DOI: 10.4018/IJSDS.2016040102 Copyright © 2016, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. International Journal of Strategic Decision Sciences Volume 7 • Issue 2 • April-June 2016 A Bi-Objective Vehicle Routing Problem with Time Window by Considering Customer Satisfaction Masoud Rabbani, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran Mahyar Taheri, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran Mohammad Ravanbakhsh, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran ABSTRACT The Vehicle Routing Problem (VRP) by considering Time Windows is an essential and a reality optimization problem consisting in the determination of the set of routes with minimum distance to carry goods, by using some vehicles with capacity constraint; vehicles must visit customers within a time frame. In the recent years, many numbers of algorithm have been considered to solve a single objective formulate of VRPTW problem, such as Meta-heuristic, bender’s decomposition, column generation and so on. This paper considers not only the minimum distance and the number of vehicles used to carry goods for customers. The customer satisfaction by considering the priority of the customers is considered which leads to service the customer as soon as possible. In this paper, the MOPSO and NSGAII approaches applied to solve the problem and then the authors compare the results of them; finally, they analysis the sensitivity of the capacity constraint for the vehicles KeyWORDS Customer Satisfaction, Multi Objective Optimization, Priority, Time Window, Vehicle Routing Problem 1. INTRODUCTION The vehicle routing problem is an integer programming problem that looks forward to service a number of customers with determined vehicles. It has always been represented as a problem that looks for optimum delivery or assortment of some routes from one or several depots to customers, subject to some constraints such as capacity constraint. For comprehensive details, (see, e.g., Laporte, 1992). For the first time, this problem was proposed by Dantzig and Ramser (1959), and has been studied broadly; (see, e.g., Solomon, 1987; Liu and Lai, 2009). The vehicle routing problem with time windows considers the time windows for each customer and sets the servicing of the customer to start and finish in their time windows. In the recent decade, this problem has attracted more and more attention from researchers. Vehicle routing is an essential activity for firms in the recent decade. For instance, in the United States, transportation cost shares more or less 10% of the gross domestic product (Bowersox and Calantone, 1998). From an economical point of view, improving the routing efficiency is more important than increasing fuel prices. The vehicle routing problem regards the planning of a set of minimum-cost vehicle routes, starting from and finishing in one or more than one depots, by some vehicles with a known capacity that service a set of customers with determined demands. Each customer is serviced by only one vehicle, and all the customers must be allotted to the vehicles without 16