The Capacitated Lot Sizing Problem with Batch Ordering: A MILP and Heuristic Approach

Abstract

This article presents a mixed integer linear programming method and a heuristic algorithm to deal with the problem of multi-period, multiple-product batch purchases, with a finite time horizon, considering delivery times, order placement costs and independent batch size for each product. The objective of this problem is to minimize the costs of placing purchase orders and inventory. This problem is motivated by its application in a marketing company that handles the sale of fashion products (footwear and accessories) through catalogs and for which excess inventory represents a major problem given the short life cycle of its products. Experimental results show that the heuristic algorithm is able to obtain feasible solutions that improve in cost by up to 37% the best integer solutions reported by the model when it reaches the time limit. To validate the efficiency of the algorithm, a real scenario was solved for a trading company, obtaining results that improve by 28% compared to the current company’s situation. These results show that the heuristic approach is promising in terms of the quality of the solution and the computational time required.