Data envelopment analysis approaches for two-level production and distribution planning problems

In this paper, we focus on a two-level production and distribution planning problem in the field of supply chain management, and examine the situations where the leader does not fully know the manufacturing technologies of the follower. In such a situation, the parameters representing the manufacturing technologies cannot be explicitly used to formulate the follower’s production planning problem. To overcome this difficulty, we propose formulations that implicitly express manufacturing technologies by using the input-output data observed from the production activities of the follower, incorporating the idea of data envelopment analysis (DEA). Assuming that the follower has multiple production facilities, we consider two possibilities of the observable input-output data and formulate two corresponding production planning problems; firstly, that only the input-output data aggregated for all the production facilities can be observed collectively, and secondly, that the input-output data for each of the production facilities can be observed separately. To clarify the validity of these DEA approaches, we compare them with the conventional formulation with technological coefficients using a numerical example.