A robust multi-supplier multi-period inventory model with uncertain market demand and carbon emission constraint

Abstract

The multi-period inventory management determines the optimal order quantity of products at the beginning of each period, which is an important research issue in supply chain management. In this paper, we propose a robust multi-supplier multi-period inventory model with uncertain market demand and uncertain unit carbon emission in transportation. We select product quality, ordering cost, service level, and emergency capacity as evaluation criteria for each supplier, employ analytic hierarchy process (AHP) technique to comprehensively evaluate and score each supplier. According to the evaluated score, the order weight for each supplier is obtained. In our model, we develop carbon emission constraint based on the carbon cap and carbon trading mechanism. As for uncertain market demand and uncertain unit carbon emission in transportation, we construct Box+Ball and Budget uncertainty sets to characterize various model uncertainties. The robust inventory model is a semi-infinite programming model, and cannot be solved directly. We transform the semi-infinite programming model into a mixed-integer second-order cone-programming (MISOCP) one via cone duality theory. Finally, the effectiveness of the proposed optimization method is illustrated by a case study.