Fair transfer price and inventory holding policies in two-enterprise supply chains

A key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant. In this paper, we present a mathematical programming formulation for fair, optimised profit distribution between echelons in a general multi-enterprise supply chain. The proposed formulation is based on an approach applying the Nash bargaining solution for finding optimal multi-partner profit levels subject to given minimum echelon profit requirements. The overall problem is first formulated as a mixed integer non-linear programming model. A spatial and binary variable branch-and-bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree, a mixed integer linear programming problem is solved. The solution comprises interfirm transfer prices, production and inventory levels, flows of products between echelons, and sales profiles. The applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes.