Offering a Mathematical Model and Heuristic Method for Solving Multi-Depot and Multi-Product Vehicle Routing Problem with Heterogeneous Vehicle (original) (raw)
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2015
Vehicle Routing Problem (VRP) is one of the most challenging problems in combinatorial optimization. Objective of VRP is to find minimum length route starts and ends in a depot. There are some additional constraints such as more than one depot, service time, time window, capacity of vehicle, and many more. These are cause of VRP variants. Vehicle Routing Problem with Time Windows (VRPTW) is a variant of VRP with some additional constrains, that are number of requests may not exceed the vehicle capacity, as well as travel time and service time may not exceed the time window. Multi Depot Vehicle Routing Problem (MDVRP) has number of depots serving all customers, a number of vehicles distributing goods to customers with a minimum distance of distribution route without exceeding the capacity of the vehicle. Many researches have presented algorithms to solve VRPTW and MDVRP. This article discusses solution characteristics of VRPTW and MDVRP algorithms, and their performance. VRPTW algori...
Sustainable Development Research
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.
International Journal of Recent Technology and Engineering
This paper introduces the multi depot vehicle routing problem (MDVRP) with location depot, a hard combinatorial optimization problem arising in several applications. The MDVRP with location depot based on two well-known NP-hard problems: the facility location problem (FLP) and the multi depot vehicle routing problem (MDVRP) with location depot. In the first phase, the problem consists of selecting on which sites to install a warehouse and assigning one and only one warehouse to each customer. In the second phase, for each depot, we search to solve a vehicle routing problem (VRP), multiple vehicles homogenous leave from a single depot and return to the same one. Each route must respect the capacity of each vehicle. The goal of this problem is to minimize the total distances to the performed routes. The MDVRP with location depots is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to solve this problem. In this work, we propose a method to solve it to optimality. The proposed procedure initially uses K-means algorithm to optimize the location selection and customer assignment, then planning the routes from the selected warehouses to a set of customers using Clarke and Wright saving method. The routes from the resulting multi-depot vehicle-routing problem (MDVRP) are improved using a Genetic Algorithm (GA). The proposed approach is tested and compared on a set of twelve benchmark instances from the MDVRP literature. The computational experiments confirm that our heuristic is able to find best solutions.
A systematic review of multi-depot vehicle routing problems
Systematic Literature Review and Meta-Analysis Journal
Multi-Depot Vehicle Routing Problem (MDVRP) is a heuristic optimization problem that capture interest of several researchers' for its applicability to real-life situations. The variant of MDVRP are solved with some certain constraints such as service time, time window, vehicle capacity, travelled distance etc. these makes MDVRP to cover several situations In this, 76 studies related to MDVRP from 2012 to 2022 were systematically reviewed. The studies are review based on their constraints and an application through various fields. The goal of this research is to examine the contemporary state of MDVRP and its applications. To achieve this goal, we formed a comprehensive search process which was employed on high rated scientific journals databases. The search process resulted to numerous important research papers in the research domain which were theoretically reviewed. The research papers found are screened based on the titled, abstract, year of publication and exhaustive reading...
A metaheuristic algorithm for the Multi-Depot Vehicle Routing Problem
This paper proposes a metaheuristic algorithm to solve the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDHFVRP). The problem consists of determining the customers and the vehicles to be assigned to each used depot and the routes to be performed to fulfill the demands of a set of customers. The objective is to minimize the sum of the fixed cost associated with the used vehicles and of the variable traveling costs related to the performed routes. The proposed approach is based on a modified genetic algorithm, which generates an initial population with heuristic solutions obtained from the well-known (LKH) heuristic algorithm for the TSP together with the solution of a mathematical model for the shortest path problem. In addition, two recombination methods and a mutation operator are considered. Computational experiments on benchmark instances show that the proposed algorithm can obtain high-quality solutions within short computing times.
Uncertain Supply Chain Management, 2019
This paper presents a model to solve the multi-objective location-routing problem with capacitated vehicles. The main purposes of the model are to find the optimal number and location of depots, the optimal number of vehicles, and the best allocation of customers to distribution centers and to the vehicles. In addition, the model seeks to optimize vehicle routes and sequence to serve the customers. The proposed model considers vehicles' traveled distances, service time and waiting time while guaranteeing that the sum of these parameters is lower than a predetermined value. Two objective functions are investigated. First objective function minimizes the total cost of the system and the second one minimizes the gap between the vehicles' traveled distances. To solve the problem, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is developed. The efficiency of the MOICA is demonstrated via comparing with a famous meta-heuristics, named Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Based on response surface methodology, for each algorithm, several crossover and mutation strategies are adjusted. The results, in terms of two well-known comparison metrics, indicate that the proposed MOICA outperforms NSGA-II especially in large sized problems.
On Solving the Multi-depot Vehicle Routing Problem
Smart Innovation, Systems and Technologies, 2015
The Mult i-Depot Veh icle Routing Problem (MDVRP), an extension of classical VRP, is a NP-hard problem for simu ltaneously determining the routes for several vehicles fro m mu ltip le depots to a set of customers with demand and then return to the same depot. Main goal of this thesis is to solve MDVRPSD in three phases. Firstly we've used nearest neighbour classification method for grouping the customers, then Su m of Subset method have been used for routing. Finally the routes are optimized using greedy method. The routes obtained using these methods are better for the vehicles considering demands of the customers. As an input we consider here some customers position, the depots position. Also the demand is in itialized randomly. Here we solve the problem for 4 depots to 10 depots. The input customer ranges fro m 20 to 50. Then by using the three-phases the problem is solved for the input combinations. Actually the main target to solve this problem is to reduce the number of vehicles needed to serve the customers. We have to serve the customers of a definite route by a vehicle. So if the routes are min imized then number of needed vehicles is also min imized. The t ime is also an impo rtant issue. So the time is also measured for solving the whole problem with three-phases. So at the last part of the paper the performance is measured according to time for solving the problem and the number of vehicle needed for each of the problem.
A new hybrid algorithm for multi-depot vehicle routing problem with time windows and split delivery
International Journal of Industrial and Systems Engineering, 2012
Effective coordination of distribution operations of a manufacturing organization is paramount since it represents the major cost component of the logistic supply chain. In order to deal with high demand of orders with shorter lead time, distributed warehouse concept is introduced and this is currently being practiced. Furthermore, due to inherent deficiencies in VRP, rules have been extended to accommodate large scale orders by splitting the delivery. Artificial Intelligences (AI) based approaches widely used in the literature to solve VRP problems with extensions. In this research, hybrid algorithm (SATS) is developed based on Simulated Annealing (SA) and Tabu Search (TS) techniques to improve the solution quality of the complex Multi Depot Vehicle Routing Problem with Time Windows and Split Delivery (MDVRPTWSD). The simulation results reveal that SATS outperform in solution quality and the computational time.
Latin American applied …, 2003
The vehicle routing problem (VRP) has become a crucial industrial issue for its impact on product distribution costs. Though quite important in practice, the time-constrained version of the VRP accounting for several types of vehicles and mdepots, called the extended VRP with time windows (m-VRPTW), has received less attention. Since it is an NP-hard problem, most of the current approaches to m-VRPTW are heuristic, thus providing good but not necessarily optimal solutions. This work presents a novel MILP mathematical framework for the m-depot heterogeneous-fleet VRPTW problem. The new optimization approach permits to find both the optimal vehicle route/schedule and the fleet size by choosing the best set of preceding nodes for each pickup point. To get a significant reduction on the problem size to tackle larger m-VRPTW problems, some elimination rules have been embedded in the MILP framework. When applied to a pair of examples, it was observed a remarkable saving in computer costs with regards to prior VRPTW optimization methods.
The Multi-Depot Split-Delivery Vehicle Routing Problem: Model and Solution Algorithm
Logistics and supply-chain management may generate notable operational cost savings with increased reliance on shared serving of customer demands by multiple agents. However, traditional logistics planning exhibits an intrinsic limitation in modeling and implementing shared commodity delivery from multiple depots using multiple agents. In this paper, we investigate a centralized model and a heuristic algorithm for solving the multi-depot logistics delivery problem including depot selection and shared commodity delivery. The contribution of the paper is threefold. First, we elaborate a new integer linear programming (ILP) model, namely: Multi-Depot Split-Delivery Vehicle Routing Problem (MDSDVRP) which allows establishing depot locations and routes for serving customer demands within the same objective function. Second, we illustrate a fast heuristic algorithm leveraging knowledge gathering in order to find near-optimal solutions. Finally, we provide performance results of the proposed approach by analyzing known problem instances from different VRP problem classes. The experimental results show that the proposed algorithm exhibits very good performance when solving small and medium size problem instances and reasonable performance for larger instances.