The multi-level warehouse layout problem with uncertain information: uncertainty theory method

Abstract

This paper investigates the multi-level warehouse layout problem with indeterminate factors, in which the monthly demands and horizontal transportation distances are described by uncertain variables. We first consider the distribution function of the total cost for transportation. Second, two uncertain models, namely, the chance-constrained programming model and the chance-maximum programming model, are developed to lay out the multi-level warehouse under uncertainty. Some properties of the models are discussed to solve the models. The properties point out that the optimal solution to the chance-constrained programming model is equivalent to a corresponding deterministic model. Additionally, we also discuss the relation between the chance-constrained programming model and the chance-maximum programming model, which leads to an effective approach to search for the optimal solution to the chance-maximum programming model. Finally, a numerical experiment is illustrated to show the ideas of the proposed models.