Multi Depot Research Articles

Generating multi depot vehicle scheduling problems with known optimal tours

Validation of heuristics that aim to solve efficiently vehicle scheduling problems is usually done by generating random datasets and comparing one approach versus another. How far from the optimal solution are their results is usually not known, especially for larger workloads. The Multiple-Depot Vehicle Scheduling Problem (MDVSP) is a well-known and important optimization problem that aims to assign a set of trips to a fleet of vehicles provided by several depots in order to minimize the total cost of empty travel and waiting. Addressing the need to test different heuristics on various problem types, our paper introduces several generation algorithms that create random MDVSP instances, of any size, with known optimum. In order to evaluate the results, we have used both an exact MDVSP solver and a fast heuristic, analyzing the correctness and the runtime performance. Empirical testing indicates that these instances are still difficult to solve which means that they could provide a valuable tool for measuring the scalability of various MDVSP heuristics.

Integrated optimization of transportation, inventory and vehicle routing with simultaneous pickup and delivery in two-echelon green supply chain network

The economic concern, environmental awareness related legislations, and potential recycling benefits are the main motives that have changed the dimension of supply chain network with environmentally effective transportation and efficient scrap collection system. This paper investigates the two echelon supply chain network of the battery manufacturing industry. This deals with an integrated optimization procedure for solving the green transportation problem and inventory problem in the first echelon, and the capacitated multi depot (Distribution center/Collection center) heterogeneous green vehicle routing problem with simultaneous pickup and delivery in the second echelon. The minimization of the green objective function comprising inventory carrying cost, transportation cost and carbon emission cost are considered in this work. The focus of this paper is to formulate the problem in the Mixed Integer Non-Linear Programming model and to solve the four problem instances (P1 – P4) using GAMS 23.5 and Simulated Annealing Algorithm (SAA) with swap neighbourhood solution method. The experimental results show that the integrated approach with SAA provides a better solution than the sequential approach. The robustness test is carried out with four typical problem instances which show that the proposed SAA provides near optimal solutions. The model analysis is demonstrated with different components of the objective function which will help the top management to take appropriate decisions in the context of cost savings. The performance comparison reveals that the proposed SAA (SAA-1) has given better results than the Simulated Annealing Algorithm with insertion method (SAA-2).

Simulated Annealing Algorithm for Multi Depot Two-Echelon Capacitated Vehicle Routing Problem

Although urban freight transport is a significant contributor to the development of a country, it has adverse effects on the environment and the quality of life in urban areas. To reduce these adverse effects, we can deploy sustainable city logistic strategies. Scheduling and routing of vehicles is a crucial decision in city logistic strategies. Hence, in this paper, we solve the Multi-Depot Two Echelon Capacitated Vehicle Routing Problem (MD2E-CVRP), which is a variant of Vehicle Routing Problem (VRP) with heterogeneous fleets at both levels. Since VRP is NP-hard, we have proposed a Simulated Annealing (SA) based heuristic solution algorithm and have tested it on the standard 2E- CVRP and MD2E-CVRP instances. The results obtained from SA have a good solution quality at just one-fiftieth of computational time using CPLEX and was found to be faster than Adaptive Large Neighborhood Search (ALNS) with only a marginal drop in solution quality.

Utilizing Ant Colony Optimization and Intelligent Water Drop for Solving Multi Depot Vehicle Routing Problem

Multi-depot vehicle routing problem (MDVRP) is a real-world variant of the vehicle routing problem (VRP). MDVRP falls under NP-hard problem where trouble in identifying the routes for the vehicles from multiple depots to the customers and then, returning to the similar depot. The challenging task in solving MDVRP is to identify optimal routes for the fleet of vehicles located at the depots to transport customers’ demand efficiently. In this paper, two metaheuristic methods have been tested for MDVRP which are Ant Colony Optimization (ACO) and Intelligent Water Drop (IWD). The proposed algorithms are validated using six MDVRP Cordeau’s data sets which are P01, P03, P07, P10, P15 and P21 with 50, 75, 100, 249, 160 and 360 customers, respectively. Thus, the results using the proposed algorithm solving MDVRP, five out of six problem data sets showed that IWD is more capable and efficient compared to ACO algorithm.

Logistic Optimization for Multi Depots Loading Capacitated Electric Vehicle Routing Problem From Low Carbon Perspective

In this paper, a multi depots capacitated electric vehicle routing problem where client demand is composed of two-dimensional weighted items (2L-MDEVRP) is addressed. This problem calls for the minimization of the transportation distance required for the delivery of the items which are demanded by the clients, carried out by a fleet of electric vehicles in several depots. Since the 2L-MDEVRP is an NP-hard problem, a heuristic algorithm combined variable neighborhood search algorithm (VNS) and space saving heuristic algorithm (SSH) is proposed. The VNS algorithm is used to solve the vehicle routing problem (VRP) sub-problem, and the SSH algorithm is used to solve the bin packing problem (BPP) sub-problem. We propose the space saving heuristic to find the best matching solution between the next loading item and the feasible loading position. The SSH-VNS algorithm is tested by using benchmark instances available from the literature. The results show that the SSH-VNS algorithm has better performance compared with other published results for solving capacity vehicle routing problem (CVRP) and two-dimensional capacity vehicle routing problem (2L-CVRP). Some new best-known solutions of the benchmark problem are also found by SSH-VNS. Moreover, the effectiveness of the proposed algorithm on 2L-MDEVRP is demonstrated through numerical experiments and a practical logistic distribution case. In the last section, the managerial implications and suggestions for future research are also discussed.

Bi-level multi-objective combinatorial optimization using reference approximation of the lower level reaction

Abstract Bi-level optimization has gained a lot of interest during the last decade. This framework is suitable to model several real-life situations. Bi-level optimization problems refer to two related optimization tasks, each one is assigned to a decision level (i.e., upper and lower levels). In this way, the evaluation of an upper level solution requires the evaluation of the lower level. This hierarchical decision making necessitates the execution of a significant number of Function Evaluations (FEs). When dealing with a multi-objective optimization context, new complexities are added and imposed by the conflicting objectives and their evaluation techniques. In this paper, we aim to reduce the induced complexity using approximation techniques in order to obtain the lower level optimality. To this end, ideas from multi-objective optimization have been extracted, improved, and hybridized with evolutionary methods to build an efficient approach for Multi-objective Bi-Level Optimization Problems (MBLOPs). In this work, three techniques are suggested: (1) a complete lower level approximation Pareto front procedure, (2) a reference-based approximation selection procedure, and (3) a sub-set reference-based approximation selection one. The proposed variants are applied to a new multi-objective formulation of a well-known combinatorial problem integrating two systems in the supply chain management, namely, the Bi-level Multi Depot Vehicle Routing Problem (Bi-MDVRP). The statistical analysis demonstrates the efficiency of each algorithm according to a set of metrics. Indeed, a large number of savings are detected which confirms the efficiency of our proposals for solving combinatorial optimization problems.

The design of a liquefied natural gas (LNG) distribution network of a company operating in México

This paper presents a modification of the Multi Depot Multi Period Vehicle Routing Problem with heterogeneous fleet (MDMPVRPHF) to consider capital expenditures and operating expenses (MDMPVRPHFMR). The aim is to design a product distribution network and minimize the total delivery cost. The MDMPVRPHF only considers transportation costs with transportation restrictions. In this paper, the purpose is to solve a real'life freight distribution problem that considers capital expenditures and operation expenses. The MDMPVRPHFMR is formulated as a mixed integer programming model. The results of the application of both models to a real case of study demonstrate the advantages presented by the MDMPVRPHFMR over the MDMPVRPHF. Hence, management restrictions must be considered when designing a real-life freight distribution problem. The study case is to develop a liquefied natural gas distribution model based on a real company operating in México.

An Improved Genetic Algorithm for Solving Multi Depot Vehicle Routing Problems

The classical Vehicle Routing Problem (VRP) tries to minimise the cost of dispatching goods from depots to customers using vehicles with limited carrying capacity. As a generalisation of the TSP, the problem is known to be NP-hard and several authors have proposed heuristics and meta-heuristics for obtaining good solutions. The authors present genetic algorithm-based approaches for solving the problem and compare the results with available results from other papers, in particular, the hybrid clustering based genetic algorithm. The authors find that the proposed methods give encouraging results on all these instances. The approach can be extended to solve multi depot VRPs with heterogeneous fleet of vehicles.

An Improved Heuristic Based on Clustering and Genetic Algorithm for Solving the Multi-Depot Vehicle Routing Problem

Abstract: 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.

Improvement Route for Distribution Solutions MDVRP (Multi Depot Vehicle Routing Problem) using Genetic Algorithm

The Supply Chain Management Division (SCM) of KM Rubber Company is responsible for delivering the sole product, crumb rubber, from its various factories in Sumatera to the destination ports for further delivery to customers or export destinations. The aim of this study is to provide the improved route for the depot distribution to each destination ports with the shortest time and distance. Writing stage begins with preliminary studies, followed by the identification of the problem, determine the purpose of research, data collection, data processing that contains the initial distribution system optimization solved by methods of transportation and distribution of a new route that is resolved by Genetic Algorithm, and closed by the analysis and conclusions. The manual calculation method to obtain the optimal route gives a total transport distance of 8832.12 km; while the distribution of the proposed route using Genetic Algorithms generate total distance routes as far as 5188.06 km. As the distance is shorter the new route will generate minimal costs and shorter travel time.

Comparison of GA-Shift Neighbourhood Mutation and GA-Pairs Exchange Mutation with Multi Cut Point Crossover in Solving RICH-VRP

This research was focused on a heterogeneous fleet of passenger ships to solve multi depot by using genetic algorithm (GA) to solve combinatorial problem i.e. vehicle routing problem (VRP). The objective of this study is to compare the roulette wheel selection, multi cut point crossover, and shift neighbourhood mutation with roulette wheel selection, multi cut point crossover, and pairs exchange mutation to minimize the sum of the fuel consumption travelled, the cost for violations of the ship draft and sea depth, and penalty cost for violations of the load factor; maximize number port of call; and maximize load factor. Problem solving in this study is how to generate feasible route combinations for rich VRP that meets all the requirements with optimum solution. Route generated by roulette wheel selection, multi cut point crossover, and shift neighbourhood mutation could decrease fuel consumption about 19.4350% compared to roulette wheel selection, multi cut point crossover, and pairs exchange mutation about 18.6738%.

A heuristic method for location-inventory-routing problem in a three-echelon supply chain system

Abstract Location-inventory-routing problem belongs to the class of NP-hard problems. It needs a heuristic method to solve the problem in large scales so it can be applied in a real system case. This paper develops a heuristic method for location-inventory-routing problem in a three-echelon supply chain system where inventory decisions are made in the three involved entities. The involved entities in the system are single supplier, multi depots, and multi retailers. The demand of the retailers is probabilistic, single product, and following a normal distribution. The heuristic method consists of two stages, which are constructive stage and improvement stage. At the improvement stage, there are three phases developed to improve solution iteratively. The phases are location phase, inventory phase, and routing phase. SA (simulated annealing) is used at the improvement stage to improve the solution. The heuristic method is evaluated using instances and the solutions are compared to the MINLP (mixed integer nonlinear programming) model. Average gap between the heuristic method and the MINLP model is 0.55% in terms of total cost. The proposed heuristic is applied in a real system case which is food supply chain system of DKI Jakarta to design a new supply chain system that can increase availability. The new design can increase the availability from 76% to 95%.

A REVIEW OF SINGLE AND POPULATION-BASED METAHEURISTIC ALGORITHMS SOLVING MULTI DEPOT VEHICLE ROUTING PROBLEM

Multi-Depot Vehicle Routing Problem (MDVRP) arises with rapid development in the logistics and transportation field in recent years. This field, mainly, faces challenges in arranging their fleet efficiently to distribute the goods to customers by minimizing distance and cost. Therefore, the decision maker needs to specify the vehicles to reach the particular depot which, serves the customers with the predetermined capacity. Hence, to solve the stated problems, there is a need to apply metaheuristic methods to get minimal transportation costs. This article reviews on single and population-based metaheuristic methods solving MDVRP from the year 2013 until 2018. The methods discussed were simulated annealing (SA), variable neighborhood search (VNS), ant colony algorithm (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). From the previous works, it can be concluded that the application of population based metaheuristic gives better solutions in solving MDVRPs. Keywords: Metaheuristic, Multi Depot, MDVRP

Optimization of a small-scale LNG supply chain

Due to an increased interest in small to medium scale liquefied natural gas (LNG) use, a mathematical model has been developed to aid the decision making on tactical aspects in the design of such LNG logistic chains. The focus of the work is on inter-terminal maritime transportation between a set of supply ports and a set of sparsely distributed receiving ports with given demands. Similar problems have been largely studied in literature, but our approach differs in including simultaneously load splitting features, multi depots and a multiple journeys between ports on the same route. The model, which considers the LNG distribution by a heterogeneous fleet of ships, applies mixed integer linear programming to find the supply chain structure that minimizes costs associated with fuel procurement. A case study illustrating the features of the model is presented, where a base case is initially solved. An extensive sensitivity analysis is presented which demonstrates how the optimal solution evolves under different conditions (i.g. LNG price in the supply ports, time horizon and berthing time). A preliminary attempt to tackle uncertainty in the demand is also made. Finally, the performance of the model on a set of larger problems is reported, demonstrating its efficiency.

Modeling of multi depot vehicle routing problem for petroleum products

The paper is devoted to modeling multi depot vehicle routing problem (VRP) with capacity constraints for petroleum products delivery. Applying efficient metaheuristics algorithms combined with local search procedures, we present how to get suboptimal solutions for this NP-hard problem in an acceptable time. Some parallel computing techniques are also used to reduce the execution time. Experimental results are performed by the case of VRP for petroleum products.

The Bi-Objective Location-Routing Problem based on Simultaneous Pickup and Delivery with Soft Time Window

The location-routing problem is the most significant and yet new research field in location problems that considers simultaneously vehicle routing problem features with original one for achieving high-quality integrated distribution systems in beside of the global optimum. Simultaneous pickup and delivery based on time windows are the two main characteristics of logistic management that have been used separately in most of the location routing problem in spite of their various real-life application with together. Furthermore, distribution manager always trying to create a distributed system layout along with the lowest total system cost and enhancing service levels for providing all customers satisfaction. Accordingly, in the current paper is considered the mentioned gap, that is to say the bi-objective capacitated location-routing problem based on simultaneous pickup and delivery with soft time window and multi depots (BOCLRPSPDSTW). For achieving the main goal, bi-objective mixed-integer linear programming model for BOCLRPSPDSTW, on the one hand minimizing summation of all problem costs and on the other hand, for meeting customer service level minimizing maximum summation of delivery times and service times are addressed. To solve the presented model, NSGAII and NRGA are proposed and at last efficiency of the anticipated solutions are depicted by testing them in a data set.

The close–open mixed multi depot vehicle routing problem considering internal and external fleet of vehicles

Distribution of finished goods from depots to predetermined customers and collection of goods and wastes are practical and challengeable optimization and logistics problems; therefore, appropriate management of transportation system can help companies decrease their costs and consequently earn more benefits. Several kinds of vehicle routing problems (VRPs) have been studied in the literature. In this paper, we will combine multi-depot vehicle routing problem (MDVRP) and close–open mixed vehicle routing problem (COMVRP), assuming that the fleet of vehicles is heterogeneous. Also, in this problem, contractors are used to meet a part of customers’ requirements. The objective of the problem is to minimize the total cost of serving customers. To efficiently deal with the problem, a new mixed integer programming (MIP) model as well as a new hybrid metaheuristic is proposed. Moreover, analytic hierarchical process is utilized in hybridization of the genetic algorithm. The computational experiments are conducted to compare the results of HGA, GA and MIP solver, CPLEX.

GIS Utilization for Delivering a Time Condition Products

As population is increasing rapidly all over the world, the need for delivering products is being more difficult especially for conditional products (products with life time). Many Customers require conditional products to be delivered to their locations. Distribution center may have multi depots (multi store branches) instead of one depot. Every depot has limited number of vehicles to minimize cost. Capacities of these vehicles are based on two dimensions (weight and volume). Geographic information system (GIS) is used for localizing customers’ destinations. Then OD Cost Matrix is used to assign every customer destination to the least cost depot to be served from it. Finally Network analyst is used to solve the vehicle routing problem generating final route directions for every vehicle and calculating the best time for lunch break of drivers automatically. This case study is applied on Mansoura city in Egypt.

A survey on the inventory-routing problem with stochastic lead times and demands

The integration of the different processes and players that compose the supply chain (SC) is essential to obtain a better coordination level. Inventory control and distribution management are the two processes that researchers have identified as the key to gain or lose in efficiency and effectiveness in the field of logistics, with a direct effect on the synchronization and overall performance of SCs. In practical situations demand is often not deterministic, and lead times are also variable, yielding a complex stochastic problem. In order to analyze the recent developments in the integration of these processes, this paper analyzes the state of the art of the information management in the SC, the relationship between inventory policies and available demand information, and the use of optimization methods to provide good solutions for the problem in single and multi depot versions.

A real-life Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet: Formulation and Adaptive Large Neighborhood Search based Matheuristic

In this paper, a new rich Vehicle Routing Problem that could arise in a real life context is introduced and formalized: the Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet. The goal of the problem is to minimize the total delivery cost. A heterogeneous fleet composed of vehicles with different capacity, characteristics (i.e. refrigerated vehicles) and hourly costs is considered. A limit on the maximum route duration is imposed. Unlike what happens in classical multi-depot VRP, not every customer may/will be served by all the vehicles or from all the depots. The planning horizon, as in most real life applications, consists of multiple periods, and the period in which each route is performed is a variable of the problem. The set of periods, within the time horizon, in which the delivery may be carried out is known for each customer. A Mixed Integer Programming (MIP) formulation for MDMPVRPHF is presented in this paper, and an Adaptive Large Neighborhood Search (ALNS) based Matheuristic approach is proposed, in which different destroy operators are defined. Computational results, pertaining to realistic instances, which show the effectiveness of the proposed method, are provided.