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

Document Type : Original Manuscript


1 MSc, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Assistant Professor, Faculty of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


The location-routing problem is the most significant and yet new research field in location problems that considers simultaneously vehicle routing problem features with original one for achieving high-quality integrated distribution systems in beside of the global optimum. Simultaneous pickup and delivery based on time windows 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 real-life application with together. Furthermore, distribution manager always trying to create a distributed system layout along with the lowest total system cost and enhancing service levels for providing all customers satisfaction. Accordingly, in the current paper is considered the mentioned gap, that is to say the bi-objective capacitated location-routing problem based on simultaneous pickup and delivery with soft time window and multi depots (BOCLRPSPDSTW). For achieving the main goal, bi-objective mixed-integer linear programming model for BOCLRPSPDSTW, on the one hand minimizing summation of all problem costs and on the other hand, for meeting customer service level minimizing maximum summation of delivery times and service times are addressed. To solve the presented model, NSGAII and NRGA are proposed and at last efficiency of the anticipated solutions are depicted by testing them in a data set.


  • A Location-routing problem is considered
  • A bi-objective multi-depot capacitated location-routing problem based on simultaneous pick up and delivery with soft times window is studied
  • This study addresses the minimization of summation of all problem costs
  • Simultaneous pick up and delivey is considered