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).     

Variable neighborhood search for the inventory routing and scheduling problem in a supply chain

The inventory, routing and scheduling decisions are three major driving factors for supply chain performance. Since they are related to one another in a supply chain, they should be determined simultaneously to improve the decision quality. In the past, the inventory policy, vehicle routing and vehicle scheduling are determined sequentially and separately. Hence, the total cost (inventory, routing and vehicle costs) would increase. In this paper, an integrated model for the inventory routing and scheduling problem (IRSP) is proposed. Since searching for the optimal solution for this model is a non-polynomial (NP) problem, a metaheuristic, variable neighborhood search (VNS), is proposed. The proposed method was compared with other existing methods. The experimental results indicate that the proposed method is better than other methods in terms of average cost per day.     

A construction and improvement heuristic for a liquefied natural gas inventory routing problem

We present a large scale ship routing and inventory management problem for a producer and distributor of liquefied natural gas (LNG). The problem contains multiple products, inventory and berth capacity at the loading port and a heterogeneous fleet of ships. The goal is to create an annual delivery program to fulfill the producer’s long-term contracts at minimum cost, while maximizing the revenue from selling LNG in the spot market. To solve this problem we have developed a construction and improvement heuristic (CIH).The CIH is a multi-start local search heuristic that constructs a set of solutions using a greedy insertion procedure. The solutions are then improved using either a first-descent neighborhood search, branch-and-bound on a mathematical formulation, or both. Tests on real-life instances show that the CIH provides good solutions in a short amount of time.     

A mixed integer nonlinear programming model and heuristic solutions for location,inventory and pricing decisions in a closed loop supply chain

We analyze a network design problem for a closed-loop supply chain that integrates the collection of the used products with the distribution of the new products. We present a mixed integer nonlinear facility location-inventory-pricing model to decide on the optimal locations of the facilities, inventory amounts, prices for new products and incentive values for the collection of right amount of used products in order to maximize the total supply chain profit. We develop heuristics for the solution of this model and analyze the effectiveness of these heuristics and the effects of the parameters on this system through numerical experiments.     

A local search method for periodic inventory routing problem

Inventory routing problem considers inventory allocation and routing problems simultaneously, in which the replenishment policies and routing arrangement are determined by the supplier under the vendor managed inventory mode. What we consider here is a periodic inventory routing problem that once the delivery time, quantity and routing are determined, they will remain the same in the following periods. The problem is modeled concisely, and then it is decomposed into two subproblems, inventory problem and vehicle routing problem. The inventory problem is solved by proposing a local search method, which is achieved by four operators on delivery quantity and retailer’s demand. Insertion operator aims to insert a new replenishment point of a retailer while removal operator is to remove a replenishment point. Besides, addition operator is adopted as an assistant tool, and crossover operator is proposed for some special cases. We also propose a tabu search method to solve the routing problem. Finally, the computational results show that the method is efficient and stable.     

An effective heuristic for solving a combined cargo and inventory routing problem in tramp shipping

In this paper a vendor managed inventory (VMI) service in tramp shipping is considered. VMI takes advantage of introducing flexibility in delivery time and cargo quantities by transferring inventory management and ordering responsibilities to the vendor which in this case is a shipping company. A two-phase heuristic is proposed to determine routes and schedules for the shipping company. The heuristic first converts inventories into cargoes, thus turning the problem into a classic ship routing and scheduling problem. It then uses adaptive large neighborhood search to solve the resulting cargo routing and scheduling problem. The heuristic iteratively changes the cargoes generated to handle the customer’s inventories, based on the information obtained from an initial solution. Computational results are presented, discussed and compared with exact solutions on large realistic instances. The results reveal the potential savings from converting traditional contracts of affreightment to an integrated VMI service. The factors that influence the benefits obtainable through VMI are also analyzed.     

A multi-phase heuristic for the production routing problem

This study considers the production routing problem where a plant produces and distributes a single item to multiple retailers over a multi-period time horizon. The problem is to decide on when and how much to produce and stock at the plant, when and how much to serve and stock at each retailer, and vehicle routes for shipments such that the sum of fixed production setup cost, variable production cost, distribution cost, and inventory carrying cost at the plant and retailers is minimized. A multi-phase heuristic is proposed for the problem. The proposed heuristic is a mathematical programming-based heuristic that relies on formulating and solving restricted versions of the problem as mixed integer programs. The computational experiments on benchmark instances show favorable results with regard to the quality of the solutions found at the expense of higher computing times on large instances. In particular, the heuristic managed to find new best solutions for the 65% of benchmark instances.     

A heuristic method for the vehicle routing problem with mixed deliveries and pickups

The vehicle routing problem with deliveries and pickups is a challenging extension to the vehicle routing problem that lately attracted growing attention in the literature. This paper investigates the relationship between two versions of this problem, called “mixed” and “simultaneous”. In particular, we wish to know whether a solution algorithm designed for the simultaneous case can solve the mixed case. To this end, we implement a metaheuristic based on reactive tabu search. The results suggest that this approach can yield good results.     

A novel two-phase heuristic method for vehicle routing problem with backhauls

This paper raises a novel two-phase heuristic method to solve vehicle routing problems with backhauls. Differing from other vehicle routing problems, we consider the travel speed of vehicle to be time dependent, which will be used for the model of rush hour in an urban city. In the first phase, the original solution is generated by extending traditional heuristic methods and in the second phase, the reactive tabu search algorithm is used to optimize the original solution. We verified that this algorithm is efficient in a number of standard test cases. After comparison with the closest neighboring search algorithm, we found that the results of two-phase heuristic methods are more reasonable.     

A hybrid genetic algorithm based heuristic for an integrated supply chain problem

Supply chain management is becoming an essential component of efficient decision-making for companies, as they are increasingly implementing optimization strategies in order to improve their business performance. In this paper we develop a capacitated multi-echelon joint location-inventory model, according to which a single product is distributed from a manufacturer to retailers through a set of warehouses, the locations of which are to be determined by the model. Each retailer is assigned exactly one warehouse, while each warehouse can serve multiple retailers. The model decides where to locate warehouses, assigns retailers to the warehouses and decides the times between orders at the warehouses and the retailers, so as to minimize the cost of operating the supply chain. Notably, the model considers capacity constraints for each warehouse, ensuring that the reorder quantity is below the capacity limit. We develop a genetic algorithm (GA) based heuristic to solve the problem and the GA is validated on small size problems by comparing its solution to the optimal solution obtained by the General Algebraic Modeling System (GAMS). We focus our attention on specifically customizing the GA and thus an experimental analysis is carried out to find the optimal parameter setting for the GA as well as to obtain insights on the effect of the various GA parameters. Finally, a sensitivity analysis is conducted to show the effect of the capacity constraints.     

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 Web-based tool and a heuristic method for cooperation of manufacturing supply chain decisions

Supply chain issues have been given much attention. Various technologies and concepts have been applied to improving and optimizing supply chain performance. However, few methods to explore supply chain inter-relationships, detect process key problems and co-ordinate planning processes in different supply chain partners are available. A Web-based co-ordinated planning process supported by quality function deployment (QFD) approach is proposed in this research. The planning method is focused on integrating planning processes in supply chains by optimizing each planning process and interactively adjusting key parameters in different business processes. The QFD approach is employed to inter-relate different business processes and detect key problems through Internet technique application, so that the global solution can be heuristically improved. The planning method imitates the real-world supply chain planning environment and provides a mechanism for decision-makers to communicate with quantitative information in planning processes through the Web system. An illustrative case study in packaging industry is conducted to describe the planning procedure. The result of the example shows prospect of the method in improving supply chain cooperation. The approach is expected to facilitate supply chain planning and support managers to solve targeted problems more efficiently.     

A two-stage heuristic method for vehicle routing problem with split deliveries and pickups

The vehicle routing problem （VRP） is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups （VRPSPDP） is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.     

Simulation-based heuristic method for container supply chain network optimization

With the emerging of free trade zones (FTZs) in the world, the service level of container supply chain plays an important role in the efficiency, quality and cost of the world trade. The performance of container supply chain network directly impacts its service level. Therefore, it is imperative to seek an appropriate method to optimize the container supply chain network architecture. This paper deals with the modeling and optimization problem of multi-echelon container supply chain network (MCSCN). The problem is formulated as a mixed integer programming model (MIP), where the objective is subject to the minimization of the total supply chain service cost. Since the problem is well known to be NP-hard, a novel simulation-based heuristic method is proposed to solving it, where the heuristic is used for searching near-optimal solutions, and the simulation is used for evaluating solutions and repairing unfeasible solutions. The heuristic algorithm integrates genetic algorithm (GA) and particle swarm optimization (PSO) algorithm, where the GA is used for global search and the PSO is used for local search. Finally, computational experiments are conducted to validate the performance of the proposed method and give some managerial implications.     

A heuristic for the vehicle routing problem with due times

This paper studies the vehicle routing problem with due times. The vehicles are supposed to visit customers within the due times, and a penalty cost is imposed in case the vehicle arrives past the due times. The objective is to minimize the weighted sum of the traveling time of vehicles and the tardiness of the service customers receive. A mixed integer programming formulation and a heuristic based on the tabu search for a practical use are suggested. Route-perturb and route-improvement method for the neighborhood generation is proposed. Performances are compared with other heuristics appeared in the literature using the bench-mark data set modified to be fit to the model. It is shown that the suggested heuristic gives a good solution in a short computation time.     

供应链中车辆路径问题的改进模拟退火算法

车辆路径的优化是供应链优化中的重要环节。设计了一种改进的模拟退火算法用于求解有客户需求、车辆最大载重量和最大行驶距离三个约束条件的车辆路径问题。主要改进在于：编码方案采用客户编号的顺序编码,并设计专门的解码方法能够把三种约束全都纳入考虑,再综合运用三种邻域生成算子提高局部搜索能力,采用基本的线性降温方式控制降温过程。运用此算法针对同一算例,采用三种不同的降温系数进行了仿真实验,得到了更好的配送方案。实验结果表明该算法不仅求解速度快,而且寻优能力也有显著增强。     

A simulated annealing heuristic for the capacitated location routing problem

The location routing problem (LRP) is a relatively new research direction within location analysis that takes into account vehicle routing aspects. The goal of LRP is to solve a facility location problem and a vehicle routing problem simultaneously. We propose a simulated annealing (SA) based heuristic for solving the LRP. The proposed SALRP heuristic is tested on three sets of well-known benchmark instances and the results are compared with other heuristics in the literature. The computational study indicates that the proposed SALRP heuristic is competitive with other well-known algorithms.     

A location–inventory supply chain problem: Reformulation and piecewise linearization

In this paper, we study a two-echelon inventory management problem with multiple warehouses and retailers. The problem is a natural extension to the well-known one-warehouse multi-retailer inventory problem. The problem is formulated as a mixed integer non-linear program such that its continuous relaxation is non-convex. We propose an equivalent formulation with fewer non-linear terms in the objective function so that the continuous relaxation of the new model is a convex optimization problem. We use piecewise linearization to transform the resulting MINLP to a mixed integer program and we solve it using CPLEX. Through numerical experiments, we compare the solutions obtained by solving the new formulation using CPLEX with two previously published Lagrangian relaxation based heuristics to solve the original mixed integer non-linear program. We demonstrate that the new approach is capable of providing almost the same solutions without the need of using specialized algorithms. This important contribution further implies that additional variants of the problem, such as multiple products, capacitated warehouses and routing, can be added to result in a problem that will again be solvable by commercial optimization software, while the respective Lagrangian heuristics will fail to solve such variants or extended problems.     

A generalized exchange heuristic for the capacitated vehicle routing problem

We consider the problem of dispatching the minimum number of vehicles from a central depot to make deliveries to a set of clients with known demands. The objective is to minimize the total distance travelled, subject to vehicle capacity requirements. We present a new heuristic algorithm for solving this problem. The algorithm is based on generalized edge-exchange search procedures, and relaxation of the capacity requirements. Computational results, based upon standard test problems with up to 249 customers, indicate that our heuristic compares favourably with known heuristics in terms of solution quality.     

A tabu search heuristic for the truck and trailer routing problem

Two new construction heuristics and a tabu search heuristic are presented for the truck and trailer routing problem, a variant of the vehicle routing problem. Computational results indicate that the heuristics are competitive to the existing approaches. The tabu search algorithm obtained better solutions for each of 21 benchmark problems.