Multi‐objective models for lot‐sizing with supplier selection

In this paper, two multi‐objective mixed integer non‐linear models are developed for multi‐period lot‐sizing problems involving multiple products and multiple suppliers. Each model is constructed on the basis of three objective functions (cost, quality and service level) and a set of constraints. The total costs consist of purchasing, ordering, holding (and backordering) and transportation costs. Ordering cost is seen as an ‘ordering frequency’‐dependent function, whereas total quality and service level are seen as time‐dependent functions. The first model represents this problem in situations where shortage is not allowed while in the second model, all the demand during the stock‐out period is backordered. Considering the complexity of these models on the one hand, and the ability of genetic algorithms to obtain a set of Pareto‐optimal solutions, we apply a genetic algorithm in an innovative approach to solve the models. Comparison results indicate that, in a backordering situation, buyers are better able to optimize their objectives compared to situations where there is no shortage. If we take ordering frequency into account, the total costs are reduced significantly.