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Integrating Operational Hedging of Exchange Rate Risk in the Optimal Design of Global Supply Chain Networks Pantelis Longinidis, Michael C. Georgiadis, and George Kozanidis Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b00349 • Publication Date (Web): 26 May 2015 Downloaded from http://pubs.acs.org on May 30, 2015

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Industrial & Engineering Chemistry Research

Integrating Operational Hedging of Exchange Rate Risk in the Optimal Design of Global Supply Chain Networks Pantelis Longinidis†, Michael C. Georgiadis‡*, George Kozanidis § †

Department of Engineering Informatics & Telecommunications, University of Western Macedonia,

Karamanli & Lygeris Street, 50100 Kozani, Greece ‡

Department of Chemical Engineering, Aristotle University of Thessaloniki, University Campus,

54124 Thessaloniki, Greece §

Department of Mechanical Engineering, University of Thessaly, Leoforos Athinon, Pedion Areos,

38334 Bolos, Greece *

Corresponding author email: [email protected] ABSTRACT

Supply chain network (SCN) design and operation is a strategic and adding value process for all synchronous companies. In the face of globalization, several issues should be contemplated and incorporated in decision support systems in order to assist towards effective decision making in this area. Exchange rate risk is one such issue as more and more SCNs are becoming global in order to benefit from cost efficiencies in their inputs and seize upon revenue opportunities for their outputs. This work aims to enrich the SCN design and operation literature by introducing a Mixed-Integer Non M1 ACS Paragon Plus Environment


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Linear Programming (MINLP) model that integrates operational hedging against exchange rate risk within SCN design and operation decisions. By exploiting the properties of the MINLP model it is reformulated into an exact Mixed-Integer Linear Programming (MILP) model that is solved to global optimality. A real case study from a consumer goods company is utilized in order to show model’s functionality and benefit. The model could assist and support SCN managers in effective decision making in the strategic level. KEYWORDS Global supply chains; Exchange rate risk; Supply chain network design; Operational hedging

1. Introduction Globalization has been the dominant trend in business landscape since the latter quarter of the 20th century. Its influence to supply chain network (SCN) management is apparent as nowadays the vast majority of companies source their materials and components from around the globe, operate multiple assembly or manufacturing units geographically dispersed in the world, and market their products worldwide. Companies aim to benefit from global sourcing and manufacturing cost efficiencies and from revenue opportunities in new markets with burgeoning populations and increased purchasing power parity. They are struggling to design and operate value adding SCNs capable of managing complexities and vulnerabilities of globalization and mitigating associated risks. Exchange rate exposure is a major risk that global SCNs face.1 Plants, warehouses, and distribution centers are all facilities whose operation generates expenditures paid in domestic currency. Suppliers are paid for their raw materials in their local currency while customers pay for products in their domestic currency. Since exchange rates fluctuate over time, cash outflows and inflows are changing accordingly and pose great threats to company’s financial and competitive position.

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Operational hedging is a strategy designed to eliminate risk, attributed to exchange rate volatility, through operational means. Its implementation is instrumental in diminishing exchange rate exposure of multinational companies2 and, thereby, in enchasing their market value.3 The basic idea underlying operational hedging is that effective counterbalancing actions in a processing network, such as shifting processing among different types of locations, multiple sourcing, adjusting distribution network, holding safety stocks, and selecting markets to be served, downsize risk.4 For example, a car maker with sales operations in a variety of foreign countries could establish manufacturing plants in the countries where its sales operations are located and also generate more expenses denominated in the currencies of its main markets. The option to proximate production sites with market sites is a pure operational hedging strategy that eliminates exchange rate exposure, as eloquently featured in a real case study of BMW group.5 The challenge of mitigating exchange rate risk in the SCN setting, through operational hedging, has been early underlined in the literature.6, 7 Although the literature on SCN design is vast and populated of several optimization models – stochastic,8-10 multiobjective,11-13 multiechelon,14-16 multiproduct,17 multifunctional,18, 19 – integrating a plethora of aspects essential for decision making, such as redesign issues,20-22 disruptions,23-25 reverse flows,26-28 environmental concerns,29-31 financial management,32-36 inventory theory,37-39 and energy,40-42 just to name a few, the exchange rate risk hedging studies has been limited. Huchzermeier and Cohen43 proposed a stochastic dynamic programming formulation for global manufacturing strategy options under exchange risk in order to evaluate the tradeoffs associated with globalization versus localization. Their hierarchical approach demonstrated that flexibility in a facility network with excess capacity provides options to hedge exchange rate fluctuations in the longer term. Dasu and Li44 studied the optimal operating policies, under exchange rate variability, of a firm operating plants in different countries by developing a two country, single market, stochastic dynamic M3 ACS Paragon Plus Environment


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programming model. Kazaz et al.45 developed a comprehensive approach to an aggregate productionplanning problem, in an actual global manufacturing network, tailored to respond optimally to the change in the information structure until and after the realization of the spot exchange rates. To mitigate the risk of currency exchange, they examined two types of operational hedging: production hedging (i.e., the firm deliberately produces less than the total demand), and allocation hedging (i.e., the firm deliberately decides not to serve certain markets). Goh et al.46 presented a multistage stochastic model for the global SCN problem with profit maximization and risk minimization objectives. Exchange rate uncertainty was one of the considered risks while a solution methodology along with an algorithm, designed by the authors, treat the problem. Yi and Reklaitis47 proposed a mathematical optimization framework in which the material and currency flows of multinational companies were considered simultaneously, whilst focusing on the impact of macroscopic economic factors such as exchange rates and taxes on lot sizing and timing decisions of supply chain operations. The supply chain was modeled as a batch-storage network with recycling streams and the objective function involved minimizing the opportunity costs of annualized capital investments and currency/material inventories minus the benefit to stockholders in the base currency. In a recent work, Singh et al.48 introduced a model for the multistage global SCN problem incorporating a set of risk factors, with one of them being exchange rate risk. Optimal decisions regarding the facility locations and quantity flows between echelons in the global supply chain were based on initial information for the risk factors all of which were modeled as additional costs in the SCN. However, the relevant studies in the SCN design literature that considered exchange rate risk in their modeling frameworks are focused on the optimal deployment of resources or on performance benchmarking between alternative network structures and not on the optimal SCN configuration. Our work aims to fill this void in the literature by introducing a SCN design model that yields the optimal configuration under a variety of exchange rate realizations and integrates operational hedging actions M4 ACS Paragon Plus Environment

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that mitigate exchange rate risk. The proposed model will assist managers in strategic decision making within the supply chain domain. The rest of the paper is structured as follows. Section 2 introduces the problem and presents its mathematical formulation. The applicability of the proposed model is illustrated, through a real case study, in Section 3 followed by concluding remarks, managerial implications and further research directions.

2. Problem definition and mathematical formulation 2.1. Problem statement A SCN with five echelons – suppliers, plants, warehouses, distribution centers, and customer zones – is considered, as shown in Figure 1. Both suppliers and customer zones are in predetermined locations in contrast to plants, warehouses and distribution centers where their location will be selected from a set of potential alternatives. In order to satisfy forecasted product demands of customer zones, plants produce products by purchasing materials from suppliers and utilizing several resources (equipment, utilities, manpower, etc.). These products are transferred to customer zones in a downstream sequential fashion throughout warehouses and distribution centers.



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Currency Zone B

Currency Zone A

Currency Zone D Currency Zone C Currency Zone E Currency Zone F

Suppliers

Plants

Warehouses

Distribution Centers

Customer Zones

Figure 1. The supply chain network considered in this study The design and operation of the SCN generates costs. Establishment of plants, warehouses and distribution centers, contracting with suppliers, purchasing and handling of materials, production and transportation of products, handling and storing of products at warehouses and distribution centers. All plants, warehouses and distribution centers belong in a known currency zone and are considered subsidiaries of the parent company owning the SCN. Through a centralized cash flow management system, monitored by the parent company, all generated costs are assigned to the origin node and settled in local currency of the provider whereas all generated revenues are collected in customers’ local currency. Since there is a time lag between cost generation/settlement and between revenue generation/collection, inflows and outflows of this system are vulnerable to exchange rate fluctuations. We assume a one time period window between generation and settlement/collection. If the spot rate in a future time point exceeds/fails its corresponding current forward rate for a specific currency and the company has a negative/positive net position, inflows minus outflows, in this currency an unfavorable money loss takes place. This is formulated in the form of exposure cost attributed to exchange rate risk. Spot rates express the price quoted for the immediate settlement of a currency whereas forward rates express the price quoted for a currency settled in a future time period. M6 ACS Paragon Plus Environment

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The objective is to minimize the overall design and operational and the foreign exchange exposure cost of the SCN and determine its optimal configuration and operation under uncertainty in product demand and exchange rates. Constraints are applied to suppliers for their minimum/maximum material availability, to plants for their production capacity, material balances, inventories, and availability of production resources, to potential warehouses and distribution centers for their material balances, inventories and product handling capacities, and to minimum/maximum transportation flow of products within the SCN. The SCN decisions to be determined by the proposed model are: (a) the number, location and capacity of plants, warehouses and distribution centers to be established, (b) the number of suppliers to be contracted, (c) the transportation links that need to be established in the network, (d) the number and timing of closing/opening plants, warehouses and distribution centers, (e) the number and timing of cancelling contact with suppliers, (f) the production rates at plants, (g) the flows of materials and products in the network, (h) the unfulfilled demand, (i) the inventory levels at each plant, warehouse and distribution center. At each time period the net position in each currency is evaluated and if it is considered exposed, either net positive position with future spot rates below those of forward rates or net negative position with future spot rates above those of forward rates, the operational hedging process is triggered through shutting down facilities, terminating purchasing contract with suppliers, and leaving a fraction of demand unsatisfied. The two stage modeling framework incorporates uncertainty in product demands and in exchange rates through a scenario tree approach. This includes “here-and-now” decisions implemented at the initial stage of the planning period (see category (a) in previous paragraph) and “wait-and-see” decisions implemented when information pertaining to uncertain parameters in a given period becomes available at the end of the preceding period (see category (b) – (i) in previous paragraph) resulting in each scenario branch breaking into multiple branches at these points. As shown in Figure 2, uncertain M7 ACS Paragon Plus Environment


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[]

[]

[]

parameters are product demand ( ), currency spot rate ( ), and currency forward rate ( ) while at each time period, after the first, there are two outcomes for these parameters expressing an optimistic and a pessimistic condition. The total number of the scenarios (denoted with the superscript [s]) is based on the time periods included in the planning horizon t, the two possible conditions in each time period ξ, and the fact that in the first time period we assume only one possible condition. The total number of scenarios s is determined by the formula . The proposed model handles any one of these

scenarios by multiplying each scenario with its probability to occur ( [] ) where the probability of all

scenarios will add up to one. Parameter values are provided by decision makers as they have the vital data, information, knowledge, and experience of the underline factors influencing and determining how these values will be realized under each situation and in each time period.

Uncertain Parameters (d cilt, srct, cfrct)

s1

s2

s3 Decisions (b)-(i)

s4

Decisions (a) Time Period 1

Time Period 2

Time Period 3

Time

Figure 2. The scenario tree representation

2.2. Mathematical model The SCN design problem described in the previous section is formulated as MINLP model M1 aiming to minimize the total excepted design, operational and exposure cost during a planning horizon taken over all scenario realizations and under a set of structural, operational, and risk mitigating constraints. M8 ACS Paragon Plus Environment

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By exploiting the properties of the MINLP model M1 it is reformulated into an exact MILP model M1 that is solved to global optimality.

2.2.1. Network structure constraints

[]

[]

At each time period an established plant ( ) should be open ( ) or closed ( ). In a similar []

[]

fashion, an established warehouse ( ) should be open ( ) or closed ( ) and an established []

[]

distribution center ( ) should be open ( ) or closed ( ). = + ∀ ∈ , ∈ !, " ∈ #, ∈ $ []

[]

= + ∀ ∈ , % ∈ &, " ∈ #, ∈ $ []

[]

= + ∀ ∈ , ' ∈ (, " ∈ #, ∈ $ []

[]

(1) (2) (3)

When a plant or warehouse or distribution center is established at the end of a time period then all consecutive time periods this plant or warehouse or distribution center should continue to exist. , ≤ ∀ ∈ , ∈ !, " ∈ #

, ≤ ∀ ∈ , % ∈ &, " ∈ # , ≤ ∀ ∈ , ' ∈ (, " ∈ #

(4) (5) (6)

A plant or warehouse or distribution center belonging to a currency zone where operational hedging is possible ( * ) could close only if it has been opened at least one time in a previous time period. Constraints (7) to (9) stress this condition for plants, warehouses, and distribution centers, respectively.

[]

≤ + ∗ ∀ ∈ * , ∈ !, " ∈ #, ∈ $ ∗ -

[]


(7)


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[] []

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≤ + ∗ ∀ ∈ * , % ∈ &, " ∈ #, ∈ $ []

∗ -

(8)

≤ + ∗ ∀ ∈ * , ' ∈ (, " ∈ #, ∈ $ []

∗ -

(9)

Transportation links between consecutive echelons in the SCN are possible only if both the origin node (supplier, plant, warehouse, distribution center) and the destination node (plant, warehouse, distribution center, customer zone) are contracted or open. A transportation link between a supplier and []

[]

a plant (.,/→, ) is possible only if both the supplier is contracted (0/ ) and the plant is open. .,/→, ≤ 0/ ∀ ∈ , 1 ∈ 2, ∈ !, " ∈ #, ∈ $ []

[]

.,/→, ≤ ∀ ∈ , 1 ∈ 2, ∈ !, " ∈ #, ∈ $ []

(10)

[]

(11) []

Similarly, a transportation link between a plant and a warehouse (3,→, ) and between a []

warehouse and distribution center (4,→, ) are possible if both pairs of nodes are open. Constraints (12) to (15) formulate these conditions while constraint (16) states that a transportation link between a []

distribution center and a customer zone (5,→, ) could exist only if distribution center is open. 3,→, ≤ ∀ ∈ , ∈ !, % ∈ &, " ∈ #, ∈ $ []

[]

(12)

[]

[]

(13)

[]

[]

(14)

3,→, ≤ ∀ ∈ , ∈ !, % ∈ &, " ∈ #, ∈ $

4,→, ≤ ∀ ∈ , % ∈ &, ' ∈ (, " ∈ #, ∈ $

4,→, ≤ ∀ ∈ , % ∈ &, ' ∈ (, " ∈ #, ∈ $ []

[]

5,→, ≤ ∀ ∈ , ' ∈ (, 6 ∈ 7, " ∈ #, ∈ $ []

[]


(15) (16)

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2.2.2. Product flow constraints Product flow within each transportation link established in the SCN is restricted to an upper limit that []

the link can afford. Between a plant and a warehouse the quantity of products transferred (8,→, ) is

:; bounded to an upper limit (9, → ) provided that their transportation link exists. In the same vein, the []

quantity of products transferred between a warehouse and a distribution center (8,→, ) and between

:; :; distribution center and a customer zone (8,→, ) cannot exceed 9, → and 9,→ , respectively, and []

provided that their corresponding transportation links are active. :; 8,→, ≤ 9, → 3,→, ∀< ∈ =, ∈ , ∈ !, % ∈ &, " ∈ #, ∈ $ []

[]

:; 8,→, ≤ 9, → 4,→, ∀< ∈ =, ∈ , % ∈ &, ' ∈ (, " ∈ #, ∈ $ []

[]

:; 8,→, ≤ 9, → 5,→, ∀< ∈ =, ∈ , ' ∈ (, 6 ∈ 7, " ∈ #, ∈ $ []

[]

(17) (18) (19)

On the other hand, there is usually a minimum total quantity of products, regardless of type, that is needed to justify the establishment of a transportation link between successive echelons in the SCN. In particular, the total quantity of all products transferred from a plant to a warehouse should exceed a minimum requirement (9> → ) provided that their transportation link is active. In an analogous manner, the total quantity of all products transferred from warehouses to distribution centers and from > > distribution centers to customer zones should be at least 9 → and 9→ , respectively, and provided

that their corresponding transportation links are active. Constraints (17) to (19) express mathematically the upper bounds requirements whereas constraints (20) to (22) those for the lower bounds. + 8,→, ≥ 9> → 3,→, ∀ ∈ , ∈ !, % ∈ &, " ∈ #, ∈ $ ∈?

[]

[]

> + 8,→, ≥ 9 → 4,→, ∀ ∈ , % ∈ &, ' ∈ (, " ∈ #, ∈ $ ∈?

[]

[]


(20)

(21)


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+ 8,→, ≥ 9> → 5,→, ∀ ∈ , ' ∈ (, 6 ∈ 7, " ∈ #, ∈ $ ∈?

[]

[]

(22)

2.2.3. Mass balances constraints Because of the multiperiod nature of our model and the capability of holding inventories in its three intermediate nodes, mass balances are essential and should be expressed in mathematical terms. Along []

those lines, at the end of each time period inventories held in plants (= ) should be equal to the []

previous time period inventories along with the difference between products produced (A ) and []

products transferred to warehouses. In the case of warehouses, inventories held (= ) should be equal to the previous time period inventories along with the difference between products received from plants []

and products send to distribution centers. Similarly, in distribution centers inventories held (= ) should be equal to the previous time period inventories along with the difference between products received from warehouses and products send to distribution centers. Finally, in customer zones the products []

received from all distribution centers equals the corresponding demand ( ), as no inventories are kept. Constraints (23) to (26) express all of the above mass balances. However, constraint (26) will be modified latter in order to encompass an operational hedging option. = = =, + A − + 8,→, ∀< ∈ =, ∈ !, " ∈ #, ∈ $ []

[]

[]

∈C

[]

= = =, + + 8,→, − + 8,→, ∀< ∈ =, % ∈ &, " ∈ #, ∈ $ []

[]

∈D

[]

∈E

[]

= = =, + + 8,→, − + 8,→, ∀< ∈ =, ' ∈ (, " ∈ #, ∈ $ []

[]

∈C

[]

∈F

[]


(23)

(24)

(25)

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+ 8,→, = ∀< ∈ =, ∈ , 6 ∈ 7, " ∈ #, ∈ $

∈E

[]

[]

(26)

2.2.4. Capacity and resource availability constraints Capacities of all intermediate nodes can take values between a minimum and a maximum limit provided that the corresponding node is established. In constraint (27) the capacity of plants (G ) is

between a minimum threshold (H> ) and a maximum limit (H:; ). In the same manner, constraints (28) and (29) bound capacities of warehouses (G ) and distribution centers (G ) between a range.

H> ≤ G ≤ H:; ∀ ∈ , ∈ !, " ∈ #

> :; H ≤ G ≤ H ∀ ∈ , % ∈ &, " ∈ #

H> ≤ G ≤ H:; ∀ ∈ , ' ∈ (, " ∈ #

(27) (28) (29)

However, capacities of nodes should have the space to place all inventories required to operate efficiently the SCN. Driven by this objective, constraints (30) to (32) force capacities to be at least higher than the space occupied by inventories via transforming their quantity to space equivalent. Coefficient I transforms inventory held in plants to capacity occupied, coefficient I transforms

inventory held in warehouses to capacity occupied, and coefficient I transforms inventory held in distribution centers to capacity occupied. G ≥ + I = ∀ ∈ !, " ∈ #, ∈ $ ∈?

[]

G ≥ + I = ∀% ∈ &, " ∈ #, ∈ $ ∈?

[]


(30)

(31)


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G ≥ + I = ∀' ∈ (, " ∈ #, ∈ $ []

∈?

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(32)

:; Production in plants cannot exceed a maximum production capacity (J ) for each product

> whereas a minimum output for each product (J ) is needed in order to economically justify the

operation of the plant. Constraint (33) bounds production capacity between the aforementioned limits provided that the plant is open. Moreover, at each plant production process is realized by utilizing several common production resources (equipment, manpower, utilities, etc.) from several production lines. This share usage is not unlimited but based to the availability of these resources in each plant. :; Constraint (34) express this maximum availability ( K ) condition by transforming production to

resources consumption through coefficient (LK ).

> :; J ≤ A ≤ J ∀< ∈ =, ∈ , ∈ !, " ∈ #, ∈ $ []

:; + LK A ≤ K ∀ ∈ M, ∈ !, " ∈ #, ∈ $ ∈?

[]

(33)

(34)

2.2.5. Inventory constraints In SCNs inventories are an effective medium to handle unpredicted production disturbances and unforeseen demand booms. Safety stocks are acting as an insurance against stockouts and as a mean to increase customer service. Constraints (35) to (37) force inventories in each node of the SCN to be at least more than a percent of total product flow distributed to all consecutive nodes. Particularly, constraint (35) formulates safety stock requirement at each plant by utilizing a safety stock coefficient (N ) while constraints (36) and (37) employ N and N in order to express safety stock requirements in warehouses and distribution centers, respectively.


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= ≥ N + 8,→, ∀< ∈ =, ∈ !, " ∈ #, ∈ $ []

∈C

[]

(35)

= ≥ N + 8,→, ∀< ∈ =, % ∈ &, " ∈ #, ∈ $ []

∈E

[]

(36)

= ≥ N + 8,→, ∀< ∈ =, ' ∈ (, " ∈ #, ∈ $ []

∈F

[]

2.2.6. Supply constraints

(37)

[]

At each plant, materials purchased from suppliers ($>,/→, ) should be enough in order to produce

> products and also these purchases should be bounded between a minimum quantity ( >/ ) that justifies

:; contracting and a maximum quantity ( >/ ) afforded by the connection link. Constraint (38) utilizes a

coefficient that relates materials to products (P> ) and formulates material purchases to be sufficient for production output while constraint (39) forces purchases to be between the aforementioned range provided that the corresponding transportation link is active. + P> A = + $>,/→, ∀R ∈ S, ∈ !, " ∈ #, ∈ $ ∈?

[]

/∈Q

[]

> :; >/ .,/→, ≤ $>,/→, ≤ >/ .,/→, ∀R ∈ S, ∈ , 1 ∈ 2, ∈ !, " ∈ #, ∈ $ []

[]

[]

(38)

(39)

2.2.7. Currency flow constraints The parent company owning the SCN has currency outflows directed to all its subsidiaries nodes (plants, warehouses, distribution centers) in order to settle all generated costs. On the other hand, currency inflows are derived from customer zones for sold products and also from opening /closing of nodes. When a node is closing the company has a currency inflow from several activities, such as property leasing, selling of carbon emission rights, termination of contracts for equipment maintenance M15 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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and workforce training, etc. In contrast, when a node opens all aforementioned activities decreasing currency inflows. Constraint (40) formulates currency inflows in each currency zone, where operational hedging is possible, as a result of four terms. The first term is the revenues generated from sales and is the product of price (1 ) and quantity send to customer zones. The second term increases/decreases currency inflows by TU when a plant was open/closed and closes/opens. In the same way, the third TU term increases/decreases currency inflows by when a warehouse was open/closed and

TU closes/opens. Finally the last term, increases/decreases currency inflows by when a distribution

center was open/closed and closes/opens. TU V,/→ $>,/→, []

∈D

/∈Q

[]

[]

>∈a /∈Q ∈D

_` \^ ?a + + + > + $>,/→, + + + A + + + WW= + =, X⁄2X >∈a ∈D

/∈Q

[]

∈? ∈D

[]

[]

∈? ∈D

[]

[^ YZ + + + + , → 8,→, + + e − , f ∈? ∈D ∈C

[]

∈C

_` ?a + + + + 8,→, + + + WW= + =, X⁄2X ∈? ∈C

∈D

[]

∈? ∈C

[]

[]

(41)

[^ YZ + + + + , → 8,→, + + e − , f ∈? ∈C ∈E

[]

∈E

_` ?a + + + + 8,→, + + + WW= + =, X⁄2X ∈? ∈E

∈C

[]

∈? ∈E

[]

[]

[^ * + + + + , → 8,→, ∀ ∈ , " ∈ #, ∈ $ ∈? ∈E ∈F

[]

YZ In warehouses the costs charged are fixed cost of warehouse establishment ( ), periodic cost

_` ?a of handling products ( ), periodic inventory cost ( ), and periodic cost of transportation

[^ (, → ). In distribution centers the costs charged are fixed cost of distribution center establishment

_` ?a YZ ( ), periodic cost of handling products ( ), periodic inventory cost ( ), and periodic cost of

[^ transportation (, → ). A more detailed explanation of these cost elements will be presented in Section

3.2.10 as they are included in the objective function.

2.2.8. Exchange rate exposure constraints Inflows and outflows are exposed to exchange rate fluctuations since there is a one time period window between revenue generation/collection and between cost generation/settlement. In particular, when in a specific time period the spot rate exceeds current forward rate and in the previous time period the net position in a currency is negative (inflows are less than outflows) then the net negative position is exposed. On the other, when in a specific time period the spot rate is below current forward rate and in M17 ACS Paragon Plus Environment


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Page 18 of 39

the previous time period the net position in a currency is positive (inflows are more than outflows) then the net positive position is exposed. For each currency, where operational hedging is possible, constraints (42) and (43) activate the binary variable .ijk only if the spot rate ( ) exceeds []

[]

current forward rate ( ) whereas constraints (44) and (45) activate the binary variable .ij []

[]

only if we have a negative net position in the previous time period. Finally, constraints (46) and (47) assure that the binary variable expressing whether we have an exposed net negative currency position []

(.ij ) is activated only if both previous mentioned binary variables are active. l l

[]

[]

[]

[]

o .ijk ∀ ∈ * , " ∈ #, ∈ $ − 1n ≤ &

(42)

o W.ijk − 1X ∀ ∈ * , " ∈ #, ∈ $ − 1n ≥ &

(43)

[]

[]

[] [] * o .ij [] V }~>

u

YZ \^ [^ + + e − , f + + + A + + + + , → 8,→, xyyyyyyyzyyyyyyy{ xyyyzyyy{ ∈E ∈? ∈D ∈? ∈D ∈C xyyyyyyyzyyyyyyy{ }K> ~>~K }~>

[]

[]

K:>|K:> :K~} |:>

|K}>

[^ [^ _` + + + + , → 8,→, + + + + ,→ 8,→, + + + > + $>,/→, xyyyyyyyyzyyyyyyyy{ xyyyyyyyzyyyyyyy{ ∈? ∈C ∈E ∈? ∈E ∈F >∈a ∈D /∈Q xyyyyyyzyyyyyy{ []

[]

K:>|K:> :K~} :K~~

K:>|K:> :K~} }K> ~>~K

:>}> :K~} |:>

_` _` + + + + 8,→, + + + + 8,→, xyyyyyyyzyyyyyyy{ ∈? ∈C ∈D yyyy{ ∈? ∈E ∈C xyy yyyyyzyyy []

[]

[]

:>}> :K~} }K> ~>~K

:>}> :K~} :K~~

[] [] [] [] ?a ?a + + + WW= + =, X⁄2X + + + WW= + =, X⁄2X xyyyyyyyyyyzyyyyyyyyyy{ ∈? ∈D ∈? ∈C xyyyyyyyyzyyyyyyyy{ >/~>K :K~} :K~~

>/~>K :K~} |:>

[] [] [] \]^ ?a T[ [] + + + WW= + =, X⁄2X + + / 0/ + + + + >,/→ $>,/→, xyyyyyyyyyzyyyyyyyyy{ xyyzyy{ ∈? ∈E >∈a /∈Q ∈D /∈Q xyyyyyyyzyyyyyyy{ >/~>K :K~} }K> ~>~K

>K:>

|K:>

+ + + + [] − V

H:; H> :; H > H _` > ?a

minimum capacity of plant j

maximum capacity of distribution center k minimum capacity of distribution center k maximum capacity of warehouse m minimum capacity of warehouse m unit handling cost of material n at plant j that belongs to currency zone c unit inventory cost of product i at plant j that belongs to currency zone c M33 ACS Paragon Plus Environment


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\^

[^ , →

_` ?a [^ , →

_` ?a [^ , → YZ

YZ YZ \]^ >,/→

T[ /

[]

[]

TU TU TU

:; J > J

:; 9, →

:; 9, →

:; 9, →

9> → 9> →

> 9 → :;

K

:; >/ > >/

Page 34 of 39

unit production cost of product i at plant j that belongs to currency zone c unit transportation cost of product i transferred from plant j that belongs to currency zone c to warehouse m unit handling cost of product i at distribution center k that belongs to currency zone c unit inventory cost of product i at distribution center k that belongs to currency zone c unit transportation cost of product i transferred from distribution center k that belongs to currency zone c to customer zone l unit handling cost of product i at warehouse m that belongs to currency zone c unit inventory cost of product i at warehouse m that belongs to currency zone c unit transportation cost of product i transferred from warehouse m that belongs to currency zone c to distribution center k fixed cost of establishing plant j that belongs to currency zone c fixed cost of establishing distribution center k that belongs to currency zone c fixed cost of establishing warehouse m that belongs to currency zone c unit purchasing cost of material n from supplier v that belongs to currency zone c transferred to plant j fixed cost of contracting supplier v that belongs to currency zone c current forward rate of each currency c contract settled at the end of time period t under scenario s demand for product i from customer zone l that belongs to currency zone c during time period t under scenario s flow related to closing/opening warehouse m that belongs to currency zone c flow related to closing/opening distribution center k that belongs to currency zone c flow related to closing/opening plant j that belongs to currency zone c maximum production capacity of plant j for product i during time period t minimum production capacity of plant j for product i during time period t maximum quantity of product i that can be transferred from plant j to warehouse m maximum quantity of product i that can be transferred from distribution center k to customer zone l maximum quantity of product i that can be transferred from warehouse m to distribution center k minimum total quantity of products that can be transferred from plant j to warehouse m minimum total quantity of products that can be transferred from distribution center k to customer zone l minimum total quantity of products that can be transferred from warehouse m to distribution center k total rate of availability of resource r at plant j maximum availability of material n by supplier v during time period t minimum availability of material n by supplier v during time period t M34 ACS Paragon Plus Environment

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:; d []

spot rate of currency c during time period t under scenario s maximum unsatisfied demand for product i from customer zone l that belongs to currency zone c during time period t under scenario s price of product i sold in customer zone l that belongs to currency zone c coefficient relating capacity of plant j to inventory of product i held

1 I

I I N

coefficient relating capacity of distribution center k to inventory of product i held coefficient relating capacity of warehouse m to inventory of product i held safety stock coefficient for product i held in plant j

N N LK

safety stock coefficient for product i held in distribution center k safety stock coefficient for product i held in warehouse m coefficient of rate of utilization resource r in plant j to produce product i

P>

coefficient relating material n required to produce product i in plant j

o &

[]

coefficient expressing the occurrence probability of scenario s a sufficient large positive number

Continuous variables (denoted with capital letters)

G$_

Integrating Operational Hedging of Exchange Rate ... - ACS Publications

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