An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

Abstract

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied.Unit of measure: min.Symmetry 2018, 10, 650 9 of 20 Table 6 lists the problem configurations for the three cases, including the number of periods, number of suppliers, number of vehicles, size of the transportation network, number of variables for the MIP, and number of constraints for the MIP. In the first case, there are five periods, the number of suppliers is five, the number of vehicles is three, the transportation network is 6 × 6, and the numbers of variables and constraints for the MIP model are 931 and 1171, respectively. In the second case, there are seven periods, the number of suppliers is nine, the number of vehicles is four, the transportation network is 10 × 10, and the numbers of variables and constraints for the MIP model are 3903 and 3977, respectively. In the third case, there are nine periods, the number of suppliers is 12, the number of vehicles is five, the transportation network is 13 × 13, and the numbers of variables and constraints for the MIP model are 9758 and 9919, respectively.

Scenario Analysis–Based Decision and Coordination in Supply Chain Management with Production and Transportation Scheduling

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Development of a Novel Freight Railcar Load Planning and Monitoring System

“…The authors compare the model to the CVRP with sequence-based pallet loading without axle weight restrictions and conclude that not including axle weight restrictions may induce major violations of axle weight limits. Kang et al [23] define the problem as follows: heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. Different types of vehicles have different loading capacities and different travelling distance limits.…”

“…Consequently, popular metaheuristics such as genetic algorithms, tabu search and simulated annealing, as well as heuristics based on the familiarity with the real problem, are often used to solve cargo loading problems. There were numerous papers in the past that used genetic algorithms (GA) for the CLP, while many papers do so even today [23,27,28]. Consequently, the paper [28] presents an adaptive GA, based on the general loading mathematical model aiming to maximize space utilization.…”

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

“…Although the TSP is an old problem whose origin is not well known, many studies on it are still carried out, as is the case with [4]. The VRP is addressed in studies dedicated to graph theory and algorithms [5] and, especially, several research works related to different problems involving vehicles and routes were published considering symmetry aspects [6][7][8][9][10]. As global trade expanded and led to a significant growth in the demand for transport, the resolution of VRPs, introduced by Dantzig and Ramser [11], became increasingly essential for enterprises looking to efficiently manage their transport and coordinate their supply chain.…”