Theory and Methodology
A global supply chain model with transfer pricing and transportation cost allocation

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Abstract

We present a model for the optimization of a global supply that maximizes the after tax profits of a multinational corporation and that includes transfer prices and the allocation of transportation costs as explicit decision variables. The resulting mathematical formulation is a non-convex optimization problem with a linear objective function, a set of linear constraints, and a set of bilinear constraints. We develop a heuristic solution algorithm that applies successive linear programming based on the reformulation and the relaxation of the original problem. Our computational experiments investigate the impact of using different starting points. The algorithm produces feasible solutions with very small gaps between the solutions and their upper bound (UB).

Introduction

The design and management of global supply chains are nowadays one of the most active research topics in global logistics. Vidal and Goetschalckx (1997) identify several lacking features and opportunities for research in the methodology for the strategic and tactical design of global logistics systems. Much of the research ignores relevant international factors such as transportation mode selection, the allocation of transportation cost among subsidiaries, the inclusion of inventory costs as part of the decision problem, the explicit inclusion of suppliers, and the nonlinear effects of international taxation. Additionally, many global supply chain models assume that transfer prices are fixed and given.

A transfer price is the price that a selling department, division or subsidiary of a company charges for a product or service supplied to a buying department, division, or subsidiary of the same firm (Abdallah, 1989). Transfer Pricing (TP) is one of the most controversial topics for multinational companies (MNCs). According to O'Connor (1997), “TP is the most important international tax issue facing multinationals today, and is expected to remain so for the near future.” In his survey of over 200 MNCs, 80% of them identified TP as the number one issue they have to face. Most researchers on global logistics have considered TP a typical accounting problem rather than an important decision opportunity that significantly affects the design and management of a global supply chain. In general, when a logistics analyst attempts to determine the optimal flows of products among facilities, the price of a product is almost always considered a given parameter. However, this is not the case in real global logistics systems since management can determine the transfer price with some degree of flexibility within given limits.

Undoubtedly, the TP problem is much more than an accounting problem. TP policies have significant effects on performance evaluation and motivation of subsidiary managers. Abdallah (1989) remarks that making TP decisions for MNCs is an important, complex, flexible, and complicated task because it affects other major functions of the firm such as marketing, production, location, transportation, and finance.

The impact of TP policies on taxable income, duties, and management performance is significant. According to Nieckels (1976), small changes in transfer prices may lead to significant differences in the after-tax profit of a company. On the other hand, the arbitrary manipulation of transfer prices (as presented by Cohen et al., 1989) is currently under careful observation by tax authorities and is strictly penalized. Despite these limitations and based on current regulations, in most of the cases, companies have some range of values for their transfer prices. According to Stitt (1995), the Organization for the Economic Cooperation and Development (OECD) defines a range of an acceptable transfer price rather than a single `correct' transfer price. Abdallah (1989) comments on the difficulty of using market prices as the selected TP policy in an international environment, mainly because of the diversity of economic environments and transportation costs. Moreover, there will always exist a tradeoff between the low transfer price desired by the buyer division, and the high transfer price desired by the seller division.

Several researchers have addressed the TP problem as an integral component of the optimization of a global supply chain. Nieckels (1976) presents a nonlinear mathematical model to determine optimal transfer prices and resource allocation in a multinational textile firm. His formulation includes transfer prices as decision variables and a linear objective function for maximizing the global net income after taxes. One limitation of this model is that it assumes that the company has a central distribution center from which all products are distributed to the sales subsidiaries. A second shortcoming of this model is that it does not include Bill of Materials (BOM) constraints, although these are significant to the real system. Instead, the problem is formulated as a raw material based model using some transformations of products into raw materials. Finally, the author does not address the decision of allocating transportation costs since they are always charged to the destination subsidiary.

Nieckel's solution approach begins with a heuristic procedure that assigns initial values to the transfer prices, equal to either their lower or their upper bound (UB). The remaining program is a linear program that is solved for the optimal flows. Given these flows, the set of transfer prices becomes variable again. To find the new set of transfer prices, a systematic heuristic procedure based on the sign of the derivative of the objective function with respect to the transfer prices is then applied. The solution method iterates between the optimization of the linear program and the heuristic procedure to change transfer prices until no further increase in the objective function is possible. According to the author, when the solution procedure stops, a local optimum is found. Although mentioned for further research, Nieckels does not attempt to calculate an UB on the solution to the problem in order to test the performance of his heuristic.

Cohen et al. (1989) present a preliminary formulation of a normative model that is a dynamic, nonlinear mixed integer programming formulation. The model is nonlinear due to the inclusion of transfer prices and decision variables to allocate overhead costs to plants. The objective function considers the maximization of the firm's after tax profit. Transfer prices are treated as a markup for each product, applied on the production cost plus the shipping cost, which includes tariffs. This constitutes a shortcoming of this model since in most cases the tariffs depend on the value of the transferred products and in the paper they are considered given as a part of the shipping cost per unit. The solution approach is a hierarchical process that iterates between solving mixed integer programs to determine optimal flows and supplier contracts, and optimal markups. This process is repeated until a local optimum has been reached. Since the markups do not have an upper bound, the resulting solution may generate a strong reduction of taxes that would not be acceptable to tax authorities.

No computational experience is presented in this paper, but the authors state that some variants of the model have been successfully developed by them and/or other researchers. One of these is the work by Cohen and Lee (1989), who describe a single-period multicommodity model that analyzes resource deployment decisions faced by a personal computer manufacturer. It is important to note that this is the only model that considers the decision of allocating transportation costs to either the origin or the destination by formulating binary variables. However, in the presented solution process, this decision is made externally and the corresponding binary variables are fixed in the model.

In one of the most comprehensive models to date, Arntzen et al. (1995) present a multi-period, multicommodity mixed integer program to optimize the global supply chain at the Digital Equipment Corporation. The objective function considers the minimization of variable production costs, inventory costs, shipping costs, fixed production and production `style' costs, minus the savings from duty drawbacks and duty relieves. All these terms are weighted by a factor α. The objective function also contains production time and transportation time terms, weighted by a factor (1−α). It is not clear how the model manages two different units of measure in the objective function beyond a user assigned weight. The TP decision problem is not included in the formulation. In addition, taxes are only indirectly considered as a part of variable production costs. The authors report on the use of `nontraditional methods', such as elastic constraints, row factorization, cascaded problem solution, and constraint-branching enumeration. However, it is not clear from the paper exactly which solution method has been applied.

More recently, Canel and Khumawala (1997) propose a mixed-integer single-product model for the optimization of a global supply chain. The authors include TP decisions in their analysis, but they fix the transfer prices to either their lower or UB before solving the model. Additionally, transportation costs are allocated to the destination subsidiary. As a consequence, this model does not include the TP problem and the allocation of transportation costs as part of the decision process.

The explicit inclusion of global suppliers is ignored in most of the models described above. Furthermore, inventory costs and their impact on the decision of selecting a transportation mode, which is very important in an international scenario, are not considered in most of them.

This paper presents a tactical global supply chain model that extends previous research by simultaneously considering TP, transportation cost allocation, inventory costs, and their impact on the selection of international transportation modes. Additionally, we provide an integrated and efficient procedure to obtain near-optimal solutions and their UB to realistic cases. In Section 2 we present some general considerations about TP. In Section 3 we describe the basic characteristics of the model, and in Section 4 we illustrate the solution approach. Section 5 contains some computational experiments, and finally, in Section 6 we present some conclusions and insights for further research.

Section snippets

Basic considerations on transfer pricing

The determination of transfer prices is one of the most difficult problems that MNCs have to face. The problem is to find adequate transfer prices so that the global corporate goals are satisfied and the performance measures are fair for all the firm's subsidiaries and divisions (Eccles, 1985). According to O'Connor (1997), the problem originates from the conflicts between the general goals of the global corporation and the internal goals of its subsidiaries, and from the constraints imposed by

The model

Fig. 4 illustrates the system under consideration. The suppliers are classified into two groups: internal suppliers and external suppliers. For the external suppliers there is no possible decision with respect to transfer prices since they sell directly to the company using market prices. For the internal suppliers a set of optimal transfer prices for the period under consideration is to be determined by the model. The manufacturing plants receive components and raw materials from the

General structure of the problem

Clearly, Problem P(x,t,v,p) is a non-convex optimization problem with a linear objective function, a set of linear constraints, and a set of bilinear equalities. The problem has the following general structure:P(x,t,v,p)MaximizedT0vsubject tocTrx+dTrv+xTArt+xTBrp=fr;r=1,2,…,m,Cxb,Tl⩽t⩽Tu,0p1,x⩾0,t⩾0,v⩾0,where Ar,Br(r=1,2,…,m)andC are the matrices of coefficients; b the right-hand side vector of flow-related constraints; cr(r=1,2,…,m),dr(r=0,1,2,…,m) the vectors of coefficients; fr(r=1,2,…,m)

Computational experience

The procedure described in the previous Section has been implemented using AMPL connected with CPLEX. All the experiments have been done in an IBM RS6000 model 590 with 512 MB of RAM. We have conducted extensive computational experiments using diverse starting points and two sets of instances of different sizes. All instances have been carefully generated to approximate real instances as much as possible. The main characteristics of these instances are shown in Table 3. In what follows, we

Conclusions and further research

In this paper we have presented a global supply chain model that includes explicitly TP and transportation cost allocation as decision variables. The model also considers the selection of transportation modes based on approximate expressions for the inventory costs generated by the utilization of each transportation mode. Since the resulting problem is NP-hard, we have developed a heuristic successive LP-solution procedure and UBs to test its performance. Our computational experience shows

Acknowledgements

This research was partially funded by the Instituto Colombiano para la Ciencia y la Tecnologia, COLCIENCIAS; by the Universidad del Valle, Cali, Colombia; and by the Fulbright Commission, administered by the Latin American Scholarship Program for the American Universities (LASPAU).

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