Single-item lot-sizing and scheduling problem with deteriorating inventory and multiple warehouses

This paper introduces a Single-Item Lot-sizing and Scheduling Problem with Multiple Warehouses (SILSP-MW). In this problem, the inventory deteriorates over time, depending on the warehouse conditions, so multiple warehouses with dierent technologies are considered in this study. Each warehouse has a specied deterioration rate and holding cost. The purpose of the SILSP-MW is to determine production periods and quantities, and to select the appropriate warehouse to hold the inventory in each period, such that specied demand in each period is being satised while the total cost is minimized. We shall present a Mixed-Integer Linear Programming (MILP) formulation to model the problem. Moreover, a Simulated Annealing (SA) algorithm will be presented to solve this problem. We will evaluate the performance of the algorithm by computational experiments with small- and medium-sized examples. In addition, a full factorial design is developed to investigate the eect of the model parameters on the proposed SA algorithm