Transfer prices for multienterprise supply chain optimization

A key issue in supply chain optimization involving multiple enterprises is the determination of policies that optimize the performance of the supply chain as a whole while ensuring adequate rewards for each participant. In this work, a mathematical programming formulation is presented for fair, optimized profit distribution between members of multienterprise supply chains. The proposed formulation is based on a novel approach applying game theoretical Nash-type models to find the optimal profit level for each enterprise subject to given minimum profit requirements. A modeling framework for distributed profit optimization for an n-enterprise supply chain network is first presented. The supply chain planning problem is then formulated as a mixed-integer nonlinear programming model including a nonlinear Nash-type objective function. Model decision variables include intercompany transfer prices, production and inventory levels, resource utilization, and flows of products between echelons, subject to a deterministic sales profile, minimum profit requirements for each enterprise. and various resource constraints. A separable programming approach is finally applied utilizing logarithmic differentiation and approximations of the variables of the objective function. The resulting model is of the mixed-integer linear programming form. The applicability of the approach is demonstrated through case studies based on industrial processes relevant to process systems engineering.