A heuristic algorithm for optimal fleet composition with vehicle routing considerations

This paper proposes a fast heuristic algorithm for solving a combined optimal fleet composition and multi-period vehicle routing problem. The aim of the problem is to determine an optimal fleet mix, together with the corresponding vehicle routes, to minimize total cost subject to various customer delivery requirements and vehicle capacity constraints. The total cost includes not only the fixed, variable, and transportation costs associated with operating the fleet, but also the hiring costs incurred whenever vehicle requirements exceed fleet capacity. Although the problem under consideration can be formulated as a mixed-integer linear program (MILP), the MILP formulation for realistic problem instances is too large to solve using standard commercial solvers such as the IBM ILOG CPLEX optimization tool. Our proposed heuristic decomposes the problem into two tractable stages: in the first (outer) stage, the vehicle routes are optimized using cross entropy; in the second (inner) stage, the optimal fleet mix corresponding to a fixed set of routes is determined using dynamic programming and golden section search. Numerical results show that this heuristic approach generates high-quality solutions and significantly outperforms CPLEX in terms of computational speed.     

A label based ant colony algorithm for heterogeneous vehicle routing with mixed backhaul

Vehicle heterogeneity and backhaul mixed-load problems are often studied separately in existing literature. This paper aims to solve a type of vehicle routing problem by simultaneously considering fleet heterogeneity, backhaul mixed-loads, and time windows. The goal is to determine the vehicle types, the fleet size, and the travel routes such that the total service cost is minimized. We propose a multi-attribute Label-based Ant Colony System (LACS) algorithm to tackle this complex optimization problem. The multi-attribute labeling technique enables us to characterize the customer demand, the vehicle states, and the route options. The features of the ant colony system include swarm intelligence and searching robustness. A variety of benchmark instances are used to demonstrate the computational advantage and the global optimality of the LACS algorithm. We also implemented the proposed algorithm in a real-world environment by solving an 84-node postal shuttle service problem for China Post Office in Guangzhou. The results show that a heterogeneous fleet is preferred to a homogenous fleet as it generates more cost savings under variable customer demands.     

A tabu search algorithm for the heterogeneous fixed fleet vehicle routing problem

In the heterogeneous fixed fleet vehicle routing problem there are different types of vehicles and a given number of vehicles of each type. The resolution of this problem consists of assigning the customers to the existing vehicles and, in relation to each vehicle, defining the order of visiting each customer for the delivery or collection of goods. The objective is to minimize the total costs, satisfying customers’ requirements and visiting each customer exactly once. In this paper a tabu search algorithm is proposed and tested on several benchmark problems. The computational experiments show that the proposed algorithm produces high quality solutions within an acceptable computation time. Four new best solutions are reported for a set of test problems used in the literature.     

A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited availability of vehicles. The main objective is to minimize the fixed vehicle cost and the distribution cost, where the latter can be defined with respect to en-route time (T) or distance (D). The proposed unified algorithm is able to solve the four variants of heterogeneous fleet routing problem, called FT, FD, HT and HD, where the last variant is new. The HEA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle the heterogeneous fleet dimension. Extensive computational experiments on benchmark instances have shown that the HEA is highly effective on FT, FD and HT. In particular, out of the 360 instances we obtained 75 new best solutions and matched 102 within reasonable computational times. New benchmark results on HD are also presented.     

Multi-period Vehicle Routing Problem with Due dates

In this paper we study the Multi-period Vehicle Routing Problem with Due dates (MVRPD), where customers have to be served between a release and a due date. Customers with due dates exceeding the planning period may be postponed at a cost. A fleet of capacitated vehicles is available to perform the distribution in each day of the planning period. The objective of the problem is to find vehicle routes for each day such that the overall cost of the distribution, including transportation costs, inventory costs and penalty costs for postponed service, is minimized. We present alternative formulations for the MVRPD and enhance the formulations with valid inequalities. The formulations are solved with a branch-and-cut algorithm and computationally compared. Furthermore, we present a computational analysis aimed at highlighting managerial insights. We study the potential benefit that can be achieved by incorporating flexibility in the due dates and the number of vehicles. Finally, we highlight the effect of reducing vehicle capacity.     

The multi-shift vehicle routing problem with overtime

In this paper, we study a new variant of the vehicle routing problem (VRP) with time windows, multi-shift, and overtime. In this problem, a limited fleet of vehicles is used repeatedly to serve demand over a planning horizon of several days. The vehicles usually take long trips and there are significant demands near shift changes. The problem is inspired by a routing problem in healthcare, where the vehicles continuously operate in shifts, and overtime is allowed. We study whether the tradeoff between overtime and other operational costs such as travel cost, regular driver usage, and cost of unmet demands can lead to a more efficient solution. We develop a shift dependent (SD) heuristic that takes overtime into account when constructing routes. We show that the SD algorithm has significant savings in total cost as well as the number of vehicles over constructing the routes independently in each shift, in particular when demands are clustered or non-uniform. Lower bounds are obtained by solving the LP relaxation of the MIP model with specialized cuts. The solution of the SD algorithm on the test problems is within 1.09–1.82 times the optimal solution depending on the time window width, with the smaller time windows providing the tighter bounds.     

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.     

Routing fleets with multiple driving ranges: Is it possible to use greener fleet configurations?

This paper discusses the vehicle routing problem with multiple driving ranges (VRPMDR), an extension of the classical routing problem where the total distance each vehicle can travel is limited and is not necessarily the same for all vehicles – heterogeneous fleet with respect to maximum route lengths. The VRPMDR finds applications in routing electric and hybrid-electric vehicles, which can only cover limited distances depending on the running time of their batteries. Also, these vehicles require from long charging times, which in practice makes it difficult to consider en route recharging. The paper formally introduces the problem, describes an integer programming formulation and a multi-round heuristic algorithm that iteratively constructs a solution for the problem. Using a set of benchmarks adapted from the literature, the algorithm is then employed to analyze how distance-based costs are increased when considering ‘greener’ fleet configurations – i.e., when using electric vehicles with different degrees of autonomy.     

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.     

考虑电池损耗的电动冷藏车路径及充电策略

电池充电造成的电池损耗对企业运营成本影响较大,以不同SOC区间内一次充电造成的电池容量衰退成本模型估计电池损耗成本,研究了车辆途中可多次进入充电站充电的路径优化问题,在考虑运输成本、制冷成本、货损成本、充电时间成本、惩罚成本的基础上,将电动冷藏车的电池损耗成本纳入总成本最小的目标函数,并建立了线性规划数学模型。采用增加粒子间共享信息类型的改进粒子群算法对该模型进行求解。将改进粒子群算法应用于构造的算例中,得到包括充电策略在内的车辆最优路径方案和最小运营成本,结果表明充电上限为80%的车辆路径方案可得到最低的运营成本,同时与标准粒子群算法求得的计算结果进行了比较分析,证明该改进粒子群算法在求解该问题上的可行性。     

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.     

A mixed load capacitated rural school bus routing problem with heterogeneous fleet: Algorithms for the Brazilian context

A capacitated rural school bus routing problem featuring mixed loads, a heterogeneous fleet, and the same school starting time is here addressed. This is an important problem of the routing literature which has been attracting the attention of many researchers recently. The mixed load feature allows students from different schools to ride the same bus at the same time. Five meta-heuristic based algorithms were devised to solve the problem, and evaluated on solving four different datasets, one of them being based on a real case from Brazil. Four traditional local search neighborhood structures for vehicle routing problems were adapted and specialized to handle mixed loads and a heterogeneous fleet simultaneously. To the best of the authors knowledge, it is the first time that both features are treated jointly within an algorithm, and not as a post processing optimization step. The attained cost savings and reduction of fleet sizes suggest the suitability of a mixed load, heterogeneous fleet approach for sparsely populated rural areas. Moreover the devised framework has been embedded into a decision support system which is assisting several municipalities of the state of Minas Gerais, Brazil, to better plan their routes and reduce transportation costs.     

车辆数限制的多车型校车路径问题模型及算法研究

为适应校车路径规划中校车有多种车型且每种车型数量受限的需求,建立车辆数限制的多车型校车路径问题(HFSBRP)的数学模型,并提出一种迭代局部搜索算法进行求解。该算法借助邻域随机选择的变邻域下降搜索(VND)算法完成局部提升。局部提升过程中,首先调整车型,然后再混合使用缩减路径数和提高车辆利用率的邻域解接受策略以提高算法的寻优能力,为保证解的多样性,允许接受一定偏差范围内的邻域解。此外,为避免算法过早陷入局部最优,设计了多点交换和移动的扰动规则。基于国际基准测试案例进行模型验证和算法测试,实验结果表明了模型的正确性和算法的有效性。     

城市物流配送的混合车辆路径规划模型与优化算法

针对城市部分区域限行、物流系统中燃油车与电动车同时并存的实际情况,综合考虑客户需求量、服务时间、电动车行驶里程、已有充电设施、部分充电策略、燃油车油耗与碳排放等因素,以车辆使用固定成本、驾驶员工资、电动车的充电成本、燃油车的油耗与碳排放成本之和最小为目标构建混合车辆路径规划模型.根据模型特征设计一种改进蚁群算法求解,并采用多类型算例进行实验.实验结果表明,所提方法能在非常短的时间内给出符合决策者目标的混合车辆路径规划方案,有效降低总配送成本,减少燃油车油耗与碳排放,具有合理性、可行性与有效性.     

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.     

Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

基于暂态混沌神经网络的多车调度混合优化算法

探讨车辆调度问题的解决方法．提出一种用于求解带容量约束的多车调度问题（CVRP）的混合优化算法．该算法分为路线划分、构造初始解和改进解3个阶段：第1阶段用模糊C均值聚类算法将所有客户按车容量要求装车;第2阶段用暂态混沌神经网络方法对每条路线排序;第3阶段用禁忌搜索法改进得到的解．最后采用标准问题进行仿真计算,通过与其他算法的比较,说明该算法是求解CVRP问题可行且高效的方法．     

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.     

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.     

Hybrid column generation and large neighborhood search for the dial-a-ride problem

Demographic change towards an ever aging population entails an increasing demand for specialized transportation systems to complement the traditional public means of transportation. Typically, users place transportation requests, specifying a pickup and a drop off location and a fleet of minibuses or taxis is used to serve these requests. The underlying optimization problem can be modeled as a dial-a-ride problem. In the dial-a-ride problem considered in this paper, total routing costs are minimized while respecting time window, maximum user ride time, maximum route duration, and vehicle capacity restrictions. We propose a hybrid column generation and large neighborhood search algorithm and compare different hybridization strategies on a set of benchmark instances from the literature.