Regulatory Factors and Capacity-Expansion Planning in Global

3364

Ind. Eng. Chem. Res. 2004, 43, 3364-3380

Regulatory Factors and Capacity-Expansion Planning in Global Chemical Supply Chains Hong-Choon Oh† and I. A. Karimi*,‡ The Logistics Institute-Asia Pacific and Department of Chemical & Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260

Capacity-expansion planning is a class of strategic supply-chain problems that has received extensive attention from both chemical engineering and operations research communities since the late 1950s. Nevertheless, to the best of our knowledge, no previous work has so far addressed these problems on a global scale while accounting for the effect of multiple key regulatory factors. This paper fills this gap in the capacity-planning research using a four-prong approach. First, it introduces and classifies key regulatory factors that can significantly influence the earnings or business operations of multinational companies. Second, it presents a new deterministic capacity-expansion-planning model in which sizes of expansions or new facilities are variables and domestic and international regulatory factors are explicitly taken into account. Third, it extends the deterministic model to address important issues such as distribution centers, outsourcing, and uncertainty in problem parameters. Last, it demonstrates the importance and effect of incorporating multiple regulatory factors in capacity-expansion-planning models using illustrative examples. 1. Introduction Manufacturing in the chemical process industry (CPI) often involves high temperatures, high pressures, and corrosive chemicals. It requires a high degree of automation and control to ensure product quality and safe operations. Most chemical plants have large production capacities to attain the necessary economies of scales. Clearly, it is not surprising that the CPI is a highly capital-intensive industry. Several major chemical companies spend more than $500 million (U.S.) annually on capital expenditures, and many oil companies spend in excess of $1 billion (U.S.). The huge capital investments in the CPI make sound and effective planning of capacity expansions extremely crucial for the continued success of chemical companies. Capacity-expansion planning involves a strategic planning of timings, locations, and sizes of future capacity expansions with decisions such as when and which existing facilities should be shutdown; when, where, and of what capacities new facilities should be constructed; or when, which, and by how much existing facilities should be expanded. Companies normally make these decisions on the basis of forecasts of the demands, prices, and availabilities of raw materials and the technology obsolescence of final products. Clearly, the quality of these strategic decisions depends on (1) the accuracy of the forecasts and (2) the effectiveness of the planning techniques that assist the business decisionmaking processes. Most chemical and manufacturing companies are global. The current competitive and dynamic environment in which companies across the globe are merging and streamlining their resources also accentuates the global nature of their businesses. * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: +65-6874-2186. Fax: +65-6779-1936). † The Logistics Institute-Asia Pacific. ‡ Department of Chemical & Biomolecular Engineering.

Clearly, this makes it imperative for companies to adopt a global perspective on the expansion decisions, i.e., consider all potential sites across the globe and take regulatory factors into account. Over the years, various nations across the globe have signed a variety of multilateral and bilateral trade agreements to facilitate and promote commerce. Some examples of such agreements are the North American Free Trade Agreement (NAFTA), Central European Trade Agreement (CETA), United States-Singapore Free Trade Agreement (USSFTA), etc. Although these trade agreements presumably attempt to create a level playing field for the global business operators, the opposing forces of protectionism and trade disagreements inevitably persist to ensure a heterogeneous network of trade barriers around the globe. Examples of such protectionist measures include the import quota imposed by the U.S. on Chinese textile imports to protect the U.S. textile industry, the refusal of China to revalue its currency (renminbi) to protect the competitiveness of its local exporters, etc. In addition to the several international trade disputes, the recent collapse of the World Trade Organization talk at Cancun, Mexico (2003), is a testimony to the divisions among the nations on regulating world trade. Hence, global business operators, including major chemical companies, must contend with the hard reality of multiple regulatory factors that can influence their economic performance greatly. In this paper, we define regulatory factors as the legislative instruments that a government agency imposes on the ownership, imports, exports, accounts, and earnings of business operators within its jurisdiction. Table 1 presents a glossary of some common regulatory factors such as import tariffs (or duties), corporate taxes, duty drawbacks, offset requirements, quantitative import restrictions, etc. The primary goals of these factors are to boost a country’s coffers or protect the interests of local businesses. The regulatory factors vary from

10.1021/ie034339g CCC: $27.50 © 2004 American Chemical Society Published on Web 05/28/2004

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3365 Table 1. Glossary of Key Regulatory Factors factor

description

remarks and/or examples

corporate tax

tax imposed by the local revenue authority on the chargeable income of a locally registered company

varies from country to country (Ireland 12.5%, Italy 38.25%, Switzerland 24.1%, etc.)

duty drawback

refund of import duty, when one exports a good with changed or unchanged conditions after having imported it or its components

three main types: (1) rejected merchandise drawback, (2) unused merchandise drawback, and (3) manufacture drawback

duty relief

refund of import duty, when one imports a good that is manufactured using locally produced materials

all European Union countries have this custom incentive

import duty

tax imposed by the local custom authority on dutiable goods imported into a country

varies between countries and depends on the country of origin of the imported goods

local content

minimum percentage (in dollar value) of the components of a finished product, which must be made in the host country where the manufacturing plant is located

Philippines requires manufacturers in the auto industry to source 40% of the raw materials from domestic suppliers

offset requirement

minimum value of goods and services that must be expended in a country in exchange for the sale of products in the same country

Australia requires 70%

quantitative import restriction

restrictions on the quantities of products imported into a country

Canada imposes a quota of 76,409 tonnes on its import of beef and veal. Beyond this limit, it imposes an import tariff of 26.5%

country to country, and we classify them into two types: domestic and international. In Table 1, local content rule and corporate taxes are domestic regulatory factors, whereas the others are international. The former govern business operations and trade activities within a country, whereas the latter regulate the transnational movement of goods and funds across international boundaries. The former are a characteristic of a single country alone, whereas the latter depend on the two countries involved in a business transaction. Because of the variety and complexity of bilateral and multilateral international trade factors and domestic regulatory factors, it is natural that an expansion decision that ignores these factors or fails to account for their effects correctly would be misplaced or misguided. Although the research on capacity-expansion problems (CEPs) dates as far back as 1959, surprisingly, no model exists to date that incorporates both domestic and international regulatory factors simultaneously and explicitly. This paper aims to highlight the critical role of the regulatory factors in capacity-expansion planning and presents a deterministic capacity-expansion problem (DCEP) model that addresses the two simplest and probably most important regulatory factors, namely, import tariffs (an international regulatory factor) and corporate taxes (a domestic regulatory factor). Furthermore, the proposed DCEP model distinguishes itself from previous work not only by allowing variable-size capacity expansions and new constructions, but also by accounting for two domestic and international regulatory factors. The deterministic model also provides an effective basis for handling uncertainty in problem parameters. Finally, this paper demonstrates the importance of accommodating regulatory factors when addressing CEPs. In what follows, we first extensively review the existing work on capacity-expansion planning to highlight the scarcity of literature considering regulatory factors. We then describe a DCEP that accounts for import tariffs and corporate taxes and present a mixedinteger linear programming (MILP) formulation for its solution. Subsequently, we demonstrate with an illustrative example the vital need for incorporating these regulatory factors in capacity-expansion decisions. We then also describe how the deterministic model can be

modified to handle three extensions of the basic CEP before we illustrate again the importance of including regulatory factors in capacity-expansion decisions with a stochastic example. 2. Previous Work So far, the literature on the manufacturing industry in general and the CPI in particular has addressed two types of capacity-expansion-planning problems, namely, deterministic and stochastic. Deterministic problems assume fixed parameters over a given planning horizon, whereas stochastic problems allow uncertainty in some parameters. The work on capacity-expansion planning began in the late 1950s. Since then, many researchers have addressed this topic. Wagner and Whitin1 presented a forward algorithm for the DCEP. In a later work, Veinott and Wagner2 demonstrated how to solve an important class of DCEPs as an ordinary or reduced transshipment problem. For this class, Veinott and Wagner3 also proposed a special algorithm that is more efficient than the linear programming algorithm. Barchi et al.4 formulated an integer programming model to represent a DCEP that involves the determination of both production and expansion plans with no backordering over given horizons. Hiller and Shapiro5 introduced a mixed-integer linear programming (MILP) model to represent a DCEP with learning effects. These learning effects include the reduction in unit manufacturing costs with cumulative production figures, as well as the decrease in market prices of the finished products over time. Sahinidis et al.6 presented a multiperiod model to address the DCEP in the CPI. The model determines new processes, expansion plans, and shutdown policies to maximize the net present value of a project given the forecasts of prices and demands of the chemicals over a long planning horizon. In a follow-up work, Sahinidis and Grossmann7 developed two reformulations for the same DCEP that allow much faster solutions than the original model. Li and Tirupati8 addressed a DCEP that includes technology types (flexible versus dedicated facilities) as decision variables. Such problems abound in industries such as steel and consumer electronics, where the tradeoff between adding expensive flexible

3366 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004

facilities and relatively cheaper dedicated facilities is crucial in capacity-expansion planning. Lee et al.9 developed a mixed-integer nonlinear programming model (MINLP) that integrates the DCEP with production and distribution considerations. They made the MINLP model convex by using an exponential transformation for the variables to eliminate the bilinear terms and used the outer approximation (OA) algorithm for its solution. Papageorgiou et al.10 reported a multiperiod MILP model for managing product portfolios in the pharmaceutical industry. Their model addresses product development and introduction along with deterministic capacity planning. Although they do account for the effect of corporate tax in their model, their capacity planning assumes prespecified sizes and costs for every possible expansion or new facility construction. Manne11 pioneered the work on the stochastic CEPs (SCEPs) by planning the future expansions of a single facility in anticipation of a growth in demand. In a later work, Giglio12 extended the single-facility problem of Manne11 to include realistic industrial situations in which the stochastic demand is a function of time and the facility has a stochastic life span. Leondes and Nandi13 presented a model for a SCEP that involves multiple plants with multiple demand locations and allows uncertain demands. Paraskevopoulos et al.14 introduced a sensitivity approach to address the uncertainty in single-facility expansion problems. Liu and Sahinidis15 presented a two-stage stochastic MILP model for a multiprocess CEP. They allowed a finite number of possible scenarios of prices (of raw materials and finished products), raw material availabilities, and finished product demands. They proposed a solution algorithm based on Bender’s decomposition and Monte Carlo sampling. Maravelias and Grossmann16 addressed the scheduling of regulatory tests for new products simultaneously with production and capacity-expansion planning of batch plants. They proposed a two-stage stochastic optimization approach to handle uncertainty in the outcomes of regulatory tests and developed an iterative heuristic based on the Lagrangian decomposition for solving the resulting large-scale MILP models. We see from the above discussion that, barring one work10 that incorporates corporate taxes, no attempt has been made so far to consider the effects of other regulatory factors, especially international ones such as import tariffs, in CEPs. However, the same is not true for other classes of supply-chain problems such as location-allocation problems (LAPs) and productiondistribution problems (PDPs). LAPs involve the selection of new facility locations and the allocation of production from different plants to various demand locations. We treat them as different from the CEPs, because they do not explicitly plan for capacity expansion at the facilities. PDPs entail the determination of production schedules for manufacturing plants and distribution plans for products across the entire value chain from suppliers, production plants, and distribution centers to customers. Cohen et al.,17 Arntzen et al.,18 and Goetschalckx et al.19 all included some of the regulatory factors in their PDPs. Cohen et al.17 reported a normative model framework to maximize the after-tax profit of an entire global firm in the presence an uncertain currency exchange rate. They included corporate taxes, tariffs, and local content rules. Arntzen et al.18 introduced a comprehensive MILP model that integrated import

Figure 1. Schematic for the motivating example. Total demands for the finished product are 1000, 1500, and 1500 units for years 0, 1, and 2, respectively. Table 2. Data for the Simple Motivating Example data

P1

P2

production cost ($/unit) raw material transportation cost for ($/unit) raw material price ($/unit) finished product price ($/unit) expansion cost ($) annual interest rate (%) corporate tax (%) import duty (%)

1.5 0.1 0.2 30 50 6 45 20

1.7 0.1 0.2 30 50 6 15 25

tariffs, duty drawbacks, duty relief, local content rules, and offset requirements to represent a PDP for a multinational corporation. Goetschalckx et al.19 addressed a simultaneous LAP-PDP for a group of enterprises with the objective of maximizing the total after-tax profit in the presence of import tariffs. From the above discussion, we conclude that the existing models and methodologies for CEPs are useful only in a local (national) context and are not appropriate for expansion planning with substantial transnational movements of goods and merchandise. The failure to incorporate key regulatory factors into capacity-expansion planning has virtually prevented its application in practice. Therefore, it is crucial to account for all relevant regulatory factors in the strategic planning activities of any business. An optimal solution to a CEP with a local focus will generally not be optimal when one integrates several regulatory factors into the CEP. We now consider a small and simple example to illustrate the effect of regulatory factors on the solution of a DCEP. 3. Simple Motivating Example A multinational company (MNC) owns two manufacturing plants (P1 and P2), one each in two different countries (Figure 1). These plants purchase their raw materials from the same supplier and ship their finished products directly to customers. One unit of finished product requires one unit of raw material. At present, both plants have a finished product capacity of 500 units per year. The MNC’s sales department expects the total product demand to increase from 1000 units per year this year to 1500 units per year next year. Assuming that the MNC wishes to consider capacity expansion at only one of the two plants, which plant (P1 or P2) should it expand? Using the data in Table 2, a capacity expansion of 500 units per year at P1 will lead to a net present value (NPV) of $53,784 for the MNC’s total before-tax profit (sales less expenses) for the next two years, whereas the same at P2 will lead to an NPV of $53,601. Thus, if

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3367

one ignores corporate taxes, P1 seems to be the better expansion site. However, if one considers corporate taxes and import tariffs, the corresponding NPVs for the after-tax profits are $33,750 and $34,019 for the expansions at P1 and P2, respectively. This suggests that P2 instead of P1 is the preferred expansion site. Clearly, the former decision that ignores corporate taxes and import duties is misguided and leads to a suboptimal solution. In this small and imaginary example, the numbers might be considered marginally different, but when one considers large plant capacities and millions of dollars of capital expenditure, the effect of ignoring the regulatory factors can be huge. 4. Problem Statement An MNC owns or can potentially build in future a set, IF, of processing facilities (f ∈ IF) in countries across the globe. We divide the facilities into two groups: EIF is the set of existing facilities, and FIF is the set of future (new) facilities such that IF ) EIF ∪ FIF. These internal facilities of the MNC either manufacture useful products from some raw materials (or wastes) or simply treat wastes without producing any useful products. In addition to interacting with each other in terms of receiving/supplying materials from/to each other, they (f ∈ IF) also interact with another set, EF, of external facilities (f ∈ EF) that do not belong (or are external) to the MNC. We define F ) IF ∪ EF and assume that the location and incoming and outgoing materials for each facility f ∈ F (whether existing or future, internal or external) are predetermined and known. Multiple facilities might exist at the same location or plant site. For instance, an existing plant site currently produces B and C from A and E from C and D. The site has sufficient space to build two more processes: one to produce G from C and F and the other to produce J from H. Thus, we model this plant site as four separate facilities (f ) 1-4) as follows

(f ) 1)

AfB+C

(f ) 2)

C+DfE

(f ) 3)

C+FfG

(f ) 4)

HfI

Facilities 1 and 2 exist now, whereas 3 and 4 are new facilities that the company might or might not build. For each facility f ∈ F, we group the associated materials (raw materials, products, byproducts, wastes, etc.) into two sets. IMf denotes the set of incoming materials mi (i ∈ IMf) consumed by facility f, and OMf denoting the set of outgoing materials mi (i ∈ OMf) produced by facility f. Note that we include only the materials that are relevant in terms of interaction among the facilities. For instance, suppose that an external facility f produces C and D from A and B. However, the MNC neither currently supplies or considers supplying at any time A or B to facility f nor currently needs or considers needing at any time D from facility f at any of its internal facilities. Thus, we simply set IMf as a null set and OMf ) {C}. Similarly, IMf for an internal facility f might not include products (e.g., waste products) that are inconsequential, unless we also treat the waste disposal site as a separate facility by itself. Finally, for each internal facility f (f ∈ IF), we designate one material π(f) as the primary material and

define the current production capacity (Qf0) of facility f as the rate (ton per fiscal year) at which facility f uses or produces π(f) at time zero. Note that π(f) can be an either incoming or outgoing material and that all future internal facilities (f ∈ FIF) have Qf0 ) 0. Considering a global problem, we let all facilities be located in N different nations (n ) 1, 2, ..., N) and define Fn as the set of facilities situated in nation n (f ∈ Fn, F1 ∪ F2 ∪ ... ∪ FN ) F, and Fn ∩ Fn′ ) null set for n * n′). The legislation of a host country n normally imposes several restrictions on the ownership, imports, exports, accounts, earnings, etc., of the facilities located in its jurisdiction (f ∈ Fn). The internal facilities of each country n (f ∈ IF ∩ Fn) pay corporate and other taxes collectively to the country’s revenue authorities at the end of each fiscal year. Using the sales forecast from the marketing division, the multinational company wishes to develop an optimum, strategic, and global capacity-expansion plan over a planning horizon of T fiscal years or periods (t ) 1, 2, ..., T). The objective of this plan is to maximize the net present value (NPV) of the company’s net cash flows over the planning horizon. The desired expansion plan must determine: (a) the time, location, and amount of capacity expansion of each facility f ∈ IF and (b) the actual flows of all materials to and from each facility f ∈ F during each year or period t. We make the following assumptions for the above DCEP: 1. All business intelligence data that are crucial for generating a reliable capacity-expansion plan are available. These include the forecasts for product demands, raw material requirements, raw material prices, product prices, transportation costs, operating costs, fixed and variable capacity-expansion costs, capacity-expansion limits, annual interest rates, import duties, and corporate taxes of all internal manufacturing facilities, as well as the capacities of all external supplier facilities over the T periods (fiscal years). 2. The fluctuations in currency exchange rates over the T periods are already accounted for in the business intelligence data. Hence, we express all expenditures and returns in terms of a numeraire currency. 3. Expansion-related construction activities do not affect the available production capacity of any internal facility f at any time. 4. All activities related to capacity expansion or new plant construction at any facility f ∈ IF require δ(f) periods before the expanded or new capacity becomes available. For instance, if δ(f) ) 3 and the capacity expansion or new construction begins at the start of t ) 1, then the expanded or new capacity is available only during and after t ) 4. 5. An expansion or new construction cannot begin while a preceding expansion or construction is underway. In other words, if δ(f) ) 3 and an expansion or construction begins at t ) 1, then another expansion or construction cannot begin until after the end of t ) 3. 6. The fixed costs for the expansion of an existing facility and for the construction of a new facility are different, but their linear variable costs are the same. 7. No inventory is carried forward from one period to the next at any internal facility f. This is reasonable, given that the length (one year) of each period in the planning horizon is sufficiently long. 8. Every internal facility f is liable for the tariffs on all of its imports from facilities that are outside its own


country. The import tariff is levied on the basis of the CIF20 costs (cost, insurance, and freight) of imports at facility f. This refers to the total value of goods including the purchase, insurance, and freight costs incurred in bringing the goods to the delivery facility. 9. The mass balance for each internal facility f is given by

∑ σifmi ) i∈OM ∑ σifmi

i∈IMf

f ∈ IF

f

where mi denotes material i that facility f consumes or produces and σif is analogous to the stoichiometric coefficient of a species i in a reaction except that the above balance is in terms of mass (tons) rather than moles. For example, if a facility f consumes 2 kg of A and 1 kg of B to produce 1.8 kg of C and 1.2 kg of D, then σAf ) 2, σBf ) 1, σCf ) 1.8, and σDf ) 1.2. This facility could have any of A, B, C, and D as the designated primary material. 10. For both the expansion of an internal existing facility and the construction of a new internal facility, depreciation is computed using the same formula. 11. Each internal facility has a constant lower limit on its production rate over the entire planning horizon. Thus, a facility, once it exists, must operate at or above that rate and cannot be hut down. 12. Products are shipped directly from the internal facilities to the customers, and the latter bear the costs of materials, insurance, freight, and import duties. We now present a formulation for the above-stated DCEP. Unless stated otherwise, the indexes (f, t, i, etc.) assume their full ranges of values. 5. Problem Formulation The major task in developing the expansion plan is to decide the times, locations, and amounts of capacity expansion of each internal facility. To model these decisions, we define qft as the amount (tons) by which the capacity of facility f ∈ IF increases during period t and introduce the following two binary variables and a simplifying notation yft )

{

1 if the capacity of a facility f expands during period t 0 otherwise

}

f ∈ IF zft )

{

1 if a future facility f begins construction during t 0 otherwise

}

f ∈ FIF ξft )

{

zft if f ∈ FIF 0 otherwise

}

f ∈ IF

Assumption 4 tells us that there is no incentive to begin an expansion or new construction near the end of the horizon. Thus, yft ) 0 for f ∈ IF and t > T - δ(f), and zft ) 0 for f ∈ FIF and t > T - δ(f). Similarly, a future internal facility f ∈ FIF cannot start an expansion during the first δ(f) periods, because it must be built first, so yft ) 0 for f ∈ FIF and t e δ(f). Now, the MNC cannot build a future facility f ∈ FIF more than once during the planning horizon, so we have

zf1 + zf2 + zf3 + ... + zf[T-δ(f)] e 1

f ∈ FIF

(1)

Similarly, it cannot expand the capacity of a future facility f ∈ FIF until it has built it. Therefore, we have

yft e zf1 + zf2 + zf3 + ... + zf[t-δ(f)] f ∈ FIF, δ(f) < t e T - δ(f) (2) Assumption 5 tells us that, if the MNC begins expanding an existing facility f ∈ EIF during a period t, or if it begins constructing or expanding a future internal facility f ∈ FIF during a period t, then it cannot begin another expansion during the δ(f) periods including and after period t. This constraint gives

yft + ξft + yf(t+1) + ... + yf[t+δ(f)-1] e 1 f ∈ IF, t e T - δ(f) (3) If the MNC does not begin expanding a facility f ∈ IF during a period t, then the amount of expansion (qft) must be 0. Therefore, we have

qft e yft(QU f - Qf0)

f ∈ IF

(4a)

where QU f is the maximum capacity that facility f ∈ IF can possibly have. Similarly, if an expansion or new construction occurs at facility f ∈ IF, then the capacity must expand by at least some lower limit, i.e.

qft g yftqLf + ξftQLf f ∈ IF

(4b)

where qLf is the minimum incremental expansion allowed at facility f ∈ IF and QLf is the minimum capacity of a new construction at facility f ∈ FIF. Using eqs 4a,b, we write

qft ) yftqLf + ξftQLf + ∆qft

f ∈ IF

L U L ∆qft e yft(QU f - Qf0 - qf ) + ξft(Qf - Qf ) f ∈ IF

(5)

Qft ) Qf(t-1) + yf[t-δ(f)]qLf + ξf[t-δ(f)]QLf + ∆qf[t-δ(f)] f ∈ IF (6) where Qft is the capacity of facility f ∈ IF during period t with an upper limit of QU f . The lower and upper limits on the capacities are in line with industrial practice and are based on economic analysis and space availability. To model the incoming and outgoing flows of materials for the facilities, we let Fisct denote the quantity of material i that facility s ∈ F sells to facility c ∈ F during period t, where s * c. Note that Fisct is a nonnegative variable that exists only for i ∈ OMs ∩ IMc. Because inventory does not carry over from one period to the next, the material amounts consumed (produced) must match the incoming (outgoing) material flows. Therefore, if xift and Xft, respectively, denote the actual consumption/production levels (tons/year) of materials mi and π(f) at an internal facility f ∈ IF during period t, then we must have

σπ(f)fxift ) σifXft σif Xft ) σπ(f)f(

f ∈ IF, i ∈ OMf ∪ IMf

∑

c3i∈IMc

Fifct +

∑

Fisft)

(7)

s3i∈OMs

f ∈ IF, i ∈ OMf ∪ IMf Note that only one of the two sums in the above equation


can be nonzero, as we do not allow any facility f to send and receive the same material during any period t. Furthermore, a facility f ∈ IF cannot process more than its capacity, so using eq 6, we have

f ∈ IF

Xft e Qft

(8)

Conversely, each facility f ∈ IF must respect a lower limit on its production rate t-δ(f)

Xft g XLf (φf +

∑ zfτ)

f ∈ IF

(9)

τ)1

where φf ) 1 for f ∈ EIF and 0 for f ∈ FIF. For each external facility f ∈ EF, we define Dift (i ∈ IMf) as the maximum quantity of material i that f can accept during period t and Sift (i ∈ OMf) as the maximum amount of i that f can supply during period t. Clearly, DiftSift ) 0, as we forbid simultaneous receipt and supply of the same material by any facility f. To ensure that delivery does not exceed demand and that supply does not exceed capacity, we use

∑

Fifgt +

f∈IF3i∈OMf

∑

Figft e Digt + Sigt

f∈IF3i∈IMf

g ∈ EF, i ∈ OMg ∪ IMg (10) Again, note that only one of the two terms on each side can exist in the above constraint. Whether it is an expansion or new construction, the MNC will need to do some capital expenditure. Let CEt and CBt denote the MNC’s actual capital expenditure and allotted capital budget, respectively, for period t; then, we have

CEt )

∑ [aftyft +

bft(yftqLf

+

ξftQLf

Figure 2. Material flows among the facilities in the illustrative example.

∈ F to customer c ∈ F during period t. Then, the gross income GIft of facility f ∈ IF is

GIft ) -MCftXft +

where aft is the fixed cost of expansion of an existing facility f ∈ EIF during period t, cft is the fixed cost of construction of a new facility f ∈ FIF during period t, and bft is the variable cost of expansion or new construction at an internal facility f ∈ IF during period t. Using the previous equation, we ensure that the cumulative capital expenditure does not exceed the cumulative allotted budget, i.e.

[afτyfτ + cfτξfτ + bfτ(yfτqLf + ξfτQLf + ∆qfτ)] e ∑ ∑ τet f∈IF CBτ ∑ τet

(11)

Now, to compute the MNC’s collective corporate taxes during each period t in each host nation n, we need the taxable incomes of the MNC’s facilities in that nation n. The taxable income is the gross income minus the depreciation, and the gross income is the sales minus the operating expense. The operating expense is the sum of procurement and manufacturing (or variable production) costs. To compute the corporate taxes, let Pisct, CIFisct, and IDisct denote the purchase price ($/ton), CIF cost ($/ton), and import duty ($/$ of CIF cost), respectively, of material mi (i ∈ OMs ∩ IMc) sold by supplier s

(PifctFifct) -

∑ ∑

(1 + IDisft)CIFisftFisft (12)

i∈IMfs3i∈OMs

+ ∆qft) + cftzft]

f∈IF

∑ ∑

i∈OMfc3i∈IMc

where MCft is the manufacturing cost [$/ton of π(f)] of facility f ∈ IF during period t. Depreciation is an amount that the MNC charges itself for recovering its capital investment. Various methods exist for computing depreciation, and acceptable methods differ from country to country. In this paper, we use the simplest method for computing depreciation, which is the straight-line method. Now, during the planning horizon, two depreciation charges will occur, one arising from the (old) investments before t ) 0 and the other arising from the (new) ones after t ) 0. Let the former charge be ODCft; for the latter, we define NDCfτt as the depreciation charge during period t for the capital investment at facility f ∈ IF during year τ ) 1, 2, ..., T - δ(f). Then, we obtain NDCfτt )

{

[afτyfτ + cfτξfτ + bfτ(yfτqLf + ξfτQLf + ∆qfτ)]/Lf τ + δ(f) e t e min[τ + Lf,T] 0

otherwise 1 e τ e T - δ(f), f ∈ IF (13)

where Lf denotes the project life (years) for all capital expenditures at facility f ∈ IF, which begins after the new facility or expanded capacity becomes available for production. Using eqs 12 and 13, we obtain the taxable income, TInt, of the MNC in nation n during period t as


Figure 3. Material flows among the facilities of a typical petrochemical plant.

TInt g

∑ [ ∑ ∑ PifctFifct - i∈IM ∑ s3i∈OM ∑ (1 + f∈IF∩F i∈OM c3i∈IM n

f

c

f

s

t-δ(f)

IDisft)CIFisftFisft - MCftXχft - ODCft -

∑ NDCfτt]

τ)1

(14) where eq 13 gives NDCfτt. Note that TInt is a nonnegative variable. If the tax rate ($/$ of taxable income) is TRnt (nonnegative) for nation n during period t, then the corporate tax for the MNC during period t is TRntTInt. With this expression, the NPV of the net cash flow for the MNC is

NPV )

∑∑ f∈IF t

1

(1 + r)t

[-MCftXft +

∑ ∑

PifctFifct -

i∈OMfc3i∈IMc

∑ ∑ (1 + IDisft)CIFisftFisft] - f∈IF ∑ ∑t i∈IM s3i∈OM

1

(1 + r)t [aftyft + cftξft + bft(yftqLf + ξftQLf + ∆qft)] 1 (TIntTRnt) (15) t n t (1 + r) f

s

∑∑

where r is the annual interest rate (fraction). This completes our formulation for the DCEP in the presence of corporate taxes and import duties as the regulatory factors. It comprises maximizing the NPV (eq 15) subject to eqs 1, 2, 3, 5-11, 13, and 14. We now illustrate our model with a realistic example and demonstrate the significant impact of regulatory factors. 6. Example 1 (Deterministic Case) An MNC currently owns six facilities (EIF ) {F1F6}) and is considering six new facilities (FIF ) {F7-

F12}) for possible capacity expansion over the next 10 fiscal years (t ) 1, 2, ..., T ) 10) to meet the growth forecasts in the global demands of its products. The MNC classifies its facilities as primary or secondary. The primary upstream processing facilities supply raw materials to the secondary downstream facilities (see Figure 2 for the material flows among these facilities). Figure 3 shows an existing industrial setting with material flows similar to those in this case study. Here, a crude distillation unit is the primary facility, and the steam reformer, catalytic reformer, and steam cracker are the secondary facilities. Table 3 lists the initial capacities (Qf0), capacity limits (qLf , QLf , QU f ), minimum production limits (XLf ), manufacturing costs (MCft), expansion cost coefficients (aft, bft, cft), primary materials [π(f)], mass balances (σif), etc., for all of these facilities. External facilities comprise 10 customers (C1-C10) and eight suppliers (S1-S8); thus, EF ) {C1-C10, S1S8}. These customers and suppliers are the key external business partners to whom the MNC sells its products and from whom it sources raw materials, respectively. The 12 internal facilities (IF ) {F1-F12}) and 18 external facilities (customers and suppliers) are geographically spread across 10 nations (n ) N1-N10): FN1 ) {C1, S1, F9}, FN2 ) {C2, S2, F1, F3}, FN3 ) {C3, F8}, and so on as in Table 4. Table 4 also lists the corporate tax rate for each nation. The tax rates are constant over the 10 years for all nations except N8, which has announced plans to cut the corporate tax rate from 40 to 38% in the fourth year and then to 36% in the seventh year. In a bid to attract foreign direct investments (FDI), N10 has offered to waive the corporate tax for the next four fiscal years for any MNC that invests in new facilities at the start of the planning horizon.

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3371 Table 3. Types, Initial Capacities (Tons/Day), Capacity Limits (Tons/Day), Mass Balances, Primary Materials, Project Lives, Periods for Expansion or New Construction, Annual Interest Rates, Depreciation Charges (k$), Minimum Production Limits (Tons/Day), Manufacturing Costs ($/kg), and Coefficients (k$/Ton) in Expansion Cost Expressions for the MNC’s Facilities in Example 1a facility (f)

π(f)

initial cap. (Qf0)

max cap. (QU f )

min exp. (qLf )

min const. (QLf )

min prod. (XLf )

MCf1

af1

bf1

cf1

depreciation charges (ODCft)

F1b F2b F3c F4c F5d F6e F7b F8c F9d F10d F11e F12e

m2 m2 m5 m5 m7 m9 m2 m5 m7 m7 m9 m9

90 80 40 25 30 25 0 0 0 0 0 0

120 100 80 100 70 80 150 90 120 120 85 120

25 25 25 25 25 40 30 25 40 45 25 25

40 40 60 60 30 30

40 30 20 15 30 25 30 25 40 45 25 25

0.581 0.687 0.720 0.580 1.025 0.956 1.222 0.685 1.112 0.915 0.825 0.788

220 450 300 300 500 270 200 350 480 280 550 300

10 30 20 20 10 10 20 30 30 20 20 20

330 675 450 450 750 405 300 525 720 420 825 450

160.7 410.8 369.1 318.2 321.1 133.3 0.0 0.0 0.0 0.0 0.0 0.0

a F1, F2, and F7 are primary facilities, whereas all others are secondary. Each fiscal year has 300 production days at all facilities. All manufacturing costs (MCft) and expansion cost coefficients (aft, bft, and cft) increase by 3% each year. Lf (project life) ) 15 years and δ(f) ) 2 years for all constructions. The annual interest rate is constant at 6% for all facilities. All old depreciation charges (ODCft) are constant over the entire planning horizon. b Mass balance for F1, F2, and F7: m1 ) 0.3m2 + 0.3m3 + 0.3m4 + 0.1m11. c Mass balance for F3, F4, and F8: m2 ) 0.5m5 + 0.4m6 + 0.1m12. d Mass balance for F5, F9, and F10: m3 ) 0.6m7 + 0.35m8 + 0.05m13. e Mass balance for F6, F11, and F12: m4 ) 0.3m9 + 0.65m10 + 0.05m14.

Table 4. Locations of Internal Facilities (MNC’s Own Facilities) and External Facilities (Other Suppliers and Customers) in Example 1 facilities nation (n) customer supplier

corporate tax rates 100TRnt (years t)

MNC’s

N1 N2 N3 N4 N5 N6 N7 N8

C1 C2 C3 C4 C5 C6 C7 C8

S1 S2 S3 S4 S5 S6

F9 F1, F3 F8 F2, F4 F5 F7, F10, F12

N9 N10

C9 C10

S7 S8

F6 F11

21% (1-10) 38% (1-10) 18% (1-10) 40% (1-10) 24% (1-10) 40% (1-3), 38% (4-6), 36% (7-10) 26% (1-10) 0% (1-4), 36% (5-10)

Table 5. Percent Import Duties (100IDisft) on Raw Material Flows (mi, i ) 1-4) from F1, F2, F7, and S1-S8 to Internal Facilities (F1-F12)a importing facility

material mi (i)

exporting facility (% import duty)

F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

1 1 2 2 3 4 1 2 3 3 4 4

S2 (0%), others (5%) S4 (0%), others (10%) F1 (0%), S2 (0%), others (35%) F2 (0%), S4 (0%), others (80%) S5 (0%), others (55%) S7 (0%), others (65%) S6 (0%), others (70%) all (60%) S1 (0%), others (45%) F7 (0%), S6 (0%), others (65%) S8 (0%), others (30%) F7 (0%), S6 (0%), others (30%)

a Bilateral free trade agreement between N5 and N8 will commence from year three onward. This means that the import duties on material trade between S4, F2, and F4 in N5 and S6, F7, F10, and F12 in N8 will be 0 for t g 3.

Table 5 shows the import duties for material flows among the suppliers and internal facilities. Because the customers bear the import duties on their product purchases, they are of no concern to the MNC. The import duties of all products are constant over the planning horizon with one exception. From the third year onward, a bilateral free trade agreement (FTA) between N5 and N8 is expected to commence officially,

which will waive the import tariffs on product flows between these two nations. Table 6 lists the purchase and CIF costs as charged by the eight suppliers of raw materials and the transfer prices charged by the MNC’s internal facilities. The transfer prices (the prices that an internal facility charges to another internal facility) at each period are fixed according to the material type regardless of which internal facility is the seller or buyer. This is required by the revenue authorities to prevent a company from manipulating transfer prices to save taxes. We use a 3% annual inflation rate for all cost data and prices in this example. Table 7provides the demand rate expressions for the products consumed by the 10 customers. For most customers, we use a linearly increasing demand rate for each product, so that most of Table 7 gives only the demands for years 1 and 10. For three customers, we express the demand rates as nonlinear functions of year. Figure 4 shows the demand rate profiles of material m9 for the customers over the 10 years. Table 8 lists the projected supply levels of materials from various suppliers. In all cases, we assume the supply levels to increase linearly with time. The MNC has allocated $10 million for all expansionrelated activities during the first year (CB1 ) 10 M$). Furthermore, it has allocated another $12 million (CB6 ) 12 M$) for the same purpose during the sixth year of the planning horizon. Using the above data and information, we solved our model for two cases. In case 1, we included the two regulatory factors, namely, the corporate taxes and the import duties. In case 2, we did not include these factors, so we omitted eq 13 and all TInt variables and set IDisft ) TRnt ) 0. We used the CPLEX 8.1 solver within GAMS (distribution 21.2) running on a Windows XP workstation with a Pentium 4 Xeon (2.8 GHz) processor. The model for case 1 involved 17 139 continuous variables, 144 binary variables, 2750 constraints, and 35 607 nonzeros, whereas that for case 2 involved 17 059 continuous variables, 144 binary variables, 2670 constraints, and 30 739 nonzeros. CPLEX solved case 1 in 0.874 s and gave a maximum NPV of $4.53 billion, whereas it solved case 2 in 0.952 s and gave an NPV of $4.13 billion.

3372 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 6. Purchase Costs (Pisf1, $/kg) and IF (Insurance + Freight) Costs (CIFisf1 - Pisf1, $/kg) of Materials between Facilities for Year 1 (t ) 1)a material m1 shipping facility

F1

F2

material m2 F7

F1

-

-

-

F2

-

-

-

F7

-

-

-

S1

0.510 0.039 1.780 0.040 1.730 0.064 0.880 0.040 0.770 0.048 1.400 0.079 1.120 0.050 1.040 0.068

0.510 0.033 1.780 0.086 1.730 0.082 0.880 0.019 0.770 0.042 1.400 0.085 1.120 0.055 1.040 0.060

0.510 0.037 1.780 0.102 1.730 0.095 0.880 0.039 0.770 0.041 1.400 0.039 1.120 0.060 1.040 0.053

S2 S3 S4 S5 S6 S7 S8

F3

F4

0.210 0.012 0.210 0.022 0.210 0.021 2.280 0.106 1.170 0.037 1.760 0.092 0.860 0.043 0.670 0.036 1.380 0.087 2.400 0.129 1.960 0.087

0.210 0.027 0.210 0.008 0.210 0.024 2.280 0.095 1.170 0.068 1.760 0.107 0.860 0.018 0.670 0.038 1.380 0.076 2.400 0.098 1.960 0.085

material m3 receiving facility F8 F5 0.210 0.023 0.210 0.028 0.210 0.021 2.280 0.131 1.170 0.064 1.760 0.073 0.860 0.051 0.670 0.048 1.380 0.068 2.400 0.122 1.960 0.114

0.440 0.033 0.440 0.034 0.440 0.031 1.410 0.063 0.750 0.046 0.990 0.051 1.750 0.100 0.950 0.024 0.750 0.040 1.930 0.085 0.820 0.050

material m4

F9

F10

F6

F11

F12

0.440 0.033 0.440 0.034 0.440 0.033 1.410 0.032 0.750 0.035 0.990 0.048 1.750 0.084 0.950 0.050 0.750 0.048 1.930 0.091 0.820 0.043

0.440 0.039 0.440 0.033 0.440 0.011 1.410 0.062 0.750 0.048 0.990 0.048 1.750 0.076 0.950 0.046 0.750 0.015 1.930 0.074 0.820 0.037

0.180 0.021 0.180 0.024 0.180 0.020 1.550 0.064 1.210 0.072 1.860 0.074 2.160 0.099 1.700 0.092 2.110 0.114 0.730 0.018 0.800 0.049

0.180 0.023 0.180 0.027 0.180 0.019 1.550 0.082 1.210 0.067 1.860 0.084 2.160 0.086 1.700 0.076 2.110 0.095 0.730 0.046 0.800 0.019

0.180 0.024 0.180 0.028 0.180 0.011 1.550 0.085 1.210 0.064 1.860 0.108 2.160 0.089 1.700 0.102 2.110 0.052 0.730 0.045 0.800 0.044

a First row for each shipping facility is the purchase cost, and the second is the IF cost. All costs increase by 3% each year due to inflation.

Table 7. Linear Ranges or Expressions for Demandsa (Dict, Tons/Day) of Materials (mi, i ) 2-10) and Their Selling Prices ($/kg) in Example 1 i

selling price

2

1.24

3

1.49

4

1.48

5

3.98

6

3.45

7

4.12

8

4.43

9

2.80

10

3.36

C1

C2

C3

C4

C5

85.8 213.8 81.2 211.8 84.6 280.5 95.8 281.7 86.2 300.3 95.5 294.8 93.5 239.2 86.5 210.9 88.7 215.6

176.12t + 9.27 0.45t + 0.55 101.75t + 18.07 0.35t + 0.65 100.83t + 24.7 0.3t + 0.7 175.19t + 22.51 0.39t + 0.61 133.48t + 29.81 0.32t + 0.68 109.25t + 17.01 0.37t + 0.63 137.93t + 0.04 0.5t + 0.5 173.32t + 20.12 0.4t + 0.6 144.54t + 2.15 0.49t + 0.51

117.4 147.1 108.9 196.9 102.8 188.9 133.6 154.1 129.0 182.4 112.9 192.1 122.9 161.5 138.2 150.3 121.6 210.7

142.9 222.2 145.4 207.6 104.0 182.1 136.7 201.8 146.7 223.8 108.0 129.9 112.8 180.0 131.5 146.5 135.7 206.7

91.9 262.0 85.1 230.6 85.4 307.5 99.8 283.7 83.0 218.0 83.5 223.8 95.6 343.8 95.6 312.0 83.3 217.5

customer c C6 98.9 230.3 95.2 326.0 81.1 336.1 83.5 328.3 96.2 317.7 99.2 287.8 82.5 260.9 95.2 263.5 99.7 311.8

C7

C8

C9

C10


92.0 246.1 82.4 279.0 88.9 337.6 94.7 342.5 87.6 319.7 84.6 298.6 80.3 349.5 81.4 235.8 85.5 250.2


135.6 204.7 123.3 186.5 129.0 143.8 105.4 164.4 123.7 175.0 147.2 160.2 115.8 148.1 143.9 165.9 130.5 196.0

a Demand rates for customers C2, C7, and C9 are given as functions of t. For all others, the first row is the demand rate for year 1, and the second is for year 10; the demand rates for the interim years are linear extrapolations. Figure 4 illustrates the variety of demand profiles of m9 for the customers over the horizon. All prices increase by 3% each year.

Figure 5 shows the optimal expansion plans for the two cases. Clearly, the regulatory factors make the two solutions significantly different. For example, the case-1 solution suggests the construction of a new facility (F11) in N10 during the first year to capitalize on the taxfree window offered by N10 for the first four fiscal years. In contrast, the case-2 solution suggests the same construction in the sixth fiscal year. This is clearly due to the omission of the corporate tax in case 2. Because of this, the case-1 solution suggests the construction of a new facility (F12) during the sixth year, whereas the

case-2 solution suggests the same during the first year. However, apart from these differences, the decisions of expansion vs new construction and their locations are identical for the two scenarios except for F3 during year 1. The case-1 solution suggests a larger expansion than the case-2 solution. This is probably due to the budget constraint. In case 2, the budget is used for the construction of secondary facility F12 (120 tons/day), which leaves less for the expansion of F3. In case 2, a smaller secondary facility F11 (85 tons/day) is built, so more money is available for the expansion of F3.


Figure 4. Demand rate profiles of material m9 for the customers. Table 8. Linear Ranges of Projected Suppliesa (Sist, Tons/Day) of Materials (mi, i ) 1-4) from the External Suppliers in Example 1 supplier s i

S1

S2

S3

S4

S5

S6

S7

S8

1

149.3 296.0 102.3 224.3 110.4 260.7 134.7 279.2

111.3 284.1 119.1 242.1 129.2 243.2 141.7 314.8

249.0 311.6 247.4 274.5 222.9 230.2 227.2 229.2

226.7 248.6 220.1 308.3 213.1 294.6 221.5 304.0

150.0 257.6 108.0 229.6 118.9 281.5 125.1 279.0

100.8 254.6 132.3 244.5 146.0 268.4 123.1 263.8

205.0 256.8 220.6 257.5 231.4 288.2 220.2 252.1

239.9 249.2 216.3 280.5 204.9 243.5 202.8 227.1

2 3 4

a First row is the supplier’s capacity for year 1, while the second is for year 10. The capacities for the interim years are linear extrapolations.

Table 9 shows the suppliers and amounts of raw materials for the internal facilities during the 2nd, 5th, and 8th fiscal years of the horizon. The inclusion of import tariffs in case 1 leads to a superior raw material sourcing plan that avoids the costly process of procuring raw materials from the overseas suppliers and internal facilities. F4 illustrates this very well. It sources its raw material solely from a local supplier (S4) in case 1 in the 2nd and 5th fiscal years. However, in case 2, F4 gets its raw materials from local supplier S4 and overseas supplier S5 at the same time. Note that the case-1

Figure 5. Expansion plans of the two scenarios. Shaded bars denote the plans for case 1 with regulatory factors, whereas clear bars denote the plans for case 2. Bars with dashed borders denote new constructions, whereas those with continuous borders denote capacity expansions.

results use fewer suppliers than the case-2 solution in most cases. This helps establish preferred suppliers and might result in better pricing and consistency of materials. Table 10 also supplements Table 9 in supporting the notion that the inclusion of import tariffs in case 1 leads to a superior raw material sourcing plan. The percentages of raw material supply coming from dutyfree sources in case 1 equals or exceeds that in case 2 for each facility except F11. The only duty-free source of m4 for F11 is S8. F11 begins production from year 3 in case 1 and from year 8 in case 2. The supply levels of S8 are lower during years 3-7 than during years 8-10. Hence, in scenario 1, F11 has to procure more of m4 from the non-duty-free sources to meet its production requirements during years 3-7. This, in turn, results in a slightly higher percentage of duty-free sourcing for F11 in case 2 compared to case 1. Another major difference between the two case lies in the trade volumes of materials between countries. Table 11 illustrates this well for the nation pair N5N8. The average trade volume of m4 is 80 tons/day for years 8-10 in case 1. In contrast, the same for case 2 is only 16.1 tons/day. This is despite the fact that the two cases have very similar production levels of F12 during

3374 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 9. Sources of Materials and Their Flows (Tons/Day) for the Two Cases for Years 2, 5, and 8 supplier (amount, tons/day)

facility f

material mi (i)

F1 F2 F3 F4 F5 F6

1 1 2 2 3 4

Year 2 S1 (138.1), S5 (161.9) S1 (27.5), S4 (229.1) S5 (80.0) S4 (50.0) S5 (50.0) S7 (83.3)

S1 (128.0), S5 (161.9) S1 (37.6), S4 (229.1) same S4 (8.5), S5 (41.5) S6 (50.0) same

F1 F2 F3 F4 F5 F6 F10 F11 F12

1 1 2 2 3 4 3 4 4

Year 5 S1 (102.2), S5 (197.8) S1 (112.3), S4 (154.4) S5 (160.0) S4 (200.0) S5 (116.7) F1 (22.0), F2 (10.3), S7 (234.4) S6 (200.0) F2 (69.7), S8 (213.6) -

same same S5 (131.0) S4 (169.0), S5 (31.0) S2 (116.3), S6 (0.4) F1 (0.1), S7 (234.4), S8 (32.2) same S2 (218.6), S8 (181.4)

F1 F2 F3 F4 F5 F6 F8 F9 F10 F11 F12

1 1 2 2 3 4 2 3 3 4 4

Year 8 S1 (66.3), S5 (233.7) S1 (197.1), S4 (69.6) S5 (160.0) S4 (200.0) S5 (116.7) F1 (21.7), S7 (245.0) F1 (57.4), F2 (80), S5 (42.6) S2 (200.0) S6 (200.0) F1 (30.6), S1 (31.1), S8 (221.7) F1 (37.8), F2 (80), S2 (276.3)

same same S2 (19.7), S5 (111.3) same S2 (17.9), S6 (41.2), S8 (57.6) S1 (21.7), S7 (245.0) S4 (88.7), S5 (91.3) same same F2 (46.3), S1 (15.3), S8 (221.7) F1 (90.0), F2 (33.7), S2 (276.3)

case 1

Table 10. Sourcing Strategies of Internal Facilities duty-free sources (%)a f

material mi (i)

case 1

case 2

F1 F2 F3 F4 F5 F6 F8 F9 F10 F11 F12

1 1 2 2 3 4 2 3 3 4 4

0.0 51.7 2.5 100.0 100.0 90.6 0.0 0.0 97.5 76.8 20.3

same 50.7 1.6 86.8 0.0 same same same same 79.2 1.5

a Percentage computed on the basis of the total material flow over the entire planning horizon.

Table 11. Effect of the Trade Agreement on the Trade Volumes of m4 between the Internal Facilities in N5 and N8 trade volume (tons/day) case 1

case 2

8 9 10

year (t)

80.0 80.0 80.0

33.7 14.5 0.0

average

80.0

16.1

these years. In fact, this increase in trade volume in case 1 is a direct result of the FTA between N5 and N8 commencing from year three onward. In both cases, F12, which is located in N8, sources m4 from F1 and S2 in N2 and F2 in N5. However, F12 sources more m4 from F1 and less from F2 in case 2 compared to case 1. This is due to the higher CIF cost of m4 from F2 than F1. However, in case 1, the FTA between N5 and N8 makes it more attractive to obtain m4 from F2 than F1 despite the former’s higher CIF cost. Therefore, F12 uses F2 preferentially over F1 in case 1.

case 2

Figure 6 shows the production plans only for those instances in which they are different for the two cases. For instance, F1 produces more during years 1 and 2 in case 1 than in case 2. The reverse is true for F2. This is mainly due to the higher tax rate and import duty for F2 (40 and 10%, respectively) than those for F1 (38 and 5%, respectively) in case 1. In the absence of these factors, as in case 2, F2 is more attractive than F1 because of its lower CIF costs and, hence, runs at full capacity. For the rest of the planning horizon, the differences in production plans in the two cases are mainly due to the differences in the expansion or construction decisions. Although the two solutions differ in many other details, the striking difference is in their NPVs. Case 2 gives an NPV of $4.15 billion after we deduct the corporate taxes and import tariffs based on its solution. On the other hand, case 1 gives an NPV of $4.53 billion. The omission of the two regulatory factors in the capacity-planning model has obviously misguided the MNC to a significantly inferior solution. This clearly demonstrates the tremendous impact of the regulatory factors on capacity-planning decisions and the vital need to incorporate them into capacity-planning models for global chemical supply chains. Table 12 lists the NPVs of various components of the MNC’s net cash flows in the two solutions. The total sales revenue in case 1 is about 4% lower than that in case 2, because case 1 has greater internal sales than case 2, as shown in Table 13. Internal sales are $60.6 million (111.5 kton of m2 and 306 kton of m4) in case 1 compared to $23.3 million (171.8 kton of m4) in case 2. Internal sales are the sales by an internal facility to other internal facilities, whereas external sales are those to the external facilities. Greater internal sales in case 1 lower the sales revenue, because the intracompany


7. Extensions

Figure 6. Production rates of primary materials, when they differ between the solutions for cases 1 and 2. Table 12. NPVs of Cash Flow Components in M$ and Percent Differences Based on the Case-2 Results component

case 1 (M$)

case 2 (M$)

sales 11,656 12,157 manufacturing costs 1,408 1,419 material costs 3,251 3,501 insurance + freight costs 128 155 import duties 303 640 capital expenditures 17.89 17.69 corporate taxes 2,022 2,295 NPV of net cash flow 4,525 4,130 a

difference differencea (M$) (%) -501 -11 -250 -27 -337 0.20 -272 396

-4.1 -0.8 -7.1 -17.2 -52.7 1.1 -11.9 9.6

Differences are percents of the NPVs for case 2.

transfer prices for products are normally lower than their open-market prices. Nevertheless, the NPV for case 1 is 9.6% higher than that for case 2. This is because the cost savings from lower manufacturing costs, material costs, transportation costs, import duties, and corporate taxes exceed the shortfall in the total sales revenue for case 1. In absolute terms, import tariffs and corporate taxes are the top two contributors to the $396 million difference in the NPVs of the two cases. This is a clear testimony to the need for incorporating the regulatory factors (domestic and international) in capacity-expansion planning. Having illustrated the basic deterministic model, we now address two relatively straightforward extensions and the more useful and practical issue of uncertain planning scenarios.

We consider three extensions. First, we relax assumption 12 to consider the practical situation in which products go to the MNC’s distribution centers, warehouses, or storage facilities before they go to the customers. Second, we consider the possibility of outsourcing production to meet increased demands rather than expanding existing facilities or building new facilities. Third, we propose an approach to use the basic deterministic model in the real-life situation of uncertain business parameters. 7.1. Delivery via Distribution Centers. In our model, we assumed that the products are shipped directly to the customers who, in turn, bear all of the delivery charges. In circumstances where products are consolidated in the MNC’s distribution centers before being delivered to the customers, the formulation requires two simple modifications. First, we treat the distribution centers as internal facilities that contribute to the overall income of the MNC. This means that the after-tax incomes of these distribution centers become a component of the NPV in eq 15. These centers bear the material costs and delivery charges for bringing the products from other internal manufacturing facilities. In turn, they make a profit by selling and delivering products the customers. Second, the consolidated multiperiod customer orders at the distribution centers form the demand quantities that the internal facilities should fulfill. With these two simple modifications, the model will be able to weigh the different options of expanding or constructing internal manufacturing facilities on the basis of their proximities to the distribution centers. 7.2. Outsourcing of Production. Often, chemical companies have an option of outsourcing their production, in addition to the option of expansion or new construction, to meet the forecasted growth in product demands. Although our model thus far does not allow this option, it is easy to accommodate this flexibility into the model. Let Gifct denote the production quantity of material i that facility f outsources during period period t for customer c, where i ∈ OMf. Note that Gifct ) 0 for i ∈ IMf. Then, to allow for the outsourcing option in the proposed model, we replace eq 7 by

σif

∑

∑

∑

Xft + Gifct ) Fifct + Fisft σπ(f)f c3i∈IMc c3i∈IMc s3i∈OMs f ∈ IF, i ∈ OMf ∪ IMf (16) We assume that only an existing facility with nonzero production capacity during period t can execute the option of production outsourcing during this period. Normally, an upper limit on how much production can U debe outsourced by each facility f will exist. If Gift notes the upper limit on the production units of material i that facility f can outsource during period t, then t-δ(f)

Gifct e (φf + ∑ zfτ)GU ∑ ift c3i∈IM τ)1

f ∈ IF

(17)

c

Now, all of the income-related expressions in eqs 12, 14, and 15 must include the outsourcing costs. We define COifct as the unit cost ($/ton) that facility f incurs during period t for outsourcing product i to be delivered to customer c. Then, the cost of outsourcing product i for customer c by facility f during period t is GifctCOifct. We

3376 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 13. Breakdown of Salesa (M$) and Amounts (kton) of Each Material (mi, i ) 2-10) for the Internal Facilities in the Two Cases case 1 material mi (i)

a

case 2

internal sales (quantity)

external sales (quantity)

internal sales (quantity)

external sales (quantity)

2 3 4 5 6 7 8 9 10

17.7 (111.5) 0 (0) 43.0 (306.0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

418.1 (393.9) 624.7 (505.4) 260.4 (199.4) 1,773.1 (552.0) 1,228.8 (441.6) 1,920.6 (582.0) 1,204.1 (339.5) 1,158.0 (517.4) 3,007.3 (1,121.0)

0 (0) 0 (0) 23.3 (171.8) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

522.4 (505.4) 624.7 (505.4) 426.6 (333.7) 1,661.4 (517.2) 1,151.3 (413.8) 1,920.6 (582.0) 1,204.1 (339.5) 1,285.1 (571.5) 3,337.5 (1,238.3)

total

60.6

11,595.1

23.3

12,133.6

Internal sales are sales among the internal facilities, whereas external sales are sales by the internal facilities to the external facilities.

simply subtract this cost from all the income-related expressions appropriately. For instance, the expression for the gross income (GIft) becomes

GIft ) -MCftXft +

∑ ∑

i∈OMfc3i∈IMc

(1 + IDisft)CIFisftFisft -

(PifctFifct) -

∑ ∑

∑ ∑

i∈IMfs3i∈OMs

GifctCOifct

i∈OMfc3i∈IMc

f ∈ IF (18) With the above modifications, our model accommodates the outsourcing option as well. 7.3. Uncertainty in Data. Strategic planning requires data over several years. It is hard to obtain such data with a high degree of certainty. Therefore, most data required by strategic planning are necessarily uncertain. We now see how we can use our deterministic model to solve the problem in which various model parameters are uncertain or stochastic. We do this by using a simple scenario-planning approach.21 In this approach, we model each uncertain parameter in terms of several distinct scenarios, each of which represents a discrete realization of the parameter with a known probability. The objective of the SCEP will be similar to that of DCEP except that the former will involve the maximization of the expected NPV of the company’s net cash flows over the planning horizon over all possible scenarios (χ ) 1, 2, ..., NS) of the stochastic parameters. Likewise, the solution of SCEP will contain the actual flows of all materials to and from each facility f ∈ F during each period t and for every scenario χ. The need to determine the time, location, and amount of capacity expansion of each facility f ∈ IF in the DCEP remains unchanged in the SCEP. To adopt our DCEP model to address the SCEP via the aforementioned scenario-planning approach, we need three major changes to our basic model. First, we must characterize each stochastic parameter by its multiple scenarios. To this end, we add a superscript χ to the original notation of the uncertain parameter to denote its specific value for scenario χ. For instance, the demand quantity was Dift earlier, but now it becomes χ Dift , which is the demand quantity of product i by facility f during period t in scenario χ. Similarly, the variables related to productions, material flows, gross and taxable incomes, etc., all take on the same superχ χ , Fifct , GIχft, TIχnt) to identify their script (i.e., Xχft, Fisft values for the different scenarios. Second, we must modify the constraints involving the uncertain param-

eters and variables with the superscript χ. We write and enforce these constraints separately for each scenario to reflect the distinct limitations imposed by the various scenarios. For example, if the demand parameter is uncertain, then we write a set of equations, one equation for each scenario χ, in place of eq 10 as follows

Fχifgt + ∑ Fχigft e Dχift + Sigt ∑ f∈IF3i∈OM f∈IF3i∈IM f

f

g ∈ EF, i ∈ OMg ∪ IMg (19) On the other hand, we do not add the superscript χ to any decision variable such as those associated with the expansion or construction of plants (yft, zft, ξft, qft, ∆qft, Qft, CEt, CBt). Last, we must modify the objective function. Now, instead of maximizing a single NPV as in the DCEP, we must maximize the expected NPV over all possible scenarios of the uncertain parameters. To this end, we let Ψχ denote the known probability of occurrence of scenario χ. Clearly, Ψ1 + Ψ2 + Ψ3 + ... + ΨNS ) 1 must hold. Using these changes, we obtain the expected NPV (ENPV) as

ENPV )

{

1

∑χ ψχ f∈IF ∑ ∑t ∑ ∑

[-MCχft Xχft +

χ t

(1 + r ) Pχifct Fχifct -

∑ ∑

i∈OMfc3i∈IMc

IDχisft)CIFχisft Fχisft] -

(1 +

i∈IMfs3i∈OMs

1

∑∑ f∈IF t

(yftqLf + ξftQLf + ∆qft)] -

χ t

(1 + r ) 1

∑n ∑t

[aχftyft + cχftξft + bχft TIχnt TRχnt

χ t

(1 + r )

}

(20)

In other words, the optimal plan for the stochastic model will take into consideration all the stipulated scenarios of the uncertain parameters. This completes our description of how the basic DCEP model can form the basis for solving an SCEP. We now illustrate this approach with another realistic example. 8. Example 2 (Stochastic Case) In this example, we consider demand forecasts and import duties as uncertain for the entire planning horizon. We also assume that these two parameters are stochastically independent. If the numbers of scenarios for demand and import duty are NDS and NIS, respectively, then we have NS ) NDS × NIS as the total

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3377 Table 14. Linear Ranges or Expressions for Demandsa (Dict,Tons/Day) of Materials (mi, i ) 2-10) for Demand Scenario 2 in Example 2 customer c i 2 3 4 5 6 7 8 9 10

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

91.1 131.7 92.5 110.4 81.9 213.9 96.6 193.9 88.6 190.0 83.0 134.9 83.1 195.9 98.2 113.1 98.9 131.8


127.3 174.3 131.7 169.2 150.0 237.2 110.1 184.9 120.6 198.9 130.7 203.6 103.6 156.6 100.7 115.0 130.0 165.1

107.4 146.9 145.3 167.3 134.4 199.2 131.2 148.6 118.8 185.1 141.8 155.3 141.8 155.3 110.5 196.9 132.1 171.8

84.4 185.8 96.3 151.9 83.5 115.1 92.5 111.0 84.7 142.5 86.1 141.8 80.4 213.4 88.9 210.4 94.2 196.7

86.5 122.0 90.0 119.7 93.9 224.7 98.9 166.0 81.4 119.0 95.5 132.0 99.1 190.8 85.8 116.2 81.2 113.4


88.7 112.6 85.9 200.8 85.4 113.4 84.9 170.4 88.4 139.3 92.4 215.3 98.0 169.1 86.9 128.2 83.5 215.5


114.7 186.0 133.3 142.6 112.0 194.0 147.8 157.1 141.7 190.4 126.9 162.5 111.1 173.0 129.8 172.5 112.8 143.8

a Demand rates for C2, C7, and C9 are given as functions of t. For all others, the first row is the demand rate for year 1, and the second is for year 10; the demand rates for the interim years are linear extrapolations.

Table 15. Linear Ranges or Expressions for Demandsa (Dict, Tons/Day) of Materials (mi, i ) 2-10) for Demand Scenario 3 in Example 2 customer c i 2 3 4 5 6 7 8 9 10

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

93.4 215.8 93.3 232.4 97.7 317.6 90.5 276.6 80.1 268.5 82.8 248.2 92.3 229.2 83.8 262.8 82.7 323.8


129.4 163.2 129.1 174.7 106.2 153.3 145.2 220.2 122.8 158.7 106.1 136.1 112.2 162.2 131.3 152.9 111.3 140.1

134.0 171.1 108.9 143.5 125.0 146.8 148.1 207.4 126.2 208.5 117.9 192.4 134.0 152.2 141.6 168.9 130.0 144.9

85.8 278.6 96.3 210.2 93.6 335.6 97.8 222.2 83.8 262.3 85.1 283.0 83.3 208.1 82.1 262.6 85.9 270.4

88.8 224.5 89.0 267.8 81.0 312.3 87.6 347.9 84.7 280.2 97.8 265.0 83.5 186.6 96.5 318.3 80.3 283.1


86.8 354.1 91.8 355.8 95.6 363.6 91.5 307.9 91.1 199.2 86.1 199.0 94.6 305.8 92.8 310.8 91.6 282.9


113.2 146.4 142.0 178.1 146.5 208.7 133.6 202.9 132.4 162.0 109.7 194.0 149.7 217.9 144.8 172.2 150.0 178.6

a Demand rates for C2, C7, and C9 are given as functions of t. For all others, the first row is the demand rate for year 1, and the second is for year 10; the demand rates for the interim years are linear extrapolations.

number of scenarios in the stochastic model. We can compute the probability (Ψχ) of occurrence for each such scenario by multiplying the probabilities of occurrence of individual parameters. Unless stated otherwise, all parameters in this example are the same as those in example 1. The marketing division has forecasted three possible scenarios of the annual demand rates over the planning horizon. Table 7 lists the demand rate expressions for the products consumed by the 10 customers for demand scenario 1, whereas Tables 14 and 15 list the same data for demand scenarios 2 and 3, respectively. According to the sales department, all three demand scenarios are equally probable with probability one-third for each. The product prices are the same for the three demand scenarios, and they are as given in Table 7.

We consider four possible scenarios for the import duty realizations. Table 5 lists the import duties for scenario 1, where the bilateral free trade agreement (FTA) between nations N5 and N8 commences with effect from the third year onward. Table 5 also lists the same for scenario 2, where the bilateral FTA between N5 and N8 does not commence as planned. Import duty scenario 3 is similar to scenario 2 with the exception that a regional FTA among nations N1-N3 takes effect from the sixth year onward. Just as in the earlier bilateral FTA between N5 and N8, the regional FTA results in the tariff-free movement of products among the three nations. In scenario 4, both the bilateral and regional FTAs proceed as in scenarios 1 and 3, respectively. We assume that all four scenarios are equally probable with a probability of 0.25. Their probabilities

3378 Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 Table 16. Expected NPVs of Cash Flow Components in M$ and Percent Differences Based on the Case-2 Results component

case 1 (M$)

case 2 difference differencea (M$) (M$) (%)

sales 11,633 12,145 manufacturing costs 1,407 1,418 material costs 3,245 3,497 insurance + freight costs 128 155 import duties 270 615 capital expenditures 18 18 corporate taxes 2,023 2,141 NPV of net cash flow 4,544 4,301 a

-511 -11 -253 -27 -345 0 -118 243

-4.2 -0.8 -7.2 -17.6 -56.1 1.1 -5.5 5.6

Differences are percents of the expected NPVs for case 2.

of occurrence reflect the relative levels of optimism that the MNC has on the successful commencement of FTAs among the nations involved. Similarly to example 1, we solved our stochastic model for two cases. In case 1, we included the two regulatory factors (corporate taxes and import duties) and considered the 12 distinct scenarios of demand rates and import duties. In case 2, we omitted the regulatory factors and had only three scenarios of demand rates. We excluded the regulatory factors from the stochastic model by omitting the stochastic version of eq 13 and χ ) TRnt ) 0. setting TIχnt ) IDisft We used the same hardware and software for computations as in example 1. The model for case 1 involved 197 209 continuous variables, 144 binary variables, 23 980 constraints, and 367 807 nonzeros, whereas that for case 2 involved 49 639 continuous variables, 144 binary variables, 6370 constraints, and 81 403 nonzeros. The CPLEX solver solved case 1 in 25.471 s and gave ENPV ) $4.54 billion, whereas it solved case 2 in 2.972 s and gave ENPV ) $4.30 billion. As mentioned earlier, we compute the latter after we subtract the corporate taxes and import duties for each of the four distinct scenarios of import duties. As in example 1, the solutions of the two cases differ in many details, but the most striking difference is still in their expected NPVs (see Table 16). Without laboring through another round of in-depth comparison of the two solutions, we can say that the exclusion of the two regulatory factors in the stochastic capacity-planning model has once again misled the MNC to select a significantly inferior solution. This result clearly confirms the earlier assertion about the tremendous impact of regulatory factors on capacity-planning decisions, irrespective of whether one considers uncertainty in parameters. Through this example, we have demonstrated that one can use our deterministic model successfully to account for uncertainty in problem parameters. However, we must note that the scenario-planning approach did increase the solution time by a factor of 29 as compared to example 1. We expected this increase, as example 2 considered roughly 12 scenarios compared to 1 in example 1. It is well-known that the scenarioplanning approach is a simple, straightforward way to handle uncertainty, but it can be expensive in solution time when a large number of scenarios exist. Nevertheless, the importance of incorporating regulatory factors into capacity-expansion-planning models, the primary focus of this paper, still holds regardless of the efficiency of our scenario-planning approach. 9. Conclusion This paper has presented a new MILP model for deterministic capacity-expansion planning and material

sourcing in global chemical supply chains. Furthermore, it has demonstrated how the proposed deterministic model forms a basis for addressing the uncertainty in problem parameters. This paper has introduced and classified the major regulatory factors that can influence strategic decisions in the design and operation of chemical supply chains and has modeled and highlighted the effects of two important regulatory factors (corporate tax and import duty) in the capacity-planning decisions. This is in contrast to the existing models in the literature. The proposed models (deterministic and stochastic) treat the sizes of capacity expansions and new facility capacities as decision variables rather than prespecified fixed numbers, and they incorporate key supply-chain operation decisions, such as the sourcing of raw materials and the actual facility production rates, that can critically affect the strategic capacity-planning decisions. Although developed with a perspective of the CPI, the model’s generic nature makes it applicable to deterministic capacity-expansion planning in other manufacturing industries. For instance, by a simple modification or addition of some constraints, the proposed model can easily accommodate the requirements associated with new product development and introduction in the pharmaceutical industry and decisions about technology selection (flexible versus dedicated facility) in the consumer electronics industry. To the best of our knowledge, a capacity-expansion-planning model similar to the one presented here and with the aforementioned features for the deterministic capacity-expansionplanning problems does not exist in the literature. In addition to highlighting the importance of regulatory factors, this paper also identifies new research opportunities in the area of capacity-expansion planning. Import tariffs and corporate taxes are just only two of the several regulatory factors that directly influence the earnings of multinational manufacturing firm. Other regulatory factors such as repatriation taxes, withholding taxes, duty drawbacks, duty relief, offset requirements, etc., are also important, and capacity-expansion-planning models must account for them as well to achieve better decisions. To this end, the major challenges that researchers face include developing methods to translate these factors effectively into mathematical formulations and to solve the resulting complex SCEPs efficiently. Acknowledgment The authors acknowledge the financial support for this work under a Strategic Research Program Grant 00221050030 from the Agency for Science, Technology & Research (A*STAR), Singapore. The authors also thank Professor Marc Goetschalckx and Professor Martin Savelsbergh from Georgia Institute of Technology for valuable discussions during various stages of this project. Nomenclature Indexes c, s ) customer or supplier facility, respectively f, g ) internal or external facility, respectively (supplier, producer, or customer) i ) material n ) nation t, τ ) fiscal year χ ) scenario of uncertain parameter realizations

Ind. Eng. Chem. Res., Vol. 43, No. 13, 2004 3379 Sets EF ) external facilities from which the MNC sources raw materials or to which it sells finished products EIF ) existing facilities that the MNC owns Fn ) facilities located in nation n FIF ) future facilities that the MNC might build IF ) facilities owned by the MNC currently or in the future IMf ) incoming materials consumed by facility f OMf ) outgoing materials produced by facility f Parameters aft ) fixed cost of capacity expansion at facility f during period t bft ) variable cost of capacity expansion or new construction at facility f during period t cft ) fixed cost of constructing a facility at facility f during period t CBt ) MNC’s capital budget for capacity expansion or new facility construction during period t CEt ) MNC’s capital expenditure during period t CIFisft ) cost + insurance + freight charges of shipping a unit of material mi from supplier s to facility f during period t COifct ) cost that facility f incurs for outsourcing the production of a unit of material mi delivered to customer c during period t Dict ) demand for material mi by customer c during period t U Gift ) upper limit on the units of material mi that facility f can outsource during period t IDisft ) import duty imposed on material mi being shipped from supplier s to facility f during period t Lf ) project life of capital expenditure at facility f MCft ) variable production cost of manufacturing one unit of primary product π(f) by facility f during period t N ) number of countries NS ) number of scenarios of uncertain parameter realizations Pifgt ) unit selling price (exclusive of insurance and freight) of material mi charged by facility f to a different facility g during period t qLf ) lower limit on expansion size at facility f Qf0 ) initial capacity of facility f at time zero QLf ) lower limit on the size of new facility f QU f ) upper limit on the capacity at facility f r ) annual interest rate Sist ) amount of material mi that supplier s can supply to the MNC during period t T ) number of fiscal years in the planning horizon TRnt ) corporate tax rate in nation n during fiscal year t XLf ) lower limit on the number of units of primary product π(f) consumed or produced by facility f during every period t δ(f) ) number of years for each expansion or construction activity at facility f π(f) ) primary product associated with facility f σif ) coefficient of material mi in the mass balance equation of facility f φf ) binary parameter that is 1 if Qf0 > 0 and 0 otherwise ψχ ) probability of occurrence of scenario χ Variables Fifct ) units of material mi shipped from facility f to customer c during period t Fisft ) units of material mi shipped from supplier s to facility f during period t Gifct ) units of material i for customer c that facility f outsources during period t GIft ) gross income of facility f during period t

NDCfτt ) depreciation charge of facility f during period t due to capital expenditure during τ Qft ) production capacity of facility f at period t TInt ) taxable income of the MNC in nation n during period t xift ) units of material mi consumed or produced by facility f during period t Xft ) units of primary product π(f) consumed or produced by facility f during period t yft ) 1 if the MNC expands capacity at facility f during period t, 0 otherwise zft ) 1 if the MNC builds a new facility f during period t, 0 otherwise ∆qft ) amount of capacity expansion or construction at facility f during period t that is beyond the minimum allowed level Abbreviations CIF ) cost, insurance, and freight CPI ) chemical process industry FTA ) free trade agreement MNC ) multinational company NPV ) net present value

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Received for review December 27, 2003 Revised manuscript received April 16, 2004 Accepted April 26, 2004 IE034339G

Regulatory Factors and Capacity-Expansion Planning in Global

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