Risk sharing for internal resources conflict in two-stage process with slacks-based measure

Taking the two-stage process that the outputs from the first stage are taken as the inputs for the second stage as example, internal resources conflict refers to the mismatch in amount of intermediate products between two efficient stages. Although the existing centralized models can eliminate this conflict by maximizing the efficiency of entire system. In many real-world situations, however, because of decentralized organizational structure of system and independent operational mechanism of stages, each decentralized stage wants to maximize its own efficiency. This leads to the internal resources conflict, which is called the risk of mismatch in this paper. Therefore, this paper proposes the risk sharing strategy to eliminate such conflict by sharing this risk between two decentralized stages, and the slacks-based measure mixed integer linear program (MILP) model is developed to ensure that the risk allocated to each decentralized stage is minimal. Finally, the proposed method is illustrated through two examples. The results show that the proposed method can not only identify the target intermediate products to solve the potential conflict, but also make the efficiency score of inefficient system higher than that of inefficient system measured by the centralized method of “free” link constraint.