The Bi-Objective Location-Routing Problem Based on Simultaneous Pickup and Delivery with Soft Time Window

The location-routing problem, while being new, is the most significant research field in location problems; features of vehicle-routing problem have been simultaneously considered along with the original problem for achieving high-quality integrated distribution systems, in addition to the global optimum. Contribution to the existing research presents the bi-objective multi-depot capacitated location-routing problem based on simultaneous pickup and delivery with soft time window (BOCLRPSPDSTW). Reasonable grounds that exhorted authors to get involved in this area and whence arising simultaneous pickup and delivery based on time window are the two main characteristics of logistic management that have been used separately in most of the location routing problem in spite of their various reallife applications with each other. Furthermore, market world competition circumstances always compel distribution managers to try creating a distribution system layout along with the lowest total system cost and enhancing service levels for providing customers’ satisfaction, such that they can make the perpetuity of the distribution systems possible in the competition. Accordingly, to achieve the main goal within the demonstrative bi-objective mixed-integer linear programming model for BOCLRPSPDSTW, this study addresses the minimization of summation of all problem costs and minimization of maximum summation of delivery times and service times for meeting customer service level with respect to simultaneous pickup and delivery with soft time windows. Since this type of problem is NP-hard, NSGAII and NRGA are proposed to attain the Pareto frontier for the given problem. To validate the performance of the proposed algorithms in terms of solution quality and diversity levels, various problems are carried out, and their efficiency based on some comparison metrics is compared.