Modelling and solving of a lot sizing problem for multiple items and multiple periods with shortage

This paper presents a multi-period inventory lot sizing scenario, where there is multiple product and single suppliers. It constructs a goal programming model to determine the order quantities of each product in each period. In this model, three goals are considered: 1) meeting the total available periodic budget, 2) meeting the buyer's maximum acceptable quality, 3) minimise the shortage. Constructing the approach in this way effectively reduces the risk of purchasing. The proposed approach provides flexibility to decision maker in multi-period procurement lot-sizing decisions. In other words, the purchase of any product in any period is determined as by the possibility to get closer to the goals defined in the model. It solves utilising GAMS and meta-heuristic algorithms, and analyses the efficiency of the heuristics. Efficiency of the proposed algorithm by comparing genetic algorithm in large size problems show the proposed algorithm has also better efficiency than genetic algorithm.