Inventory management for one warehouse multi-retailer systems with carbon emission costs

Abstract

In this paper, we study inventory management for the one warehouse multi-retailer (OWMR) system with considering carbon emissions, in which we determine the reorder intervals for the warehouse and the retailers while minimizing the inventory ordering and holding cost and the carbon emission cost. We consider the carbon emissions from the holding and replenishing inventory activities in the OWMR system, and calculate the carbon emissions based on the frequency of the inventory replenishment at the warehouse and the retailers. We focus on stationary and integer-ratio policies, and formulate the problem as an optimization model with a convex objective function and a set of integer-ratio constraints. We relax the integer-ratio constraints, and introduce an algorithm to solve the corresponding relaxed problem to optimality in O(nlogn) times, where n represents the number of retailers. Based on the optimal solution of the relaxed problem, we build an integer-ratio policy, i.e., power-of-two (POT) policy, with 94% optimality for the primal problem. The computational results show that with considering the carbon emission cost, the reorder intervals of the warehouse and the retailers both increase, and that the integrated model proposed in this paper has more superiorities in terms of reducing the system-wide cost and the carbon emissions.