The single vehicle routing problem with deliveries and selective pickups

The single vehicle routing problem with deliveries and selective pickups (SVRPDSP) is defined on a graph in which pickup and delivery demands are associated with customer vertices. The difference between this problem and the single vehicle routing problem with pickups and deliveries (SVRPPD) lies in the fact that it is no longer necessary to satisfy all pickup demands. In the SVRPDSP a pickup revenue is associated with each vertex, and the pickup demand at that vertex will be collected only if it is profitable to do so. The net cost of a route is equal to the sum of routing costs, minus the total collected revenue. The aim is to design a vehicle route of minimum net cost, visiting each customer, performing all deliveries, and a subset of the pickups. A mixed integer linear programming formulation is proposed for the SVRPDSP. Classical construction and improvement heuristics, as well as a tabu search heuristic (TS), are developed and tested on a number of instances derived from VRPLIB. Computational results show that the solutions produced by the proposed heuristics are near-optimal. There is also some evidence that the best solutions identified by the heuristics are frequently non-Hamiltonian and may contain one or two customers visited twice.     

多中心半开放式送取需求可拆分的车辆路径优化

针对多中心半开放式送取需求可拆分的车辆路径问题,构建了以车辆配送距离最短为目标的多中心半开放式送取需求可拆分的数学模型。设计大变异邻域遗传算法进行求解,采用二维染色体编码及顺序交叉策略,同时运用大变异策略和邻域搜索策略提高算法全局和局部的寻优能力,通过算例对比验证了所提模型与算法的有效性。算例实验表明,大变异邻域遗传算法在求解多中心物流配送车辆路径问题上求解质量较优、求解效率较高、求解结果较为稳定,同时验证了联合配送下多中心半开放式送取需求可拆分的配送模式优于独立配送下单中心送取需求可拆分的配送模式。研究成果不仅拓展了车辆路径问题,还可为相关快递物流企业配送优化提供决策参考。     

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.     

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 parallel variable neighborhood search for the vehicle routing problem with divisible deliveries and pickups

A well-known variant of the vehicle routing problem involves backhauls, where vehicles deliver goods from a depot to linehaul customers and pick up goods from backhaul customers to the depot. The vehicle routing problem with divisible deliveries and pickups (VRPDDP) allows vehicles to visit each client once or twice for deliveries or pickups. In this study, a very efficient parallel approach based on variable neighborhood search (VNS) is proposed to solve VRPDDP. In this approach, asynchronous cooperation with a centralized information exchange strategy is used for parallelization of the VNS approach, called cooperative VNS (CVNS). All available problem sets of VRPDDP have been successfully solved with the CVNS, and the best solutions available in the literature have been significantly improved.     

An adaptive local search algorithm for vehicle routing problem with simultaneous and mixed pickups and deliveries

The Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD) is an extension to the classical Vehicle Routing Problem (VRP), where customers may both receive and send goods simultaneously. The Vehicle Routing Problem with Mixed Pickup and Delivery (VRPMPD) differs from the VRPSPD in that the customers may have either pickup or delivery demand. However, the solution approaches proposed for the VRPSPD can be directly applied to the VRPMPD. In this study, an adaptive local search solution approach is developed for both the VRPSPD and the VRPMPD, which hybridizes a Simulated Annealing inspired algorithm with Variable Neighborhood Descent. The algorithm uses an adaptive threshold function that makes the algorithm self-tuning. The proposed approach is tested on well-known VRPSPD and VRPMPD benchmark instances derived from the literature. The computational results indicate that the proposed algorithm is effective in solving the problems in reasonable computation time.     

An improved differential evolution algorithm for vehicle routing problem with simultaneous pickups and deliveries and time windows

The vehicle routing problem with simultaneous pickups and deliveries and time windows (VRP-SPDTW) is the problem of optimally integrating forward (good distribution) and reverse logistics (returning materials) for cost saving and environmental protection. We constructed a general mixed integer programming model of VRP-SPDTW. The model contained some classical vehicle routing problems as special cases. We proposed an improved differential evolution algorithm (IDE) for solving this problem. In the algorithm, we firstly adopted the novel decimal coding to construct an initial population, then used some improved differential evolution operators unlike the existing algorithm, and in mutation operation, we used an integer order criterion based on natural number coding method. We introduced a penalty technical to publish the infeasible solution. In addition, in the crossover operation, we designed a self-adapting crossover probability that varied with iteration. We did some numerical experiments, and the results showed that the proposed method is effective for solving VRP-SPDTW.     

A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries

The vehicle routing problem with simultaneous pick-up and deliveries, which considers simultaneous distribution and collection of goods to/from customers, is an extension of the capacitated vehicle routing problem. There are various real cases, where fleet of vehicles originated in a depot serves customers with pick-up and deliveries from/to their locations. Increasing importance of reverse logistics activities make it necessary to determine efficient and effective vehicle routes for simultaneous pick-up and delivery activities. The vehicle routing problem with simultaneous pick-up and deliveries is also NP-hard as a capacitated vehicle routing problem and this study proposes a genetic algorithm based approach to this problem. Computational example is presented with parameter settings in order to illustrate the proposed approach. Moreover, performance of the proposed approach is evaluated by solving several test problems.     

Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries

In parallel with the growth of both domestic and international economies, there have been substantial efforts in making manufacturing and service industries more environmental friendly (i.e., promotion of environmental protection). Today manufacturers have become much more concerned with coordinating the operations of manufacturing (for new products) and recycling (for reuse of resources) together with scheduling the forward/reverse flows of goods over a supply chain network. The stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries (STT-VRPSPD) is one of the major operations problems in bi-directional supply chain research. The STT-VRPSPD is a very challenging and difficult combinatorial optimization problem due to many reasons such as a non-monotonic increase or decrease of vehicle capacity and the stochasticity of travel times. In this paper, we develop a new scatter search (SS) approach for the STT-VRPSPD by incorporating a new chance-constrained programming method. A generic genetic algorithm (GA) approach for STT-VRPSPD is also developed and used as a reference for performance comparison. The Dethloff data will be used to evaluate the performance characteristics of both SS and GA approaches. The computational results suggest that the SS solutions are superior to the GA solutions.     

Metaheuristics for the traveling salesman problem with pickups, deliveries and handling costs

This paper studies the Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs. The subproblem of minimizing the handling cost for a fixed route is analyzed in detail. It is solved by means of an exact dynamic programming algorithm with quadratic complexity and by an approximate linear time algorithm. Three metaheuristics integrating these solution methods are developed. These are based on tabu search, iterated local search and iterated tabu search. The three heuristics are tested and compared on instances adapted from the related literature. The results show that the combination of tabu search and exact dynamic programming performs the best, but using the approximate linear time algorithm considerably decreases the CPU time at the cost of slightly worse solutions.     

Vessel routing with pickups and deliveries: An application to the supply of offshore oil platforms

This paper presents a new routing problem, the Vessel Routing Problem with Selective Pickups and Deliveries (VRPSPD), an extension of existing pickup and delivery problems that arises in the planning of logistics operations in the offshore oil and gas industry. The VRPSPD is a single-vessel model that can lead to significant economic improvements to the current planning scheme without having a very large impact on the operations. In addition, we formulate a Multi-Vessel Routing Problem with Pickups and Deliveries (mVRPPD) that leads to even larger economical gains, but also entails more important changes in the current planning and operations. To quantify and justify the benefits of the VRPSPD and mVRPPD, an industry case based on real data was constructed and solved for 300 days. The VRPSPD is solvable with a commercial solver for most real-size instances. However, for the mVRPPD on the largest instances, it was necessary to develop a state-of-the-art adaptive large neighborhood heuristic search to reduce computational time.     

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.     

Testing local search move operators on the vehicle routing problem with split deliveries and time windows

The vehicle routing problem (VRP) is an important transportation problem. The literature addresses several extensions of this problem, including variants having delivery time windows associated with customers and variants allowing split deliveries to customers. The problem extension including both of these variations has received less attention in the literature. This research effort sheds further light on this problem. Specifically, this paper analyzes the effects of combinations of local search (LS) move operators commonly used on the VRP and its variants. We find when paired with a MAX-MIN Ant System constructive heuristic, Or-opt or 2-opt⁎ appear to be the ideal LS operators to employ on the VRP with split deliveries and time windows with Or-opt finding higher quality solutions and 2-opt⁎ requiring less run time.     

Heuristic methods for the fleet size and mix vehicle routing problem with time windows and split deliveries

This paper proposes a scatter-search (SS) approach to solve the Fleet Size and Mixed Vehicle Routing Problem with Time Windows and Split Deliveries (FSMVRPTWSD). In the Vehicle Routing Problem with Split Deliveries (VRPSD), each customer can be served by more than one vehicle, as opposed to the classical VRP in which each customer is served only once. In the FSMVRPTW, the customers must be serviced within their time windows with minimal costs using a heterogeneous fleet. Experimental testing and benchmark examples are used to assess the merit of our proposed procedure. The results show that the proposed heuristics are competitive with the best results found in the literature.     

The robust vehicle routing problem with time windows

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.     

The dynamic multi-period vehicle routing problem

This paper considers the dynamic multi-period vehicle routing problem which deals with the distribution of orders from a depot to a set of customers over a multi-period time horizon. Customer orders and their feasible service periods are dynamically revealed over time. The objectives are to minimize total travel costs and customer waiting, and to balance the daily workload over the planning horizon. This problem originates from a large distributor operating in Sweden. It is modeled as a mixed integer linear program, and solved by means of a three-phase heuristic that works over a rolling planning horizon. The multi-objective aspect of the problem is handled through a scalar technique approach. Computational results show that the proposed approach can yield high quality solutions within reasonable running times.     

The dynamic multiperiod vehicle routing problem with probabilistic information

This paper introduces the Dynamic Multiperiod Vehicle Routing Problem with Probabilistic Information, an extension of the Dynamic Multiperiod Vehicle Routing Problem in which, at each time period, the set of customers requiring a service in later time periods is unknown, but its probability distribution is available. Requests for service must be satisfied within a given time window that comprises several time periods of the planning horizon. We propose an adaptive service policy that aims at estimating the best time period to serve each request within its associated time window in order to reduce distribution costs. The effectiveness of this policy is compared with that of two alternative basic policies through a series of computational experiments.     

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.     

The capacitated vehicle routing problem with stochastic demands and time windows

The capacitated vehicle routing problem with stochastic demands and time windows is an extension of the capacitated vehicle routing problem with stochastic demands, in which demands are stochastic and a time window is imposed on each vertex. A vertex failure occurring when the realized demand exceeds the vehicle capacity may trigger a chain reaction of failures on the remaining vertices in the same route, as a result of time windows. This paper models this problem as a stochastic program with recourse, and proposes an adaptive large neighborhood search heuristic for its solution. Modified Solomon benchmark instances are used in the experiments. Computational results clearly show the superiority of the proposed heuristic over an alternative solution approach.     

The customer-centric,multi-commodity vehicle routing problem with split delivery

In this paper, we present the Customer-centric, Multi-commodity Vehicle Routing Problem with Split Delivery (CMVRPSD) whose objective is to minimize total waiting time of customers in distributing multiple types of commodities by multiple capacitated vehicles. It is assumed that a customer's demand can be fulfilled by more than one vehicle. Two classes of decisions are involved in this problem: routing vehicles to customers and quantifying commodities to load and unload. The CMVRPSD can be applied to distributing commodities in customer-oriented distribution problems for both peacetime and disaster situations. The problem is formulated in two Mixed-Integer Linear Programming (MILP) models, and a heuristic method is proposed by adapting and synthesizing Simulated Annealing (SA) and Variable Neighborhood Search (VNS) for large-scale problems. Experimental results show that the proposed hybrid algorithm outperforms other applicable algorithms such as SA, VNS, and Nearest Neighborhood heuristic.