A Hybrid Approach Based on LP Metric Method and Genetic Algorithm for the Vehicle-Routing Problem with Time Windows, Driver-Specific Times, and Vehicles-Specific Capacities

Abstract

Due to increasing population, increasing number of vehicles as well as environmental pollution, planning vehicles efficiently one of important problems nowadays. This article proposes a Multi-Objective Mixed Integer Programming (MOMIP) model for the vehicle-routing problem with time windows, driver-specific times and vehicles-specific capacities (VRPTDV), a variant of the classical VRPT that uses driver-specific travel and service times and vehicles-specific capacity to model the familiarity of the different drivers with the customers to visit. The first objective function aims to minimize traveled distance and the second objective function minimizing working duration. Since the problem is NP-hard, optimal solution for the instances of realistic size cannot be obtained within a reasonable amount of computational time using exact solution approaches. Hence, the hybrid approach based on LP metric method and genetic algorithm is proposed to solve the given problem.

An enhanced PSO algorithm to configure a responsive-resilient supply chain network considering environmental issues: a case study of the oxygen concentrator device

“…To examine the performance of the developed algorithms, we consider two measures: (1) the quality of solutions and (2) CPU time. It should be noted that CPU time is one of the critical metrics to compare the performance of the metaheuristic algorithms, which have been widely used in previous studies (see [ 21 , 48 , 63 , 68 , 88 , 91 , 92 ]). Since in small-sized instances, the global optimal solution is available, we apply the percentage relative error ( ) to assess the quality of the obtained solutions.…”

“…reducing greenhouse gases). To see other studies that considered these factors as EIs of the SC, interested readers can refer to [ 21 , 48 – 50 ]. On the other side, in general, since considering more other environmental factors might drastically increase the uncertainty of the problem, we considered the most important environmental factors based on our problem definition and case study.…”

“…Here, we explain the main reasons for employing the mentioned methods. The LP-metric method is a widely used approach to solve the multi-objective models, which has been applied in several previous studies to solve the multi-objective problems (for example, see [ 48 , 65 – 68 ]) and showed good performance. Also, the calculation in this method is simple and implementation is easy.…”

“…The LP-metric method is one of the widely used methods to solve the multi-objective models, which is more perceptible for executives compared to other methods, and in many cases of using this method, such as [ 48 , 65 – 68 , 72 ], acceptable results have been provided. In general, for the minimization objective function, the LP-metric method can be formulated as follows: …”

Robust design of a green-responsive closed-loop supply chain network for the ventilator device

“…In this section, the solution procedure of this study is presented. To solve the proposed MOMIP, we have two main challenges: (a) the proposed model is a multi-objective one and (b) the research problem is an NP-hard (Tiwari et al 2016 ; Asadi-Gangraj and Nayeri 2018 ; Çağrı et al 2018 ). In this regard, to cope with these challenges, we develop an efficient hybrid method.…”