A heuristic method for the vehicle routing problem with backhauls and inventory

The purpose of this paper is to determine the route of the vehicle routing problem with backhauls (VRPB), delivering new items and picking up the reused items or wastes, and resolve the inventory control decision problem simultaneously since the regular VRPB does not. Both the vehicle routing decision for delivery and pickup, and the inventory control decision affect each other and must be considered together. Hence, a mathematical model of vehicle routing problem with backhauls and inventory (VRPBI) is proposed. Since finding the optimal solution(s) for VRPBI is a NP-hard problem, this paper proposes a heuristic method, variable neighborhood tabu search (VNTS), adopting six neighborhood searching approaches to obtain the optimal solution. Moreover, this paper compares the proposed heuristic method with two other existing heuristic methods. The experimental results indicate that the proposed method is better than the two other methods in terms of average logistic cost (transportation cost and inventory cost).     

Vehicle routing scheduling for cross-docking in the supply chain

One of the most important factors in implementing supply chain management is to efficiently control the physical flow of the supply chain. Due to its importance, many companies are trying to develop efficient methods to increase customer satisfaction and reduce costs. In various methods, cross-docking is considered a good method to reduce inventory and improve responsiveness to various customer demands. However, previous studies have dealt mostly with the conceptual advantages of cross-docking or actual issues from the strategic viewpoint. It is also necessary, however, to considering cross-docking from an operational viewpoint in order to find the optimal vehicle routing schedule. Thus, an integrated model considering both cross-docking and vehicle routing scheduling is treated in this study. Since this problem is known as NP-hard, a heuristic algorithm based on a tabu search algorithm is proposed. In the numerical example, our proposed algorithm found a good solution whose average percentage error was less than 5% within a reasonable amount of time.     

A planning model and solution algorithm for multi-trip split-delivery vehicle routing and scheduling problems with time windows

This study proposes a daily vehicle routing model for minimizing the total cost of replenishing inventory within a supply chain. The first major contribution of this research is to allow multiple use of vehicles in a split delivery vehicle routing problem with time windows (SDVRPTW), which is more realistic for various real-life applications. The multi-trip SDVRPTW (MTSDVRPTW) is formulated using the time–space network technique, which provides greater flexibility for formulating the complicated interactions between vehicles and products when multi-trip, split delivery, and delivery time windows are simultaneously considered. The resulting formulation of the MTSDVRPTW can be categorized as an integer multi-commodity network flow problem with side constraints. A two-step solution algorithm is proposed to solve this NP-hard problem, which is the second major contribution of this research. Finally, a real-world scale numerical example is performed to demonstrate and to test the methodology. The results indicate that these vehicle routing problems can be solved effectively and efficiently and that the proposed methodology has great potential for inventory replenishment scheduling where split deliveries and multiple trips for a single vehicle are allowed and time window constraints are imposed.     

A heuristic method for the inventory routing and pricing problem in a supply chain

The inventory routing problem (IRP) in a supply chain (SC) is to determine delivery routes from suppliers to some geographically dispersed retailers and inventory policy for retailers. In the past, the pricing and demand decisions seem ignored and assumed known in most IRP researches. Since the pricing decision affects the demand decision and then both inventory and routing decisions, it should be considered in the IRP simultaneously to achieve the objective of maximal profit in the supply chain. In this paper, a mathematical model for the inventory routing and pricing problem (IRPP) is proposed. Since the solution for this model is an NP (non-polynomial) problem, a heuristic method, tabu search adopting different neighborhood search approaches, is used to obtain the optimal solution. The proposed heuristic method was compared with two other methods considering the IRPP separately. The experimental results indicate that the proposed method is better than the two other methods in terms of average profit.     

A novel learning based approach for a new integrated location-routing and scheduling problem within cross-docking considering direct shipment

One of the most important problem in supply chain management is the design of distribution systems which can reduce the transportation costs and meet the customer's demand at the minimum time. In recent years, cross-docking (CD) centers have been considered as the place that reduces the transportation and inventory costs. Meanwhile, neglecting the optimum location of the centers and the optimum routing and scheduling of the vehicles mislead the optimization process to local optima. Accordingly, in this research, the integrated vehicle routing and scheduling problem in cross-docking systems is modeled. In this new model, the direct shipment from the manufacturers to the customers is also included. Besides, the vehicles are assigned to the cross-dock doors with lower cost. Next, to solve the model, a novel machine-learning-based heuristic method (MLBM) is developed, in which the customers, manufacturers and locations of the cross-docking centers are grouped through a bi-clustering approach. In fact, the MLBM is a filter based learning method that has three stages including customer clustering through a modified bi-clustering method, sub-problems’ modeling and solving the whole model. In addition, for solving the scheduling problem of vehicles in cross-docking system, this paper proposes exact solution as well as genetic algorithm (GA). GA is also adapted for large-scale problems in which exact methods are not efficient. Furthermore, the parameters of the proposed GA are tuned via the Taguchi method. Finally, for validating the proposed model, several benchmark problems from literature are selected and modified according to new introduced assumptions in the base models. Different statistical analysis methods are implemented to assess the performance of the proposed algorithms.     

A Quantum-inspired Ant Colony Optimization for solving a sustainable four-dimensional traveling salesman problem under type-2 fuzzy variable

In this paper, a Quantum-inspired Ant Colony Optimization (Qi-ACO) is proposed to solve a sustainable four-dimensional traveling salesman problem (4DTSP). In 4DTSP, various paths with a different number of conveyances are available to travel between any two cities. In this model, we have considered a sustainable 4DTSP in terms of emission as a constraint. Since travel costs and emissions are uncertain/imprecise in nature, so here we consider type-2 variables. Sustainable development in the traveling salesman problem (TSP) sector can be divided into two major sections: economy and environmental. Sustainable TSP development requires balancing to achieve the maximum benefits for these two sectors. For increasing development in sustainable transportation, we need to use some strategies for increasing sustainability. These strategies include improving route and vehicle selection, routing plan, vehicle speed, etc. The novelties of the proposed Qi-ACO algorithm are (i) Qubit generated based on the amount of emission of the vehicle as well as travel cost between two cities, (ii) pheromone initialized and updated depends on the qubit, (iii) quantum-inspired technique makes fast computation. The proposed sustainable 4DTSP is illustrated with some numerical data. The defuzzification of type-2 fuzzy variable based on the Critical value (CV) method is used in this model. The supremacy of the proposed method is established through some statistical tests. The proposed algorithm and its modified form can be easily adapted in ship routing, supply chain problems, and other fields.     

Incorporating lateral transfers of vehicles and inventory into an integrated replenishment and routing plan for a three-echelon supply chain

This paper focuses on developing an integrated replenishment and routing plan that takes into account lateral transfers of both vehicles and inventory for a three-echelon supply chain system including a single plant, multiple distribution centers and multiple retailers. A mixed integer programming model to the overall system is formulated first, and then an optimization-based heuristic consisting of three major components is proposed. The purpose of the first component is to assign retailers to distribution centers, and determine routing schedules for each distribution center. And the remaining two components are corresponding to two smaller optimization models – a variant of the classical transportation problem modeled for determining vehicle transfer between distribution centers, and a variant of the conventional minimum cost network flow problem modeled for determining inventory replenishment and transfer. Experimental results reveal that the proposed algorithm is rather computational effectiveness, and the pooling strategy that considers both vehicles and inventory transfers is a worthy option in designing supply chain operations.     

An integrated local search method for inventory and routing decisions

The present article studies an inventory routing model which integrates two important components of the supply chain: transportation logistics and inventory control. The distribution system examined consists of customers that face product demand at a deterministic and constant rate. Customer demand is satisfied by a fixed vehicle fleet located at the central depot. The aim of the problem is to determine the timing and size of the replenishment services together with the vehicle routes, so that the total transportation and inventory holding cost of the system is minimized. In methodological terms, we propose a solution approach applying two innovative local search operators for jointly dealing with the inventory and routing aspects of the examined problem, and Tabu Search for further reducing the transportation costs. The proposed algorithmic framework was tested on a set of new benchmark instances of various scales. It produced satisfactory results both in terms of effectiveness and robustness.     

Simultaneous control of vehicle routing and inventory for dynamic inbound supply chain

This paper investigates inbound logistics for an OEM (Original Equipment Manufacturing) manufacturer, who aims at short production time and JIT policy. In such a case, it can be argued that the inbound vehicle routing schedule should be combined with incoming parts inventory control. In this paper, we propose a simultaneous control method of combining vehicle scheduling and inventory control for such dynamic inbound logistics. For the transportation control, a vehicle routing system, in which delivery jobs are made with shipments of one supplier, is proposed to generate a vehicle routes plan by considering production start time, travel time, waiting time, and loading/unloading time. To evaluate the performance of the generated vehicle routing plan, a goal model is also developed by considering vehicle operating cost, stock level exceeding penalty, and transportation efficiency. A generated vehicle routing plan can be rejected when the stock level is over the capacity and an appropriate number of vehicles for its manufacturing environment can be determined. Using real data from an LCD firm, a simulation study is conducted. The simulation results indicate that the simultaneous control approach requires fewer vehicles than the existing system and shows better efficiency of transportation. This method can also be used to determine the appropriate incoming part inventory level or the number of vehicles required in dynamic inbound logistics.     

A genetic algorithm for the vendor-managed inventory routing problem with lost sales

This paper proposes a genetic algorithm (GA) for the inventory routing problem with lost sales under a vendor-managed inventory strategy in a two-echelon supply chain comprised of a single manufacturer and multiple retailers. The proposed GA is inspired by the solving mechanism of CPLEX for the optimization model of the problem. The proposed GA determines replenishment times and quantities and vehicle routes in a decoupled manner, while maximizing supply chain profits. The proposed GA is compared with the optimization model with respect to the effectiveness and efficiency in various test problems. The proposed GA finds solutions in a short computational time that are very close to those obtained with the optimization model for small problems and solutions that are within 3.2% of those for large problems. Furthermore, sensitivity analysis is conducted to investigate the effects of several problem parameters on the performance of the proposed GA and total profits.     

A Multi-Trip Split-Delivery Vehicle Routing Problem with Time Windows for Inventory Replenishment Under Stochastic Travel Times

This study considers a multi-trip split-delivery vehicle routing problem with soft time windows for daily inventory replenishment under stochastic travel times. Considering uncertainty in travel times for vehicle routing problems is beneficial because more robust schedules can be generated and unanticipated consequences can be reduced when schedules are implemented in reality. However, uncertainties in model parameters have rarely been addressed for the problems in this category mainly due to the high problem complexity. In this study, an innovative and practical approach is proposed to consider stochastic travel times in the planning process. In the planning model, the possible outcomes of vehicle arrivals and product delivery at retailers are systematically categorized and their associated penalty and reward are estimated. Thus, unanticipated costs for every scheduling decision can be incorporated into the planning model to generate vehicle routing schedules that are more robust facing uncertain traffic conditions. To solve the model that is characterized as an NP-hard problem in a reasonable amount of time, a two-stage heuristic solution algorithm is proposed. Finally, the stochastic model is compared with the deterministic model in both planning and simulated operation stages using the data of a supply chain in Taiwan. The result confirms that the schedule generated by the stochastic model is more robust than the one created with the deterministic model because undesired outcomes such as unfulfilled demands are greatly reduced.     

基于划分的蚁群算法求解货物权重车辆路径问题

考虑单产品分销网络中的车辆路径问题(VRP:vehicle routing problem).与以往诸多研究不同的是,建立了一种带货物载重量的VRP模型(weighted VRP),即车辆在两个顾客之间行驶时的载重量也作为影响运输费用的一个因素考虑.因此,需求量较大的顾客拥有较高的车辆运输优先权.在分析了问题性质的基础上,提出一种基于划分策略的蚁群算法PMMAS求解货物权重车辆路径问题,并与其他常用的启发式算法进行比较分析,表明了算法的有效性.     

求解动态需求车辆调度问题的自适应量子遗传算法

针对物流配送过程中存在的动态车辆调度问题,即带载车量约束的实时优化车辆路径问题,提出一种自适应量子遗传算法,用于最小化配送成本.根据搜索点目标函数的变化率,提出一种自适应量子旋转门更新方式,并通过子种群适应度值的变化确定量子旋转角的方向和大小,进而引导种群进化方向,提高算法的全局搜索广泛性;设计了一种变异操作,用于保持自适应量子遗传算法的种群多样性,进而提高算法全局搜索的宽泛性;引入基于两元素搜索原则的局部搜索方法来增强算法的局部优化能力.仿真实验和算法比较验证了所提算法的有效性和优越性.     

Multiscale production routing in multicommodity supply chains with complex production facilities

In this work, we introduce the multiscale production routing problem (MPRP), which considers the coordination of production, inventory, distribution, and routing decisions in multicommodity supply chains with complex continuous production facilities. We propose an MILP model involving two different time grids. While a detailed mode-based production scheduling model captures all critical operational constraints on the fine time grid, vehicle routing is considered in each time period of the coarse time grid. In order to solve large instances of the MPRP, we propose an iterative MILP-based heuristic approach that solves the MILP model with a restricted set of candidate routes at each iteration and dynamically updates the set of candidate routes for the next iteration. The results of an extensive computational study show that the proposed algorithm finds high-quality solutions in reasonable computation times, and in large instances, it significantly outperforms a standard two-phase heuristic approach and a solution strategy involving a one-time heuristic pre-generation of candidate routes. Similar results are achieved in an industrial case study, which considers a real-world industrial gas supply chain.     

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.     

A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage

The purpose of this paper is to develop a multi-item economic order quantity (EOQ) model with shortage for a single-buyer single-supplier supply chain under green vendor managed inventory (VMI) policy. This model explicitly includes the VMI contractual agreement between the vendor and the buyer such as warehouse capacity and delivery constraints, bounds for each order, and limits on the number of pallets. To create a kind of green supply chain, tax cost of green house gas (GHG) emissions and limitation on total emissions of all items are considered in the model. A hybrid genetic and imperialist competitive algorithm (HGA) is employed to find a near-optimum solution of a nonlinear integer-programming (NIP) with the objective of minimizing the total cost of the supply chain. Since no benchmark is available in the literature, a genetic algorithm (GA) is developed as well to validate the result obtained. For further validation, the outcomes are also compared to lower bounds that are found using a relaxed model in which all variables are treated continuous. At the end, numerical examples are presented to demonstrate the application of the proposed methodology. Our results proved that the proposed hybrid procedure was able to find better and nearer optimal solutions.     

A hybrid simulated annealing algorithm for location and routing scheduling problems with cross-docking in the supply chain

The location and routing scheduling problems with cross-docking can be regarded as new research directions for distribution networks in the supply chain. The aims of these problems are to concurrently design a cross-docking center location and a vehicle routing scheduling model, known as NP-hard problems. This paper presents a two-stage mixed-integer programming (MIP) model for the location of cross-docking centers and vehicle routing scheduling problems with cross-docking due to potential applications in the distribution networks. Then, a new algorithm based on a two-stage hybrid simulated annealing (HSA) with a tabu list taken from tabu search (TS) is proposed to solve the presented model. This proposed HSA not only prevents revisiting the solution but also maintains the stochastic nature. Finally, small and large-scale test problems are randomly generated and solved by the HSA algorithm. The computational results for different problems show that the proposed HSA performs well and converges fast to reasonable solutions.     

柔性作业车间生产计划与调度集成优化求解策略

针对柔性作业车间(Flexible job-shop, FJS)生产计划(Production planning, PP)与调度紧密衔接的特点, 建立了生产计划与调度集成优化模型. 模型综合考虑了安全库存、需求损失及工件加工路线柔性等方面因素. 提出了一种基于拉格朗日松弛(Lagrangian relaxation, LR)的分解算法, 将原问题分解为计划子问题与调度子问题. 针对松弛的生产计划子问题, 提出一种新的费用结构, 以保证生产计划决策与实际情况相符, 并设计了一种变量固定—松弛策略与滚动时域组合算法进行求解. 对于调度子问题中的加工路线柔性问题, 提出了一种新的机器选择策略. 通过数值实验验证了模型与算法的有效性.     

面向不同目标偏好的CVRP多目标模型及其求解方法*

为了更有效地求解车辆路径问题、全方位地评估物流运输成本,本文提出了面向不同目标偏好的车载能力约束车辆路径问题(CVRP)的多目标优化模型(MOCVRPFDTP),其包括三种不同的偏好结构：装载与CVRP联合优化、绝对最小车辆数偏好及路径优化偏好。为了求解该模型,本文设计了算法架构及具体算法。在实验中,该模型及其求解方法对CVRP国际标准算例VRPLIB的测试结果,显示了令人满意的性能,并且它更适用于实际CVRP问题的求解。     

基于改进粒子群算法的物流配送车辆调度优化

车辆优化调度是提高物流企业运营效益的重要因素,针对标准粒子群优化算法存在的不足,提出一种改进粒子群算法（IPSO）的物流配送车辆调度优化方法。建立物流配送车辆调度优化的数学模型,将车辆与车辆路径编码成粒子,通过粒子之间的协作找到最优物流配送车辆调度优化方案,并对粒子群算法存在的不足进行了相应的改进,最后给出仿真实验对其性能进行测试。实验结果表明,IPSO算法不仅加快了物流配送车辆调度优化问题求解的速度,而且获得了最优解的概率,具有比其他调度算法更明显的优势。