A Branch-and-Cut method for the Capacitated Location-Routing Problem

Recent researches in the design of logistic networks have shown that the overall distribution cost may be excessive if routing decisions are ignored when locating depots. The Location-Routing Problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5–10 potential depots and 20–88 customers, shows that 26 instances with five depots are solved to optimality, including all instances with up to 40 customers and three with 50 customers.     

A GRASP×ELS approach for the capacitated location-routing problem

This paper addresses the capacitated location-routing problem (CLRP), raised by distribution networks involving depot location, fleet assignment and routing decisions. The CLRP is defined by a set of potential depot locations, with opening costs and limited capacities, a homogeneous fleet of vehicles, and a set of customers with known demands. The objective is to open a subset of depots, to assign customers to these depots and to design vehicle routes, in order to minimize both the cost of open depots and the total cost of the routes. The proposed solution method is a greedy randomized adaptive search procedure (GRASP), calling an evolutionary local search (ELS) and searching within two solution spaces: giant tours without trip delimiters and true CLRP solutions. Giant tours are evaluated via a splitting procedure that minimizes the total cost subject to vehicle capacity, fleet size and depot capacities. This framework is benchmarked on classical instances. Numerical experiments show that the approach outperforms all previously published methods and provides numerous new best solutions.     

A biased‐randomized metaheuristic for the capacitated location routing problem

The location routing problem (LRP) involves the three key decision levels in supply chain design, that is, strategic, tactical, and operational levels. It deals with the simultaneous decisions of (a) locating facilities (e.g., depots or warehouses), (b) assigning customers to facilities, and (c) defining routes of vehicles departing from and finishing at each facility to serve the associated customers’ demands. In this paper, a two‐phase metaheuristic procedure is proposed to deal with the capacitated version of the LRP (CLRP). Here, decisions must be made taking into account limited capacities of both facilities and vehicles. In the first phase (selection of promising solutions), we determine the depots to be opened, perform a fast allocation of customers to open depots, and generate a complete CLRP solution using a fast routing heuristic. This phase is executed several times in order to keep the most promising solutions. In the second phase (solution refinement), for each of the selected solutions we apply a perturbation procedure to the customer allocation followed by a more intensive routing heuristic. Computational experiments are carried out using well‐known instances from the literature. Results show that our approach is quite competitive since it offers average gaps below 0.4% with respect to the best‐known solutions (BKSs) for all tested sets in short computational times.     

Multi-start simulated annealing heuristic for the location routing problem with simultaneous pickup and delivery

The location routing problem with simultaneous pickup and delivery (LRPSPD) is a new variant of the location routing problem (LRP). The objective of LRPSPD is to minimize the total cost of a distribution system including vehicle traveling cost, depot opening cost, and vehicle fixed cost by locating the depots and determining the vehicle routes to simultaneously satisfy the pickup and the delivery demands of each customer. LRPSPD is NP-hard since its special case, LRP, is NP-hard. Thus, this study proposes a multi-start simulated annealing (MSA) algorithm for solving LRPSPD which incorporates multi-start hill climbing strategy into simulated annealing framework. The MSA algorithm is tested on 360 benchmark instances to verify its performance. Results indicate that the multi-start strategy can significantly enhance the performance of traditional single-start simulated annealing algorithm. Our MSA algorithm is very effective in solving LRPSPD compared to existing solution approaches. It obtained 206 best solutions out of the 360 benchmark instances, including 126 new best solutions.     

A two-phase hybrid heuristic algorithm for the capacitated location-routing problem

In this paper, we propose a two-phase hybrid heuristic algorithm to solve the capacitated location-routing problem (CLRP). The CLRP combines depot location and routing decisions. We are given on input a set of identical vehicles (each having a capacity and a fixed cost), a set of depots with restricted capacities and opening costs, and a set of customers with deterministic demands. The problem consists of determining the depots to be opened, the customers and the vehicles to be assigned to each open depot, and the routes to be performed to fulfill the demand of the customers. The objective is to minimize the sum of the costs of the open depots, of the fixed cost associated with the used vehicles, and of the variable traveling costs related to the performed routes. In the proposed hybrid heuristic algorithm, after a Construction phase (first phase), a modified granular tabu search, with different diversification strategies, is applied during the Improvement phase (second phase). In addition, a random perturbation procedure is considered to avoid that the algorithm remains in a local optimum for a given number of iterations. Computational experiments on benchmark instances from the literature show that the proposed algorithm is able to produce, within short computing time, several solutions obtained by the previously published methods and new best known solutions.     

Multi-depot vehicle routing problem: a one-stage approach

This paper introduces multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD) which is one important and useful variant of the traditional multi-depot vehicle routing problem (MDVRP) in the supply chain management and transportation studies. After modeling the MDVRPFD as a binary programming problem, we propose two solution methodologies: two-stage and one-stage approaches. The two-stage approach decomposes the MDVRPFD into two independent subproblems, assignment and routing, and solves them separately. In contrast, the one-stage approach integrates the assignment with the routing where there are two kinds of routing methods-draft routing and detail routing. Experimental results show that our new one-stage algorithm outperforms the published methods. Note to Practitioners-This work is based on several consultancy work that we have done for transportation companies in Hong Kong. The multi-depot vehicle routing problem (MDVRP) is one of the core optimization problems in transportation, logistics, and supply chain management, which minimizes the total travel distance (the major factor of total transportation cost) among a number of given depots. However, in real practice, the MDVRP is not reliable because of the assumption that there have unlimited number of vehicles available in each depot. In this paper, we propose a new useful variant of the MDVRP, namely multi-depot vehicle routing problem with fixed distribution of vehicles (MDVRPFD), to model the practicable cases in applications. Two-stage and one-stage solution algorithms are also proposed. The industry participators can apply our new one-stage algorithm to solve the MDVRPFD directly and efficiently. Moreover, our one-stage solution framework allows users to smoothly add new specified constraints or variants.     

An enhanced ant colony optimization (EACO) applied to capacitated vehicle routing problem

In this paper, an enhanced ant colony optimization (EACO) is proposed for capacitated vehicle routing problem. The capacitated vehicle routing problem is to service customers with known demands by a homogeneous fleet of fixed capacity vehicles starting from a depot. It plays a major role in the field of logistics and belongs to NP-hard problems. Therefore, it is difficult to solve the capacitated vehicle routing problem directly when solutions increase exponentially with the number of serviced customers. The framework of this paper is to develop an enhanced ant colony optimization for the capacitated vehicle routing problem. It takes the advantages of simulated annealing and ant colony optimization for solving the capacitated vehicle routing problem. In the proposed algorithm, simulated annealing provides a good initial solution for ant colony optimization. Furthermore, an information gain based ant colony optimization is used to ameliorate the search performance. Computational results show that the proposed algorithm is superior to original ant colony optimization and simulated annealing separately reported on fourteen small-scale instances and twenty large-scale instances.     

多约束选址—路径问题的改进混合遗传算法研究

选址—路径问题(LRP)同时解决设施选址和车辆路径问题,使物流系统总成本达到最小,在集成化物流配送网络规划中具有重要意义。针对带仓库容量约束和路径容量约束的选址—路径(CLRP)问题,提出了一种结合模拟退火算法的混合遗传算法进行整体求解。改进混合遗传算法分别对初始种群生成方式、遗传操作和重组策略进行改进,并实现了模拟退火的良好局部搜索能力与遗传算法的全局搜索能力的有效结合。运用一组Barreto Benchmark算例进行数值实验测试其性能,并将求解结果与国外文献中的启发式算法进行比较,验证了改进混合算法的有效性和可行性。     

考虑时变速度的多车场绿色车辆路径模型及优化算法

针对多车场绿色车辆路径问题,根据顾客的坐标位置,采用K-means聚类方法将顾客分配给不同的车场;考虑时变速度和实时载重对车辆油耗和碳排放的影响,确定车辆油耗和碳排放的度量函数;在此基础上,以车辆油耗成本、碳排放成本、车辆使用成本、驾驶员工资以及时间窗惩罚成本之和最小化作为优化目标,构建多车场绿色车辆路径模型,并根据模...     

A record-to-record travel algorithm for solving the heterogeneous fleet vehicle routing problem

In the heterogeneous fleet vehicle routing problem (HVRP), several different types of vehicles can be used to service the customers. The types of vehicles differ with respect to capacity, fixed cost, and variable cost. We assume that the number of vehicles of each type is fixed and equal to a constant. We must decide how to make the best use of the fixed fleet of heterogeneous vehicles.     

A GRASP algorithm based new heuristic for the capacitated location routing problem

Abstract

In this paper, the capacitated location-routing problem (CLRP) is studied. CLRP is composed of two hard optimisation problems: the facility location problem and the vehicle routing problem. The objective of CLRP is to determine the best location of multiple depots with their vehicle routes such that the total cost of the solution is minimal. To solve this problem, we propose a greedy randomised adaptive search procedure. The proposed method is based on a new heuristic to construct a feasible CLRP solution, and then a local search-based simulated annealing is used as improvement phase. We have used a new technique to construct the clusters around the depots. To prove the effectiveness of our algorithm, several LRP instances are used. The results found are very encouraging.     

Two memetic algorithms for heterogeneous fleet vehicle routing problems

The vehicle routing problem (VRP) plays an important role in the distribution step of supply chains. From a depot with identical vehicles of limited capacity, it consists in determining a set of vehicle trips of minimum total length, to satisfy the demands of a set of customers. In general, the number of vehicles used is a decision variable. The heterogeneous fleet VRP (HFVRP or HVRP) is a natural generalization with several vehicle types, each type being defined by a capacity, a fixed cost, a cost per distance unit and a number of vehicles available. The vehicle fleet mix problem (VFMP) is a variant with an unlimited number of vehicles per type. This paper presents two memetic algorithms (genetic algorithms hybridized with a local search) able to solve both the VFMP and the HVRP. They are based on chromosomes encoded as giant tours, without trip delimiters, and on an optimal evaluation procedure which splits these tours into feasible trips and assigns vehicles to them. The second algorithm uses a distance measure in solution space to diversify the search. Numerical tests on standard VFMP and HFVRP instances show that the two methods, especially the one with distance measure, compete with published metaheuristics and improve several best-known solutions.     

用于求解混合车辆路径问题的混合进化算法

文中研究了具有NP难度的混合车辆路径问题(Mixed Capacitated General Routing Problem,MCGRP),其是在基本车辆路径问题(Vehicle Routing Problem,VRP)的基础上通过添加限载容量约束及弧上的用户需求而衍生的。给定一列车辆数不限的车队,使车辆从站点出发向用户提供服务,服务完用户需求后仍返回站点;规定每辆车的总载重不能超过其载重量,且每个需求只能被一辆车服务且仅服务一次。MCGRP旨在求解每辆车的服务路线,使得在满足以上约束条件的情况下所有车辆的旅行消耗之和最小。混合车辆路径问题具有较高的理论价值和实际应用价值,针对该问题提出了一种高效的混合进化算法。该算法采用基于5种邻域算符的变邻域禁忌搜索来提高解的质量,并通过一种基于路径的交叉算符来继承解的优异性,从而有效地加速算法的收敛。在一组共计23个经典算例上的实验结果表明,该混合进化算法在求解混合车辆路径问题时是非常高效的。     

A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem

This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the demands of customers are fulfilled by a fleet of fixed number of vehicles with various capacities and related costs. Moreover, the vehicles start at the depot and terminate at one of the customers. This problem is an important variant of the classical vehicle routing problem and can cover more practical situations in transportation and logistics. We propose a multistart adaptive memory programming metaheuristic with modified tabu search algorithm to solve this new vehicle routing problem. The algorithmic efficiency and effectiveness are experimentally evaluated on a set of generated instances.     

行驶时间和服务时间随机的集配货一体的分批配送车辆路径优化

将铁路物流中心集配货路径问题抽象为行驶时间和服务时间随机的集送货一体的分批配送车辆路径问题进行优化.根据问题特点建立带修正的随机规划模型,对迭代局部搜索算法进行改进,设计允许分批配送的初始解构造算法、局部搜索算法和扰动机制.算例测试证实:分批配送在中等规模和大规模算例中能发挥较好的作用,大部分中等规模和大规模算例都比不允许分批配送时所得到的解更优,部分中等规模和大规模算例车辆数有所减少;配送点数随着算例规模的扩大而增加,但是配送点数占顾客点数的比例却逐步降低;随机因素随机性增加将导致目标函数增大,对分批配送点数的影响不大.     

The fleet size and mix vehicle routing problem

In this paper, we address the problem of routing a fleet of vehicles from a central depot to customers with known demand. Routes originate and terminate at the central depot and obey vehicle capacity restrictions. Typically, researchers assume that all vehicles are identical. In this work, we relax the homogeneous fleet assumption. The objective is to determine optimal fleet size and mix by minimizing a total cost function which includes fixed cost and variable cost components. We describe several efficient heuristic solution procedures as well as techniques for generating a lower bound and an underestimate of the optimal solution. Finally, we present some encouraging computational results and suggestions for further study.     

Skewed general variable neighborhood search for the location routing scheduling problem

The integrated location routing scheduling problem is a variant of the well-known location routing problem. The location routing problem consists in selecting a set of depots to open and in building a set of routes from these depots, to serve a set of customers at minimum cost. In this variant, a vehicle can perform more than a single route in the planning period. As a consequence, the routes have to be scheduled within the workdays of each vehicle. The problem arises typically when routes are constrained to have a short duration. It happens for example within the boundaries of small geographic areas or in the transportation of perishable goods. In this paper, we propose a skewed general variable neighborhood search based heuristic to solve it. The algorithm is tested extensively and we show that it is efficient and provides the proven optimal solution in a significant number of cases. Moreover, it clearly outperforms a multi-start VND based heuristic that uses the same neighborhood structures.     

A simulated annealing heuristic for the open location-routing problem

This paper introduces the open location-routing problem (OLRP) that is a variant of the capacitated location-routing problem (CLRP). OLRP is motivated from the rise in contracting with third-party logistic (TPL) companies and is different from CLRP in that vehicles do not return to the distribution center after servicing all customers. The goal of OLRP is to minimize the total cost, consisting of facility operation costs, vehicle fixed costs, and traveling costs. We propose a simulated annealing (SA)-based heuristic for solving OLRP, which is tested on OLRP instances that have been adopted from three sets of well-known CLRP benchmark instances with up to 318 customers and 4 potential depots. The computational results indicate that the proposed heuristic efficiently solves OLRP.     

An evolutionary algorithm for the multi‐objective pick‐up and delivery pollution‐routing problem

The design of sustainable logistics solutions poses new challenges for the study of vehicle‐routing problems. The design of efficient systems for transporting products via a heterogeneous fleet of vehicles must consider the minimization of cost, emissions of greenhouse gases, and the ability to serve every customer within an available time slot. This phenomenon gives rise to a multi‐objective problem that considers the emission of greenhouse gases, the total traveling time, and the number of customers served. The proposed model is approached with an ε‐constraint technique that allows small instances to be solved and an evolutionary algorithm is proposed to deal with complex instances. Results for small instances show that all the points that approach the Pareto frontier found by the evolutionary algorithm are nondominated by any solution found by the multi‐objective model. For complex instances, nondominated solutions that serve most of the requests are found with low computational requirements.     

Heuristic solutions to multi-depot location-routing problems

This paper presents a method for solving the multi-depot location-routing problem (MDLRP). Since several unrealistic assumptions, such as homogeneous fleet type and unlimited number of available vehicles, are typically made concerning this problem, a mathematical formulation is given in which these assumptions are relaxed. Since the inherent complexity of the LRP problem makes it impossible to solve the problem on a larger scale, the original problem is divided into two sub-problems, i.e., the location-allocation problem, and the general vehicle routing problem, respectively. Each sub-problem is then solved in a sequential and iterative manner by the simulated annealing algorithm embedded in the general framework for the problem-solving procedure. Test problems from the literature and newly created problems are used to test the proposed method. The results indicate that this method performs well in terms of the solution quality and run time consumed. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.Scope and purposeIn many logistic environments managers must make decisions such as location for distribution centers (DC), allocation of customers to each service area, and transportation plans connecting customers. The location-routing problems (LRPs) are, hence, defined to find the optimal number and locations of the DCs, simultaneously with the vehicle schedules and distribution routes so as to minimize the total system costs. This paper proposes a decomposition-based method for solving the LRP with multiple depots, multiple fleet types, and limited number of vehicles for each different vehicle type. The solution procedure developed is very straightforward conceptually, and the results obtained are comparable with other heuristic methods. In addition, the setting of parameters throughout the solution procedure for obtaining quick and favorable solutions is also suggested.