Simplified Swarm Optimization for the Time Dependent Competitive Vehicle Routing Problem with Heterogeneous Fleet

Nowadays, due to the development of e-commerce, delivery time has become an important factor influencing quality of distribution service. Especially in the urban distribution environment, many factors affect the distribution time, such as traffic condition on peak hours plays an important role in outcomes of the planned schedule. Hence, more and more research devoted to the “Time-depend vehicle routing problem (TDVRP)”. Consider the competitors' factors for obtaining more sales, logistics company should serve customers before other rival distributors. Such problem is called “Time-depend vehicle routing problem in a competitive environment (TDVRPC)” whose main objectives of the problem are to minimize the travel time cost and maximize the sale. Many research papers have presented mathematical models for TDVRPC. The major weakness of the above models is they donot satisfy the “first-in-first-out (FIFO)” property which guarantee that if a vehicle leaves a for at a given time, any other vehicle leaving earlier will arrive earlier. Take into account the possible ways of handling the situation with heterogeneous fleet, so a novel model for the “Time-dependent vehicle routing problem in a competitive environment with heterogeneous fleet (TDVRPCHF)” is presented to satisfy the “FIFO” property. To solve such a problem, a Simplified Swarm Optimization algorithm is proposed and it can also be promoted on the other “time-dependent vehicle routing problem”.

I. Introduction

Vehicle routing problem (VRP) have a significant role in logistics and distribution industries. The vehicle routing problem is to find the routes of customers to be visited that minimize total cost, satisfying some constraints.