Multi-item dynamic lot-sizing model with business volume discount and bounded inventory

This paper addresses multi-product dynamic lot sizing problem with bounded inventory and multi-breakpoints business volume discount. In this problem, we take into account major and minor setup costs. The discount modes involve all-units and incremental discount. A GA-based heuristic algorithm to solve the problem is designed, in which the genome is composed merely of the decision variables that indicate whether some product is purchased in some period. To handle the constraints of limited inventory, a repair operator is designed with time complexity of O(TN(log(N)+1))+O(TN(log(N)+T)) where T is the length of planning horizon and N is the number of categories to purchase. Finally, by means of the real life data originated from a dairy products dealer, the effectiveness of the proposed algorithm is validated.