CHAPTER 6 GAME-THEORETICAL MODEL FOR DECENTRALIZED
6.2 Problem Statement and Assumptions
Assume that a number of MNCs producing and selling substitutable products compete with each other worldwide via their respective two-echelon global supply chains comprising plants and DCs. These two-echelon global supply chains with market competition are referred to as the decentralized global supply chain. In each individual two-echelon global supply chain owned by an MNC, plants produce or assemble a product and DCs purchase the product from the plants and sell them to consumers. To maximize after-tax profit, each MNC involved in the decentralized global supply chains seek an optimal plan of production, distribution, pricing and transportation cost allocation, which consists of quantity of the product produced at a plant, price of the product quoted by a DC, transfer price, and the shipment of the
product and transportation cost allocation between a plant and a DC. It is interested in characterizing and finding an equilibrium solution in terms of the production-distribution, pricing and transportation cost allocation plan for each MNC involved in the decentralized global supply chain by assuming that all the MNCs which are incentive to maximize their own after-tax profit compete each other without cooperation.
Given a two-echelon global supply chain owned by an MNC, it is assumed that each DC in the global supply chain buys the product from only one plant. Such an assumption is known as the single-sourcing strategy and has been used by Huang et al.
(2005) and Romeijn et al. (2007). Since the currency exchange rate, import duty rate and income tax rate, transfer price, called the international economic parameters, vary over different countries, they should be thus taken into account by each MNC in making the optimal the production, distribution, pricing and transportation cost allocation plan for maximizing the after-tax profit. More interestingly, the MNC is able to coordinate transportation cost allocation between its plants and DCs to reduce tax paid because these plants and DCs belong to the same MNC.
Because corporate income tax rates of a country are usually comprised by several brackets, these tax brackets are numbered by consecutive integers starting from number 1, namely,
{
1, 2,..., , and assume that the larger the tax bracket number is, the}
bigger the income tax rate will be. It is further assumed that demand for the product at a DC owned by an MNC is a function of selling prices quoted by those DCs located in
The following is notation that will be used throughout this chapter, including indices, sets, parameters and decision variables.
Sets and indices
{
1, 2,...,C}
Set of MNCs involved in the decentralized global supply chains, indexed by c , where C is total number of the MNCs.M Set of countries where plants in the decentralized global supply chain are located, indexed by m .
N Set of countries where DCs in the decentralized global supply chain are located, indexed by n .
c
Pm Set of plants owned by MNC c and located in country m M∈ , indexed by i.
ci
W nm Set of DCs owned by MNC c , located in country n N∈ and purchasing the product from plant i∈Pmc, indexed by j .
{
1, 2, ,}
Sm = Set of corporate income tax brackets of country m M∈ , indexed by s.
{
1, 2, ,}
Sn = Set of corporate income tax brackets of country n N∈ , indexed by ˆs .
International economic parameters
DUTY mn Import duty rate on the value of product shipped from country m∈M to country n N∈ .
E m Currency exchange rate of country m M∈ to US dollars [US dollars/monetary units of country m ].
E n Currency exchange rate of country n N∈ to US dollars [US dollars/monetary units of country n ].
TPR m Maximal transfer price perturbation range of product imposed by tax authority of country m M∈ [monetary units of country
m∈M ].
Costs, production capacity and demand function associated with MNC c∈ C
c
TC ij Unit transportation cost excluding import duty of product shipped from plant i of MNC c to DC j of MNC
c [monetary units of the country where plant i is located /unit of product].
(
,)
c c z−c Demand function for product at DC j located in country
n∈ , owned by MNC c , where N z is selling price of the cj product quoted by DC j located in country n N∈ , and z is n−c a row vector of all the selling prices of the product quoted by those DCs located in country n but owned by the other MNCs, namely,
Decision variables associated with MNC c∈ C
c [monetary units of the country where DC j is located /unit of product].
c
α ij Fraction of transportation cost allocated to plant i of MNC c for transporting product from plant i of MNC c to DC j of MNC c .
In relation to the incorporate income tax rates, without loss of generality, it is assumed that
0 0; 0 0; s 1 s ; s 1 s, ,
m m m m m m m
TAX = U = TAX − ≤TAX U − ≤U s∈S m∈M (6.1)
TAXn0 =0;Un0=0;TAXnsˆ−1≤TAXnsˆ ;Unsˆ−1≤U snsˆ,ˆ∈S nn, ∈M (6.2) Eqns. (6.1)-(6.2) reflect the stepwise corporate income rate. For any DC j owned by
MNC c , it is assumed that demand function for the product has the partial linear continuous differentiable function with respect to vector z . It should be pointed out n−c that the price-sensitive linear demand function has been postulated by many game theoretical applications in domestic supply chain management (Corbett and Karmarker, 2001; Leng and Parlar, 2005). Our partial linear demand function defined by eqn. (6.3) is obviously more generic than those linear demand functions used in the literature.
6.3 Two Maximization Models to Characterize Behavior of an Individual MNC in