Designing a model of product arrangement and multi-warehouse location-routing problem

This paper presents a m model of product arrangement and multi-warehouse location-routing problem under uncertainty. In the first stage of the designed model, the main goal is to arrange products in packages that can be sent to the customer. The second stage aims to locate potential warehouses and optimally route vehicles. Therefore, the objective function of the first stage includes the sum of the optimal dimensions of the packages, and the objective functions of the second stage include the simultaneous optimization of location-routing costs and the amount of greenhouse gas emissions. Due to the uncertainty of the designed model and considering the demand parameters and transmission costs in the form of trapezoidal fuzzy numbers, in this paper, the robust fuzzy optimization method is used to control the uncertainty parameters. Due to the NP-Hard nature of the designed model, the invasive weed optimization is used to determine the optimal dimensions of the packages and the arrangement of products in the packages in the first stage. In addition, the NSGA II is used to find efficient solutions to the problem in the second stage.The results of model implementation in a real case study in Safir Company have shown ten efficient solutions. By reviewing the efficient solutions, the most appropriate efficient solution for the management of Safir Company in Iran is presented. In this article, a two-stage model of product packaging and vehicle routing with simultaneous pickup and delivery under uncertainty is presented, which uses the robust fuzzy optimization method to control uncertainty and different methods to solve the problem.