Self-evolution Algorithm for a multi-product dynamic lot-sizing and shipping problem with multi-freight container types

This paper analyzes a dynamic lot-sizing problem, in which the order size of multiple products and multiple container types are simultaneously considered. In the problem, each ordered products placed in a period is immediately shipped by multiple freight containers in the period. Moreover, each container has type-dependent carrying capacity restriction. The unit freight cost for each container type depends on the size of its carrying capacity and the total freight cost is proportional to the number of each container type employed. Also, it is assumed that the load size of each product is equal and backlogging is not allowed. The objective of this study is to simultaneously determine the lot-sizes and the shipment schedules that minimize the total costs, which consist of production cost, inventory holding cost, and freight cost. Because this problem is NP-hard, we propose simulated annealing algorithm (SA) and a new population-based evolutionary meta-heuristic called self-evolution algorithm (SEA) using a local search heuristic algoritnm being included. Computational results demonstrate the efficiency of the developed algorithm.