Survey on Ten Years of Multi-Depot Vehicle Routing Problems: Mathematical Models, Solution Methods and Real-Life Applications

A crucial practical issue encountered in logistics management is the circulation of final products from depots to end-user customers. When routing and scheduling systems are improved, they will not only improve customer satisfaction but also increase the capacity to serve a large number of customers minimizing time. On the assumption that there is only one depot, the key issue of distribution is generally identified and formulated as VRP standing for Vehicle Routing Problem. In case, a company having more than one depot, the suggested VRP is most unlikely to work out. In view of resolving this limitation and proposing alternatives, VRP with multiple depots and multi-depot MDVRP have been a focus of this paper. Carrying out a comprehensive analytical literature survey of past ten years on cost-effective Multi-Depot Vehicle Routing is the main aim of this research. Therefore, the current status of the MDVRP along with its future developments is reviewed at length in the paper

Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems

Due to globalization in this modern age of technology and other uncontrollable influences, transportation parameters can differ within a certain range of a given period. In this situation, a managerial position’s objective is to make appropriate decisions for the decision-makers. However, in general, the determination of an exact solution to the interval data-based transportation problem (IDTP) becomes an NP-hard problem as the number of choices within their respective ranges increases enormously when the number of suppliers and buyers increases. So, in practice, it is difficult for an exact method to find the exact solution to the IDTP in a reasonable time, specifically the large-sized problems with large interval sizes. This paper introduces solutions to the IDTP where supply, demand, and cost are all in interval numbers. One of the best interval approximations, namely the closed interval approximation of pentagonal fuzzy number, is proposed for solving the IDTP. First, in the proposed closed interval approximation method (Method-1), the pentagonal fuzzification method converts the IDTP to a fuzzy transportation problem (FTP). Subsequently, two new ranking methods based on centroid and in-center triangle concepts are presented to transfer the pentagonal fuzzy number into the corresponding crisp (non-fuzzy) value. Thereafter, the optimal solution was obtained using Vogel’s approximation method coupled with the modified distribution method. The proposed Method-1 is reported against a recent method and shows superior performance over the aforementioned and a proposed Method-2 via benchmark instances and new instances

An efficient alternative approach to solve a transportation problem

Determination of an Initial Feasible Solution (IFS) to a transportation problem plays an important role in obtaining a minimal total transportation cost solution. Better initial feasible solution can result less number of iterations in attaining the minimal total cost solution. Recently, an efficient method denoted by JHM (Juman and Hoque’s Method) was proposed to obtain a better initial feasible solution to a transportation problem. In JHM only column penalties are considered. In this paper, a new approach is proposed with row penalties to find an IFS to a transportation problem. The new method is illustrated with a numerical example. A comparative study on a set of benchmark instances shows that the new method provides the same or better initial feasible solution to all the problems except one. Thus, our new method can be considered as an alternative technique of attaining an initial feasible solution to a transportation problem

Five years of multi-depot vehicle routing problems

With vast range of applications in real life situations, the Vehicle Routing Problems (VRPs) have been the subject of countless studies since the late 1950s. However, a more realistic version of the classical VRP, where the distribution of goods is done from several depots is the Multi-Depot Vehicle Routing Problem (MDVRP), which has been the central attraction of recent researches. The objective of this problem is to find the routes for vehicles to serve all the customers at a minimal cost in terms of the number of routes and the total distance travelled without violating the capacity and travel time constraints of the vehicles, and it is handled with a variety of assumptions and constraints in the existing literature. This survey reviews the current status of the MDVRP and discuss the future direction regarding this problem

Attaining a good primal solution to the uncapacitated transportation problem

Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. The Uncapacitated Transportation Problem (UTP) is a special case of network flow optimization problem. The prime objective of this UTP is to minimize the total cost of transporting products from origins to destinations subject to the respective supply and demand requirements. The UTP consists of special network structure. Due to the special structure of this problem, the transportation algorithm is preferred to solve it. The transportation algorithm consists of two major steps: 1) Finding an Initial Feasible Solution (IFS) to TP and 2) Examining the optimality of this IFS. A better IFS generates a lesser number of iterations to obtain a Minimal Total Cost Solution (MTCS). Recently, Juman and Nawarathne (2019)’s Method was introduced to find an IFS to UTP. In this paper, the Juman and Nawarathne (2019)’s Method is improved to get a better IFS to a UTP. A comparative study on a set of benchmark instances illustrates that the new improved method provides better primal solutions compared to the Juman and Nawarathne (2019)’s Method. The proposed method is found to yield the minimal total cost solutions to all the benchmark instances

Modeling a cost benefit transportation model to optimize the redistribution process: Evidence study from Sri Lanka

This study is a case study based on Softlogic Retail (Pvt) Ltd, Sri Lanka, which is a famous consumer electronics company and market leader in Sri Lanka. This company’s outbound logistics have been considered in this research, and they are mainly forced into the redistribution process in Sri Lanka. Extra routing costs due to unreasonable consumption of additional distance have been noticed in the current redistribution process. Here, this problem is modeled as a variant of the vehicle routing problem with a heterogeneous vehicle fleet. Our objective is to minimize warehouse operation, administration, and transportation costs by imposing constraints on capacity and volume. The researchers propose new heuristic solutions to the problem. A proposed heuristic algorithm has been used to find the optimal path between clusters. The computational investigation highlights the cost savings that can be accrued by this new heuristic. The cost savings can be accrued at a rate of as much as 37.5 % compared to the company’s existing method

Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems

Due to globalization in this modern age of technology and other uncontrollable influences, transportation parameters can differ within a certain range of a given period. In this situation, a managerial position’s objective is to make appropriate decisions for the decision-makers. However, in general, the determination of an exact solution to the interval data-based transportation problem (IDTP) becomes an NP-hard problem as the number of choices within their respective ranges increases enormously when the number of suppliers and buyers increases. So, in practice, it is difficult for an exact method to find the exact solution to the IDTP in a reasonable time, specifically the large-sized problems with large interval sizes. This paper introduces solutions to the IDTP where supply, demand, and cost are all in interval numbers. One of the best interval approximations, namely the closed interval approximation of pentagonal fuzzy number, is proposed for solving the IDTP. First, in the proposed closed interval approximation method (Method-1), the pentagonal fuzzification method converts the IDTP to a fuzzy transportation problem (FTP). Subsequently, two new ranking methods based on centroid and in-center triangle concepts are presented to transfer the pentagonal fuzzy number into the corresponding crisp (non-fuzzy) value. Thereafter, the optimal solution was obtained using Vogel’s approximation method coupled with the modified distribution method. The proposed Method-1 is reported against a recent method and shows superior performance over the aforementioned and a proposed Method-2 via benchmark instances and new instances