ MHT , s(12)

f rev1tt′s = 0, fexp1tt′s = 0 ∀0 ≤ t′ − t ≤ MHT , s(13)

The hedged exchange rate for forward contractsand futures fexrctt′s is calculated in a preprocessingstep according to our assumptions as follows:

fexrctt′s = exrcts · e(irref−irc)·(t′−t)(14)

∀c,0 ≤ t′ − t ≤ MHT , s

The consideration of forward contracts in the totalcash flow of financial instruments is discussedbelow.

3.3.2 Option contractsIn our model, options always work between a cur-rency c and the reference currency. An option ispurchased and can be exercised in time periods tand t′, respectively. As only European options areconsidered, an option cannot be exercised prior toits expiration. The maximum lifetime of an optionis limited by MHT time periods. Option contractsare then modeled as follows:

callectt′s ≤ callbctt′s ∀c,0 ≤ t′ − t ≤ MHT , s(15)

putectt′s ≤ putbctt′s ∀c,0 ≤ t′ − t ≤ MHT , s(16)

callbctt′s ≥ 0,(17)

callectt′s ≥ 0,

putbctt′s ≥ 0,putectt′s ≥ 0 ∀c,0 ≤ t′ − t ≤ MHT , s

The decision variables putbctt′s and callbctt′s indi-cate the amount of currency c in scenario s forwhich puts and calls are bought in period t thatexpire in period t′. Thereby, separate hedging forrevenues and expenses is possible. The decisionvariables putectt′s and callectt′s indicate the exercisedputs and calls in period t′ that were bought inperiod t. Depending on the exchange rate changesbetween t and t′, an arbitrary fraction of optionscan be exercised in t′. Constraint sets (15) and (16)guarantee that only options that were purchased ina previous time period can be exercised. Decisionvariables associated with option contracts can onlytake values greater than zero for currencies otherthan the reference currency. We assume withoutloss of generality that the reference currency isdenoted by subscript 1 and set the correspondingvariables to zero:

callb1tt′s = 0, calle1tt′s = 0,(18)

putb1tt′s = 0,pute1tt′s = 0 ∀0 ≤ t′ − t ≤ MHT , s

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Prices of call and put options per unit of currencyc, qcallctt′s and qputctt′s, respectively, are calculated in apreprocessing step according to a discrete versionof the Garman andKohlhagenmodel (Garman andKohlhagen 1983):

qcallctt′s =exrcts

eirref (t′−t)

t′−t∑j=0

(t′ − tj

)pj · (1 − p)(t

′−t)−j(19)

· max(uj(1/u)(t′−t)−j − e(ir

ref−irc)(t′−t),0)

∀c,0 ≤ t′ − t ≤ MHT , s

qputctt′s =exrcts

eirref (t′−t)

t′−t∑j=0

(t′ − tj

)pj · (1 − p)(t

′−t)−j

(20)

· max(e(irref−irc)(t′−t) − uj(1/u)(t

′−t)−j,0)

∀c,0 ≤ t′ − t ≤ MHT , s

Here, u designates the percentage change of thespot rate and p denotes the risk-neutral probabilityof an up movement of the currency spot rate. Forsimplicity, we assume that the exercise price of anoption is always equal to the forwardexchange rate.Wewill describe the computation of exchange-ratevolatility and option prices to generate a consistentscenario tree in greater detail in section 3.5.In our model, the effects of forward and optioncontracts are taken into account in financial cash-flows for each foreign currency and the referencecurrency. These cash flows for forward and op-tion contracts are formulated in equation sets (22)and (23), respectively. The accounting variablesexpoptionbuy

ts computed in constraint set (21) con-tain all expenses incurred by buying options intime period t and scenario s.

expoptionbuyts =

∑c∈C

∑t′:0≤t′−t≤MHT

(qcallctt′s · call

bctt′s(21)

+qputctt′s · putbctt′s

)∀t, s

fcfct′s =∑

t:0≤t′−t≤MHT

(f expctt′s + f revctt′s

(22)

+ callectt′s − putectt′s) ∀c, t′, s

fcf reft′s = −∑c∈C

∑t:0≤t′−t≤MHT

(f expctt′s + f revctt′s

(23)

+callectt′s − putectt′s)· fexrctt′s

− expoptionbuyt′s ∀t′, s

3.4 Objective functions3.4.1 Maximization of expected net present

valueFor clarity, the expected net present value is com-puted in several steps:

cf refts = exrcts

(∑c∈C

pcfcts +∑c∈C

fcfcts

)(24)

+ fcf refts ∀t, s

npvs =T∑t=1

cf refts

(1 + irwacc)t

(25)

−∑c∈C

explinebuildc · exrc11 ∀s

expected_npv =∑s∈S

probs · npvs

(26)

Total cash-flows in the reference currency are com-puted for each scenario and time period in the con-straint set (24). Constraint set (25) determines thescenario-dependent net-present-values as the dif-ference of the discounted net-present-values andthe sum of the initial investment in the referencecurrency. The expected net present value over allscenarios is determined in constraint (26). At thispoint,we can state the completemodel for expectedvalue maximization as follows:

Maximize expected_npv(27)

subject to constraint sets (1) to (12),

(15) to (17) and (21) to (26)

Note that we have not enlisted non-anticipativityconstraints explicitly. These constraints areneededto take into account the timewise structure of deci-sions with respect to the given scenario tree. Often,non-anticipativity is taken into account implicitlyby the solution algorithm (e.g., by the samplingmethod given by Wu and Sen 2000) or the mod-eling environment (e.g., see the SPInE environ-ment by Valente, Mitra, Sadki, and Fourer 2009).We state some exemplary non-anticipativity con-straints for the model instance that is analyzed inour case example in section 4 in the Appendix ofthis paper.

223


3.4.2 Minimization of risk and construction ofthe efficient frontier with respect to riskand profit

To examine the effects of the integration of finan-cial instruments, riskmeasures can be added to theoptimization model and optimized in the objectivefunction. In recent years, the conditional value atrisk (CVaR) has become a widely accepted riskmeasure in the area of finance. Given a probabil-ity α, the CVaR is defined as the conditional meanvalue of the worst (1− α) * 100% of losses/profits.The CVaR was first proposed by Rockafellar andUryasev (2002). The authors also showed its com-putational tractability by representing CVaR as theoptimum of a special minimization problem. Itis well known that in the case of discrete finitedistributions, CVaR optimization problems can beformulated as linear programming problems. Tointegrate CVaR into our model, we use the follow-ing dual formulation of Fábián (2008):

Maximize CVaR

(28)

subject to

CVaR = y0 −1

1 − α

∑s∈S

probsys

(29)

y0 − ys ≤ npvs ∀s(30)

ys ≥ 0 ∀s(31)


(15) to (17) and (21) to (26)

where CVaR, y0 and ys denote | S | +2 additionalcontinuous decision variables (CVaR and y0 aregenerally unbounded). In our illustrative example,we will construct the efficient frontier of non-dominated solutions with respect to the expectednet present value and the CVaR using the followingcombined objective function:

Maximize (1 − λ) · expected_npv + λ · CVaR(32)


(15) to (17), (21) to (26)

and (29) to (31)

The parameter λ controls the weight given to theoptimization of the expected profit and the CVaR.

Therefore, λ reflects the level of risk aversion ofthe decision maker. For λ = 0 the objective func-tion (32) coincideswith the objective function (27),yielding the optimal solutionwith respect to the ex-pected profit. For λ = 1 it coincides with objectivefunction (28), yielding the solution thatmaximizesCVaR. To construct the efficient frontier, the pa-rameter λ is iterated between 0 and 1. We usuallyuse a logarithmic scale for λ to generate more solu-tionpoints in the proximity of the optimal expectedprofit solution.

3.5 Scenario generationIn this section, we describe the modeling ofexchange-rate and demand uncertainty. We startby modeling pure exchange-rate uncertaintyby means of a binomial scenario tree. Then, inthe second step, we incorporate the demanduncertainty. The consideration of exchange-rateuncertainty leads to a random factor for eachcurrency region. We model the exchange ratesas a geometric Brownian motion with constantvolatility σE (see Musiela and Rutkowski 1997for further justification). How to representmultiple stochastic factors and processes byscenario trees has been the subject of intensiveinvestigations (see Wu and Sen 2000 and thereferences therein). We discretize the stochasticprocesses by generating a binomial lattice asproposed by Cox, Ross, and Rubinstein (1979).The volatility σE of a random factor is controlledby a constant uE. Given the value S0 of a randomfactor at a certain node in the scenario tree, twosuccessors S0 · uE and S0/uE are created. Thedependency of uE and σE is given by the followingequation (see, e.g., Hull 2003: p. 211ff.):

(33) uE = eσE

The probability pup of a positive development,which means a multiplication with uE, is deter-mined as follows (see, e.g., Hull 2003: p. 211ff.):

(34) pup =eir

ref−irc − 1

uE

uE − 1

uE

The probabilities of an exemplary binomial treefor the case of 64 scenarios can be calculated as

224


Figure 1: Scenario tree with 6 stages representing joint exchange-rate and demanduncertainty.

scen.1-

1024

scen.1-256

scen.257-512

scen.513-768

scen.769-1024

exr

d

exr

d

exr d

exrd

t = 2

scen.1-64

scen.65-128scen.129-192scen.193-256

exr

d

exrdexr

d

exr d

(…)

(…)

(…)

(…)

(…)

(…)

t = 3 t = 6

scen.1

scen.2

scen.3

scen.4

exr

d

exrdexr

d

exr d

(…)

scen.1-4

(…) t = 5

scen.1021

scen.1022

scen.1023

scen.1024

exr

d

exrdexr

d

exr dscen.1021-1024

(…)

exr d

exr d

t = 1

follows:

probs = (pup)1−(s div 33) · (1 − pup)s div 33

· (pup)1−(((s−1) mod 16) div 8)

· (1 − pup)((s−1) mod 16) div 8

· (pup)1−(((s−1) mod 4) div 2)

· (1 − pup)((s−1) mod 4) div 2 ∀s

(35)

To consider the uncertain demand, we incorpo-rate demand development into the scenario tree.Figure 1 depicts the scenario tree used in our il-lustrative example in section 4, whichmodels jointexchange-rate and demand uncertainty. In thistree, each node contains four successors that rep-resent two demand developments (up / down) foreach exchange-rate development in such a way,that, for each time stage predetermined productdemand levels dmpt yield as expected values. These

demand levels can be utilized, e.g., to model lifecycle developments. Technically, for an arbitrarynode i on stage t of the scenario tree, the associatedscenario-dependent demand value dmpts is com-puted as Δi

tdmpt, where Δit represents the demand

development in this node. For the successor-nodesof node i this value is set toΔi

t · uD andΔit/uD. For

the root-node, Δ10is set to 1. The constant uD is

derived from the demand volatility σD as uD = eσD.

To consider up-and-downmovements of demandswith equal probability, the pup constant has to bemultiplied by a factor of 0.5.

4 Illustrative case example andresults

4.1 Setting and goalsIn this section, we investigate a stylized case, whichcomprises a company that manufactures three

225


products at a maximum of two production plantsin two currency regions to satisfy the demand ofits home market. Production capacity can be in-stalled in discrete steps at the domestic plant or atthe foreign plant. The exchange rates and productdemands are assumed uncertain.We presume thatthe demand developments for the three differentproducts are perfectly correlated and independentof exchange-rate fluctuations. The planning hori-zon spans over six time periods, which resultedin a scenario tree of 1024 scenarios (leafs). Notethat no production takes place in the first planningperiod because it is reserved for investment andfinancial hedging decisions. In section 4.2, we pro-vide a detailed description of the underlying data.In our analysis, we pursue the following goals:

1. In section 4.3, we analyze the impact of jointexchange-rate and demand volatility on the in-teraction of operational and financial hedging,capacity and location decisions.

2. In section 4.4, we analyze the impact of thelevel of investment expenses and fixed costs,on capacity dimensioning in particular.

3. In section 4.5, we analyze the impact of spreadsbetween interest rates of the foreign and do-mestic currency regions.

4. In section 4.6, we compare traditional strate-gic planning procedures, which usually disre-gard financial planning, with our integratedapproach.

Because the focus of this paper is not solutionmethodology, we will not conduct a thorough com-putational study in terms of model sizes and run-time. Themodel of the presented case examplewasimplemented using a mathematical programminglanguage (AMPL) and solved using IBM Cplex 12.Themajority of the resultingmodel instances weresolved in 10 minutes of runtime on a standardlaptop computer.

4.2 Setting and dataFigure 2 displays the general setting described pre-viously. The solid arcs (1) and (2) represent flowsof goods produced in the foreign and domesticplant, respectively, and transported to the cus-tomers in currency region C1. The dashed arcs (3)and (4) depict financial flows, i.e., via arc (3)

Table 1: Expected product demands.

timeperiod P1 P2 P31 0 0 02 330000 0 400003 330000 0 1200004 270000 0 1600005 200000 120000 1800006 120000 240000 180000

Table 2: Variable production expenses perunit.

P1 P2 P3domestic plant* 7.0 12.5 17.0foreign plant** 5.0 9.0 13.0

*: in thousand units of currency C1, **: in thousand units ofcurrency C2

the company covers production and transporta-tion costs incurred in the foreign production plant,and arc (4) illustrates revenues earned by the com-pany in the domestic market. Consequently, in thiscase, only processing costs incurred in the foreignplant are exposed to exchange-rate fluctuations,whereas expenses and revenues in the domesticcurrency region are not exposed to exchange-ratefluctuations.Customer demands for the three products P1 - P3are listed in Table 1. The demand figures repre-sent different life-cycle situations, i.e., an endinglife cycle for P1 and starting life cycles for P2and P3. Variable production and transportationexpenses are listed in Tables 2 and 3, respectively.Because we presume an initial exchange rate of1.0 at the beginning of the planning horizon, dataon expenses are directly comparable. We assumethat foreign production is generally cheaper thandomestic production, despite higher costs of trans-portation from the foreign production plant to thecustomer market. Table 4 shows the sales pricesper unit in the domestic market. Profit margins

Table 3: Transportation expenses per unitfrom the production plants to thecustomer market.

P1 P2 P3from domestic plant* 0.20 0.22 0.25from foreign plant** 0.80 1.00 1.20

*: in thousand units of currency C1, **: in thousand units ofcurrency C2

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Figure 2: Setting of the stylized case. Arcs (1) and (2) depict flows of goods, and arcs (3)and (4) depict financial flows.

(3)

(4)(2)

(1)

Currency region C1(domestic)

Currency region C2(foreign)

Table 4: Sales prices per unit in thedomestic customer market.

P1 P2 P3domestic market* 20.0 35.0 70.0

*: in thousand units of currency C1

per unit are relatively high. However, we do notexplicitly consider expenses for research, productdevelopment and other overhead expenses, whichhave to be deducted from the resulting profits. Asindicated previously, capacity can be installed inten discrete steps of 30,000 units per time periodfor product P1, 25,000 units per time period forproduct P2 and 20,000 units per time period forproduct P3 at both of the plants. In the followingsection, we refer to the discrete capacity steps asproduction lines. For the installation of one pro-duction line, investment expenses of 250 millioncurrency units at the beginning of the planninghorizon and fixed operating expenses of 50millioncurrency units per time period are incurred. In thefollowing section, we presume a weighted averagecost of capital irwacc of 8% and a maximal contractduration of1 time period for both types of financialhedging instruments.

4.3 The impact of exchange-rate anddemand volatility

Figure 3 shows efficient frontiers with respect torisk (CVaR 95%) and expected profit for six differ-ent levels of exchange rates and demand volatil-ities σE,D (see Appendix B for further details). Ineach of the six diagrams, four model variants arecompared, namely, one version without financialinstruments, one version with one type of financialcontract (forwardsoroptions) andoneversionwith

both types of financial contracts. The efficient fron-tiers were constructed using the objective functionand the procedure described in section 3.4.2.Figures 4 and 5 illustrate the corresponding distri-bution of capacities between the domestic and theforeign plant for the two model variants with andwithout financial hedging and six different levelsof exchange rates and demand volatilities. Eachof the twelve diagrams shows the number of pro-duction lines installed at the domestic and foreignplants for different levels of risk aversion λ.Diagram 3(a) depicts the case of pure exchange-rate uncertainty. For the solution yielding themax-imal expected net present value (ENPV = 37.2 bn.currency units) the abandonment of financial in-struments results in significant risks (CVaR95 =2.0 bn. CU). As illustrated in the correspondingcapacity diagram 4(a), this risk can be mitigatedby shifting production lines from the foreign re-gion to the domestic currency region and sacri-ficing expected profits due to higher expenses forproduction. However, using forward contracts inthis situation, the efficient frontier reduces to justone point at the upper-right corner, which indi-cates that currency risk can be completely hedgedby the use of forward contracts in the absenceof demand uncertainty. Consequently, a shift incapacity toward the domestic currency region isunnecessary, as illustrated in diagram 4(b). Con-versely, the results also confirm that option con-tracts are less efficient if only exchange-rate riskis present. This result can be explained by therisk pattern produced by option contracts. In par-ticular, the owner has the choice to exercise theoption or allow it to expire unused. Consequently,the thread of walking away with a loss incurredthrough the sunk costs of the option premium paid

227


exists when profiting from upside potentials. Inthis context, another result can be deduced fromdiagram 3(a). Operational and financial hedgingstrategies are substitutes. Without options, theagent would simply relocate production to thedomestic currency region. However, operationalhedging becomes cheaper with the use of financialoptions because the option can mitigate some, butnot all, of the exchange-rate risk. Consequently,the use of financial options yields a pareto frontthat is similar to the unhedged scenario but for bet-ter CVaR and ENPV combinations. Furthermore,due to the unbiasedness of financial markets, allof the results confirm the well-known fact thatfinancial hedging cannot solely increase expectedprofits. Asmentionedpreviously, financial hedgingand operational hedging strategies are substitutes.Consequently, if the financial instruments are notcapable of sufficiently reducing the risk, the agentcan use operational hedging to further minimizerisk. Compared with the unhedged scenario, oper-ational hedging becomes cheaper which can raiseprofits (e.g., 3(a)). If both financial instrumentscan be employed, the model generates the samesolution as the forwards-only model, which is alsovalid for the cases of increased demand uncer-tainty. In this setting, financial instruments areno longer capable of completely eliminating risk(see Figures 3(b) to 3(d)) and the volatility ofthe NPV increases. The maximal ENPV decreasesonly marginally from 37.2 bn. CU to 36.0 bn. CU,whereas the best achievable CVaR95 using forwardcontracts decreases from approximately 37 bn. CUto approximately 17 bill. CU.Although the model variant without financial in-struments tends to install fewer production linesin the domestic currency region (Figures 4(c),4(e) and 5(e)), the model variant with incorpo-rated financial instruments increases the numberof domestic production lines (Figures 4(d), 5(f)and 5(f)). With higher demand volatility, the mod-els install a smaller total number of productionlines in the cases of high risk aversion (λ-valuenear 1.0) and accept lost sales. Themaximal ENPVdecreases further with a decreasing exchange-rate volatility from 36.0 bn. CU for the caseσE = 0.45,σD = 0.25 to 34.6 bn. CU for the caseσE = 0,σD = 0.25, which seems to be counter-intuitive (Figures 3(d) to 3(f)). The correspondingcapacity diagrams 5(a) to 5(d) show that fewer do-mestic production lines are installed with decreas-

ing exchange-rate volatility. Capacity decisions areless influenced by the use of financial hedging in-struments. Diagram 3(f) clearly shows that it is notpossible to use financial hedging instruments tohedge against demand uncertainty.It is assumed that in the case of joint demandand exchange-rate uncertainty, financial instru-ments should be capable of completely hedgingthe fraction of risk that is induced by exchange-rate volatility. If this notion was valid, the mod-els 5(a) and 5(f) should yield similar capacity de-cisions. However, the two capacity diagrams differsignificantly: a significantly higher number of pro-duction lines is installed in the domestic currencyregion for the case of high exchange-rate volatilitydespite the use of financial hedging. This result in-dicates that exchange-rate uncertainty cannot becompletely eliminated by financial hedging in thepresence of demand uncertainty in our stylizedcase. Section 4.6 provides a comprehensive dis-cussion of consequences for the strategic planningof production networks and alternative planningapproaches.

4.4 The impact of investment expensesTo investigate the impact of the level of investmentexpenses, we conducted the analysis from sec-tion 4.3 for two additional variants of our modelinstance, in which we lower the levels of invest-ment expenses and fixed operating expenses to50% and 25%, respectively. These changes areimplemented in our model by multiplying invest-ment expenses clinebuildc and fixed operating ex-penses clineoperatec by a constant α with 0 ≤ α ≤ 1.The results in termsof the efficient risk/profit fron-tiers are displayed in Figure 6. A distinct decreasein fixed expenses causes an increase in expectedprofits and lower risk. However, there is an ad-ditional interesting effect, which can be identifiedin diagram 6(a) and subsequent diagrams. Dia-gram 6(a) illustrates how the efficient frontiersextend to the left (increasing potential loss of ex-pected profit) and shift to the bottom (decreasingCVaR) with increasing volatility. However, for thehighest volatility of σ = 0.45 this intuitive be-havior stops and the associated efficient frontieris shifted to the upper-right corner. For pure ex-pected profit maximization a significant increasein expected profit is evident. Thus, in this casewe observe an increase in expected profits and a

228


Figure 3: Impact of exchange-rate volatility and financial hedging on risk/profit efficientfrontiers. Generated with coinciding interest rates irC1 = 4% and irC2 = 4% in the domesticand the foreign currency region, respectively.

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%

�in�billion�un

its�of�currency�C1

Expected�net�present�value�in�billion�units�of�currency�C1

No�financial�instrumentsForwardsOptionsForwards�and�Options

(a) σE = 0.45, σD = 0

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%





(b) σE = 0.45, σD = 0.05

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%





(c) σE = 0.45, σD = 0.15

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%





(d) σE = 0.45, σD = 0.25

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%





(e) σE = 0.25, σD = 0.25

5

10

15

20

25

30

35

40

20 25 30 35 40

CVaR

�95%





(f) σE = 0, σD = 0.25

decreased risk (increasing CVaR) for an increasein exchange-rate volatility. This effect, which iscounter-intuitive, is retained for the model withfinancial hedging (cf. diagram 6(b)) and is am-plified for lower fixed expenses (cf. diagrams 6(c)to 6(f)). Figure 7 shows that lower fixed expensesand higher exchange-rate volatility produce a sig-

nificantly higher number of production lines in thedomestic and foreign currency regions. Thereby,the model gains more flexibility regarding the useof operational hedging and the impact of financialhedging instruments on capacity decisions, ENPVand decreased risk.

229


Figure 4: Impact of demand volatility and financial hedging on capacity installation underexchange-rate and demand uncertainty. Generated with coinciding interest ratesirC1 = 4% and irC1 = 4% in the domestic currency region and the foreign currency region,respectively.

05

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Capacity�in�home�country Capacity�in�foreign�country

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(f) With forwards and options, σE = 0.45, σD = 0.15

4.5 The impact of interest rate spreadsWhereas we presumed coinciding levels of interestrates of 4% in the preceding investigations, we willnow analyze the impact of interest rate spreads. Tothis end, we generated further results with interestrates of 1% and 7% in the foreign currency region.

Note that in the following discussion of results, irC1corresponds to irref . Following the same regimeconsidered above, the results are summarized inFigure 8 in terms of efficient risk/profit frontiersand in Figure 9 in terms of capacity distributions.Interest rates affect the model in two ways: First,

230


Figure 5: Impact of exchange-rate volatility and financial hedging on capacity installationund exchange rate and demand uncertainty. Generated with coinciding interest ratesirC1 = 4% and irC1 = 4% in the domestic currency region and the foreign currency region,respectively.

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interest rate spreads directly influence the proba-bilities associated with the scenario tree. Accord-ing to formula (34), a positive drift is added tothe scenario tree (and likewise to the underlyingstochastic process) if the interest rate in the for-eign currency region is smaller than that in thedomestic currency region. This drift can be in-

terpreted as a bias toward an appreciation of theforeign currency and a devaluation of the domes-tic currency, which in turn leads to an increasedimpact of exchange-rate volatility on productionexpenses at the foreign plant. The consequencesare lower expected profits and a fortified relocationof production lines toward the domestic currency

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BuR -- Business ResearchOfficial Open Access Journal of VHBGerman Academic Association for Business Research (VHB)Volume 6 | Issue 2 | November 2013 | 215--240

Figure 6: Impact of investment expenses on risk/profit efficient frontiers (with σD = 0.25).

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

�95%




��=�0.00��=�0.25��=�0.45

E

E

E

(a) No financial instruments, α = 1.0

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

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��=�0.00��=�0.25��=�0.45

E

E

E

(b) With forwards and options, α = 1.0

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

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��=�0.00��=�0.25��=�0.45

E

E

E

(c) No financial instruments, α = 0.5

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

�95%




��=�0.00��=�0.25��=�0.45

E

E

E

(d) With forwards and options, α = 0.5

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

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��=�0.00��=�0.25��=�0.45

E

E

E

(e) No financial instruments, α = 0.25

5

10

15

20

25

20 25 30 35 40 45 50

CVaR

�95%




��=�0.00��=�0.25��=�0.45

E

E

E

(f) With forwards and options, α = 0.25

region.These effects can be clearly observed indiagrams 8(c), 9(e) and 9(f). Inevitably, thedescribed effects are inversed if the domesticinterest rate is smaller than the foreign interestrate. This case can be studied by consideringthe diagrams 8(a), 9(a) and 9(b). Moreover, theresults reveal that the use of financial instrumentscontributes more effectively to risk mitigation ifthe foreign currency depreciates.Second, interest rates directly influence the for-ward rate of forward contracts according to for-mula (14) and the prices of option contracts ac-cording to formulas (19) and (20). Due to Interest

Rate Parity, the hedged exchange rate is subjectto interest changes. Forward contracts, however,cost nothing to enter, which means that the useof forward contracts is equally appealing. On theother hand, option contracts can become more orless expensive because the interest rate spread, i.e.,the difference irref − irc, impacts the strike price ofthe option. More precisely, when pricing the op-tion we have assumed that the strike price equalsthe forward rate which is in turn based on the the-ory of Interest Rate Parity. Consequently, interestchanges in either currency will change the for-ward rates and strike prices, respectively. Hence,a positive interest spread, i.e., irref > irc increases

232

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Figure 7: Impact of the level of investment expenses and fixed expenses α on capacityinstallation (with σD = 0.25).

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(h) With forwards and options, σE = 0.45, α = 0.25233


Figure 8: Impact of interest rate spreadson risk/profit efficient frontiers.Generated with σE = 0.45 and σD = 0.25.

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(a) irC1 = 4%, irC2 = 7%

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(b) irC1 = 4%, irC2 = 4%

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(c) irC1 = 4%, irC2 = 1%

the strike price of the option. Ceteris paribus, theoption becomes less expensive because the op-tion is presently out-of-the-money. If, however,irref < irc, the option is currently far in-the-moneyand possesses an intrinsic value that the optionpremium must cover. Hence, hedging against ex-change risk becomesmore expensive. Though botheffects tend to impact the optimal choice of finan-cial instruments and the number of productionlines, we observe that the first effect, i.e., the di-rect impact of appreciation or depreciation of acurrency tends to dominate.

4.6 Discussion of alternative planningapproaches

From the viewpoint of a decision maker, there arenow several approaches for handling exchange-rate uncertainty:

• Deterministic approach: This approach com-pletely neglects exchange-rate uncertainty andplans under given exchange rates. One argu-ment in favor of this approach that can befound in the literature is that exchange-raterisk can be mitigated completely by the useof financial instruments, which is confirmedby our analysis for the case of absent demanduncertainty. However, under uncertain prod-uct demand, planning solutions of the modelvariant with zero exchange-rate volatility (Fig-ure 5(a)) and solutions of the model variantwith exchange rate uncertainty and integratedfinancial hedging (Figure 5(f)) differ consid-erably, as discussed in section 4.3. Therefore,given a significant level of demand volatility,neglecting exchange-rate uncertainty does notseem to be a reasonable option for the decisionmaker.

• Stochastic approach, no financial instru-ments: This approach models exchange-rate(and demand) uncertainty explicitly butdoes not consider financial hedging. In ourillustrative case, this approach overestimatesthe impact of exchange-rate fluctuations andtends to relocate production lines to thedomestic plant too early with increasing riskaversion. It therefore does not fully exploitcost advantages for a given level of riskaversion.

• Sequential approach: An alternative approachis to construct and evaluate possible solutionsin two subsequent steps. The first step con-sists in solving the stochastic model underdemand and exchange-rate uncertainty with-out financial instruments. Second, an optimalfinancial hedging strategy is derived by an ad-equate procedure based on the optimal invest-ment and production decisions from the firststep. We implemented this approach by fixingthe optimal solution values of the stochasticmodel without financial hedging in the inte-grated model. The solutions of this approachare depicted as single points in Figure 10. It

234


Figure 9: Impact of interest rate spreads on capacity installation. Generated withσE = 0.45 and σD = 0.25.

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(a) irC1 = 4%, irC2 = 7%, no financial instruments

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(b) irC1 = 4%, irC2 = 7%, with forwards and options

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(c) irC1 = 4%, irC2 = 4%, no financial instruments

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(d) irC1 = 4%, irC2 = 4%, with forwards and options

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(e) irC1 = 4%, irC2 = 1%, no financial instruments

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(f) irC1 = 4%, irC2 = 1%, with forwards and options

can be observed that the solutions of themodelwithout financial instruments are shifted di-rectly upward by evaluating them under anoptimal financial hedging strategy. It is clearthat these solutions are not guaranteed to forman efficient frontier. However, in all cases, thisapproach is able togenerate themaximalENPVsolution and to produce a correct risk assess-ment by complementing it with the optimalfinancial hedging strategy. If no demand un-

certainty is present (Figure 10(a)), this pointcoincides with the complete efficient frontierof the integrated model, indicating that sepa-ration holds, i.e., production and hedging de-cision can be performed separately and dele-gation to an individual other than the financialmanager is possible. For increasing demanduncertainty, however, the sequential approachis not able to generate an acceptable approxi-mation of the efficient frontier of the integrated

235


model. In particular, in the case of the highestdemand volatility (Figure 10(a)), a significantgap remains, which would lead to a system-atic overestimation of currency risk associatedwith the relocation of production lines towardthe domestic currency region. An implicationof this result is that separation of the firm’sfinancial and production decisions is no longeradvisable.

• Integrated stochastic approach: Thisapproach, which we propose herein, considersexchange-rate and demand uncertainty andfinancial hedging instruments explicitlywithin one integrated model. Consequently,the approach considers that under demandand exchange-rate uncertainty the productiondecisions can no longer be delegated toan individual, which optimizes production.Rather, both decisions must be madesimultaneously by one agent. In addition,possible investment decisions are evaluatedmost realistically in terms of expectedprofit and risk by determining the optimalcombination of operational and financialhedging instruments. The integrated modelis able to consider the impact of varyingexchange-rate and demand volatilities,different levels of investment expenses,fixed expenses and interest rate spreads oncapacity location and dimensioning, which isnot possible using the previously discussedplanning approaches.

A general criticism of stochastic models concernsthe assumption that distributions of random pa-rameters are assumed to be known. Furthermore,one can argue that in a case study in which astochastic model and the data are based on thesame stochastic process, the comparison with adeterministic model always favors the stochasticmodel. However, in our view, neither statementreduces the benefit of a stochastic model for thedecision maker, which consists of the opportunityto explicitly model uncertainty by means of a sce-nario tree. The stochastic model is then able togenerate a solution that actively hedges againstuncertainty. This is not possible with a determin-istic model. Certainly, assumptions must be madeconcerning the model of uncertainty. However,much stronger assumptions must be made when

generating the data for a deterministic model (e.g.,through aggregation).Therefore, in our view, the decision maker shoulddeploy the integrated model to find the invest-ment decision that reflects best his or her levelof risk aversion and considers the various effectsthat can occur under uncertain demands and ex-change rates as demonstrated in this study, withthe greatest possible accuracy.

5 ConclusionTwoof themain risks globalmanufacturers are fac-ing today are induced by uncertain exchange ratesand product demands. Exchange-rate risk is pre-dominantly hedged by means of financial deriva-tives. Traditionally, strategic production networkplanning and financial hedging is treated sepa-rately, both in the firm’s organizations as well asin the research literature, which is the main causeof classical two-period-hedging results indicatingthat a separation theorem holds, i.e. productionand hedging decision can be performed separately,and delegation to an individual other than the fi-nancial manager is possible. In reality, however,production decisions take place at different pointsin time, putting stress on a multi-period decisionframework, and are subject to a greater varietyof risks. In this study, we presented a multi-stagestochastic programming model for the integratedplanning of strategic production network designand financial hedging under uncertain exchangerates. The analysis of our illustrative case indi-cates that the integrated model can result in betterstrategic planning decisions in terms of expectedprofit and conditional value at risk compared to thetraditional, non-integrated approach. This result isdue to the observation, that separation no longerholds for our small-scale example under combinedexchange-rate and demand uncertainty. Accord-ingly, the production decisions can no longer bedelegated to an agent who optimizes productionindividually. Rather, both decisions must be madesimultaneously by one agent.The presented model may constitute a startingpoint for further research. To solve the model formore realistic cases, a more sophisticated solu-tion framework must be developed, deploying de-composition methods for the multi-stage stochas-tic programming model and scenario aggregationtechniques tomanagemore time periods andmore

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Figure 10: Comparison of risk/profit efficient frontiers w.r.t. different planningapproaches.

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than two currency regions. The financial part of themodel should be extended to consider imperfectfinancial markets, including e.g., transaction costsor liquidity risk.

Appendix A: Non-anticipativityAbove we present the model formulation of thedeterministic equivalent in implicit form. In thisform, all of the decision variables associated witha stage of the scenario tree are indexed over allscenarios (leaves of the scenario tree). The follow-ing non-anticipativity constraints identify all of thevariables associated with a certain node of the tree.For a node i in the tree, the scenario indices ofthe variables to be identified can be determined bythe subset of leaf nodes for each of which node iis on the path from the leaf node to the root node.Note that we assume that no production is possi-ble in the first time period that is associated withthe root node of the scenario tree. We present the

non-anticipativity constraints that yield the sce-nario tree depicted in Figure 1 for the decisionvariables xijpts and callbctt′s. For the remaining vari-ables, the non-anticipativity constraints follow thesame scheme.

xi,j,p,1,s = 0 ∀i, j,p, s(36)

xi,j,p,2,256*k+s = xi,j,p,2,256*k+s+1(37)

∀i, j,p, s < 256, k ∈ {0 . . .3}

xi,j,p,3,64*k+s = xi,j,p,3,64*k+s+1(38)

∀i, j,p, s < 64, k ∈ {0 . . .15}

xi,j,p,4,16*k+s = xi,j,p,4,16*k+s+1(39)

∀i, j,p, s < 16, k ∈ {0 . . .63}

xi,j,p,5,4*k+s = xi,j,p,5,4*k+s+1(40)

∀i, j,p, s < 4, k ∈ {0 . . .255}

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callbc,1,t′,s = callbc,1,t′,s+1(41)

∀c,1 < t′ ≤ 1 +MHT , s < 1024

callbc,2,t′,256*k+s = callbc,2,t′,256*k+s+1

(42)

∀c,2 < t′ ≤ 2 +MHT , s < 256, k ∈ {0 . . .3}


(43)

∀c,3 < t′ ≤ 3 +MHT , s < 64, k ∈ {0 . . .15}


(44)

∀c,4 < t′ ≤ 4 +MHT , s < 16, k ∈ {0 . . .63}


(45)

∀c,5 < t′ ≤ 5 +MHT , s < 4, k ∈ {0 . . .255}

Appendix B: Parameters of thescenario trees in the illustrativeexampleThe values of σE,D used in our analysis are associ-ated with the following values for uE,D and pup inaccordance to equations (33) and (34), where pup

is multiplied by 0.5 to account for demand states:σE,D = 0: uE,D = 1, pup = 0.25; σE,D = 0.05:uE,D = 1.05, pup = 0.245; σE,D = 0.15: uE,D =1.16, pup = 0.23; σE,D = 0.25: uE,D = 1.28,pup = 0.22;σE,D = 0.35:uE,D = 1.42,pup = 0.205;σE,D = 0.45: uE,D = 1.56, pup = 0.195.

AcknowledgmentsWe would like to thank the anonymous refereesand the department editorKarl Inderfurth for theirveryhelpful comments and suggestions thathelpedto improve the manuscript considerably.

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Biographies

Achim Koberstein is Professor and holds the Detlef-Huebner-Chair in Logistics and Supply Chain Man-agement at Goethe-University Frankfurt, Germany. HestudiedComputer Science at theUniversity of Paderbornand the Georgia Institute of Technology, Atlanta, USA.In 2005 he received his doctorate from the University ofPaderborn. His research interests include optimizationmodels and systems for production planning, supplychain management and for the liberalized gas market aswell as optimization algorithms and solver technologyin linear and stochastic optimization.

ElmarLukas is Professor and holds the Chair in Finan-cial Management and Innovation Finance at Otto-von-Guericke University Magdeburg, Germany. He studiedPhysics and Industrial Engineering and Managementat the University of Paderborn and at the Universityof California, Berkeley. In 2003, he received his doc-torate from the University of Paderborn, where he alsoachieved his habilitation in 2008. His research interestsinclude corporate finance, option pricing, mergers andacquisitions, and industrial economics.

MarcNaumannwas a doctoral student at theDecisionSupport and Operations Research Lab of the Universityof Paderborn starting in 2009 and completed his PhDin 2012. His main research interests include airlinescheduling, scheduling in public transport, stochasticoptimization, robust optimizationand riskmanagement.

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