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 different technologies are considered in this study. Each warehouse has a specified 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 specified demand in each period is being satisfied 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 effect of the model parameters on the proposed SA algorithm.