Perishable inventory control with backlogging penalties: A mixed-integer linear programming model via two-step approximation

Abstract

This study proposes a novel approximate mixed-integer linear programming (MILP) model for the perishable inventory control problem considering non-stationary demands and backlogging penalties. Because of the existence of the waste costs incurred by outdated products in the cost function, it is difficult to apply the linearization technique employed for the non-perishable inventory control problem directly to our problem. To address this difficulty, we develop a two-step approximation method. In the first step, we approximate each expected cost to simplify the cost function, making it easy to handle. In the second step, we apply an existing linearization technique to linearize this function and then obtain the MILP model. We evaluate the proposed model in computer simulations by comparing it with other existing methods. The results show that our model closely matches a benchmark method capable of obtaining near-optimal solutions in solution quality, and it achieves a better trade-off between solution quality and computational efficiency than existing heuristics.