An empirical study on the benefit of split loads with the pickup and delivery problem

Splitting loads such that the delivery of certain loads is completed in multiple trips rather than one trip has been shown to have benefit for both the classic Vehicle Routing Problem (VRP) and the Pickup and Delivery Problem (PDP). However, the magnitude of the benefit may be affected by various problem characteristics. In this paper, we characterize those real world environments in which split loads are most likely to be beneficial. Based on practitioner interest, we determine how the benefit is affected by the mean load size and variance, number of origins relative to the number of destinations, the percentage of origin–destination pairs with a load requiring service, and the clustering of origin and destination locations. We find that the magnitude of benefit is greatest for load sizes just over one half vehicle capacity as these loads can not be combined without splitting, while they are the easiest to combine on a vehicle with splitting; increases as the number of loads sharing an origin or destination increases because there are more potential load combinations to split at each stop; and increases as the average distance from an origin to a destination increases because splitting loads reduces the trips from origins to destinations.     

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

This paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company’s pharmacy to patients’ homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks.     

Solving the pickup and delivery problem with three-dimensional loading constraints and reloading ban

In this paper, we extend the classical Pickup and Delivery Problem (PDP) to an integrated routing and three-dimensional loading problem, called PDP with three-dimensional loading constraints (3L-PDP). We are given a set of requests and a homogeneous fleet of vehicles. A set of routes of minimum total length has to be determined such that each request is transported from a loading site to the corresponding unloading site. In the 3L-PDP, each request is given as set of rectangular boxes and the vehicle capacity is replaced by a 3D loading space.This paper is the second one in a series of articles on 3L-PDP. As in the first paper we are dealing with constraints which guarantee that no reloading effort will occur. Here the focus is laid on the reloading ban, a packing constraint that ensures identical placements of same boxes in different packing plans. The reloading ban allows for better solutions in terms of travel distance than a routing constraint that was used in the first paper to preclude any reloading effort. To implement this packing constraint a new type of packing procedure is needed that is capable to generate a series of interrelated packing plans per route. This packing procedure, designed as tree search algorithm, and the corresponding concept of packing checks is the main contribution of the paper at hand. The packing procedure and a large neighborhood search procedure for routing form a hybrid algorithm for the 3L-PDP. Computational experiments were performed using 54 3L-PDP benchmark instances.     

A matheuristic approach for solving a home health care problem

We deal with a Home Health Care Problem (HHCP) which objective consists in constructing the optimal routes and rosters for the health care staffs. The challenge lies in combining aspects of vehicle routing and staff rostering which are two well known hard combinatorial optimization problems. To solve this problem, we initially propose an integer linear programming formulation (ILP) and we tested this model on small instances. To deal with larger instances we develop a matheuristic based on the decomposition of the ILP formulation into two problems. The first one is a set partitioning like problem and it represents the rostering part. The second problem consists in the routing part. This latter is equivalent to a Multi-depot Traveling Salesman Problem with Time Windows (MTSPTW).     

A covering tour approach to the location of satellite distribution centers to supply humanitarian aid

This article concerns the location of satellite distribution centers (SDCs) to supply humanitarian aid to the affected people throughout a disaster area. In such situations, it is not possible for the relief teams to visit every single home. Instead, the people are required to go to a satellite distribution center in order to obtain survival goods, provided that these centers are not too far from their homes. The SDCs are usually within walking distance. However, these SDCs need to be supplied from a central depot, using a heterogeneous and capacitated fleet of vehicles. We model this situation as a generalization of the covering tour problem, introduce the idea of split delivery, and propose an efficient heuristic approach to solve it. Numerical experiments on randomly-generated data show that, first, only very small instances can be solved efficiently using the mathematical model and, second, our heuristic produces high-quality solutions and solves real-size instances in a reasonable computing time.     

Branch-and-cut with lazy separation for the vehicle routing problem with simultaneous pickup and delivery

We propose a branch-and-cut algorithm for the VRPSPD where the constraints that ensure that the capacities are not exceeded in the middle of a route are applied in a lazy fashion. The algorithm was tested in 87 instances with 50–200 customers, finding improved lower bounds and several new optimal solutions.     

An approximation algorithm for the pickup and delivery vehicle routing problem on trees

This paper presents an approximation algorithm for a vehicle routing problem on a tree-shaped network with a single depot where there are two types of demands, pickup demand and delivery demand. Customers are located on nodes of the tree, and each customer has a positive demand of pickup and/or delivery.Demands of customers are served by a fleet of identical vehicles with unit capacity. Each vehicle can serve pickup and delivery demands. It is assumed that the demand of a customer is splittable, i.e., it can be served by more than one vehicle. The problem we are concerned with in this paper asks to find a set of tours of the vehicles with minimum total lengths. In each tour, a vehicle begins at the depot with certain amount of goods for delivery, visits a subset of the customers in order to deliver and pick up goods and returns to the depot. At any time during the tour, a vehicle must always satisfy the capacity constraint, i.e., at any time the sum of goods to be delivered and that of goods that have been picked up is not allowed to exceed the vehicle capacity. We propose a 2-approximation algorithm for the problem.     

A complementary tool to enhance the effectiveness of existing methods for heterogeneous fixed fleet vehicle routing problem

The heterogeneous fixed fleet vehicle routing problem (HFFVRP) is a variant of the standard vehicle routing problem (VRP), in which the vertices have to be served using a fixed number of vehicles that could be different in size and fixed or variable costs. In this article, we propose an integer linear programming-based heuristic approach in order to solve the HFFVRP that could be used as a complementary tool to improve the performance of the existing methods of solving this problem. Computational results show the effectiveness of the proposed method.     

An approach for analysing transportation costs and a case study

One of the important parameters in the determination of optimal transportation system is economy. Therefore, a realistic method based on the technical, economical and operational parameters of various transportation modes, namely, road, railway, and sea routes is required in the analysis of costs. This method will take into consideration the probable price escalations during the lifetime of a certain transportation system. The cost of a unit of cargo or passenger per route length should be considered since it is an indicator of economics. In this paper, an approach for transportation cost analysis based on the economic analysis of the alternative modes of cargo or passenger transportation, is presented.     

A column generation approach for the split delivery vehicle routing problem

A column generation approach is presented for the split delivery vehicle routing problem with large demand. Columns include route and delivery amount information. Pricing sub-problems are solved by a limited-search-with-bound algorithm. Feasible solutions are obtained iteratively by fixing one route once. Numerical experiments show better solutions than in the literature.     

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants.     

A powerful route minimization heuristic for the vehicle routing problem with time windows

We suggest an efficient route minimization heuristic for the vehicle routing problem with time windows. The heuristic is based on the ejection pool, powerful insertion and guided local search strategies. Experimental results on the Gehring and Homberger’s benchmarks demonstrate that our algorithm outperforms previous approaches and found 18 new best-known solutions.     

A Lagrangian relaxation-based heuristic for the vehicle routing with full container load

We address a problem of vehicle routing that arises in picking up and delivering full container load from/to an intermodal terminal. The substantial cost and time savings are expected by efficient linkage between pickup and delivery tasks, if the time of tasks and the suitability of containers for cargo allow. As this problem is NP-hard, we develop a subgradient heuristic based on a Lagrangian relaxation which enables us to identify a near optimal solution. The heuristic consists of two sub-problems: the classical assignment problem and the generalized assignment problem. As generalized assignment problem is also NP-hard, we employ an efficient solution procedure for a bin packing based problem, which replaces the generalized assignment problem. The heuristic procedure is tested on a wide variety of problem examples. The test results demonstrate that the procedure developed here can efficiently solve large instances of the problem.     

Vehicle and personnel routing optimization in the service sector: application to water distribution and treatment

We present an overview of the author’s Ph.D. thesis, supervised by P. Dejax and N. Bostel, which was defended in February 2006 at école des Mines de Nantes, France. The thesis is written in French, and is available at . It was conducted in the context of a research contract with a water distribution company. In a first section, we define multiperiod routing problems for service technicians. In a second section, we present some heuristics and a memetic algorithm used to solve these problems. The third section introduces optimal and near-optimal approaches based on column generation. Finally, we present some applications to the real-life case. The methods presented in Sects. 2, 3 and 4 were tested over several sets of problems, based on real-life statistics provided by the company.      

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).     

A tabu search heuristic for the dynamic transportation of patients between care units

The problem studied in this paper stems from a real application to the transportation of patients in the Hospital Complex of Tours (France). The ambulance central station of the Hospital Complex has to plan the transportation demands between care units which require a vehicle. Some demands are known in advance and the others arise dynamically. Each demand requires a specific type of vehicle and a vehicle can transport only one person at a time. The demands can be subcontracted to a private company which implies high cost. Moreover, transportations are subject to particular constraints, among them priority of urgent demands, disinfection of a vehicle after the transportation of a patient with contagious disease and respect of the type of vehicle needed. These characteristics involve a distinction between the vehicles and the crews during the modeling phase. We propose a modeling for solving this difficult problem and a tabu search algorithm inspired by Gendreau et al. (1999). This method supports an adaptive memory and a tabu search procedure. Computational experiments on a real-life instance and on randomly generated instances show that the method can provide high-quality solutions for this dynamic problem with a short computation time.     

A network-consistent time-dependent travel time layer for routing optimization problems

In the vehicle routing literature, there is an increasing focus on time-dependent routing problems, where the time (or cost) to travel between any pair of nodes (customers, depots) depends on the departure time. The aim of such algorithms is to be able to take recurring congestion into account when planning logistics operations. To test algorithms for time-dependent routing problems, time-dependent problem data is necessary. This data usually comes in the form of three-dimensional travel time matrices that add the departure time as an extra dimension. However, most currently available time-dependent travel time matrices are not network-consistent, i.e., the travel times are not correlated both in time and in space. This stands in contrast to the behavior of real life congestion, which generally follows a specific pattern, appearing in specific areas and then affecting all travel times to and from those areas. As a result of the lack of available network-consistent travel time matrices, it is difficult to develop algorithms that are able to take this special structure of the travel time data into account.     

A heuristic algorithm for the free newspaper delivery problem

This paper addresses the problem of finding an effective distribution plan to deliver free newspapers from a production plant to subway, bus, or tram stations. The overall goal is to combine two factors: first, the free newspaper producing company wants to minimize the number of vehicle trips needed to distribute all newspapers produced at the production plant. Second, the company is interested in minimizing the time needed to consume all newspapers, i.e., the time needed to get all the newspapers taken by the final readers. The resulting routing problem combines aspects of the vehicle routing problem with time windows, the inventory routing problem, and additional constraints related to the production schedule. We propose a formulation and different heuristic approaches, as well as a hybrid method. Computational tests with real world data show that the hybrid method is the best in various problem settings.     

An improved ant colony optimization for vehicle routing problem

The vehicle routing problem (VRP), a well-known combinatorial optimization problem, holds a central place in logistics management. This paper proposes an improved ant colony optimization (IACO), which possesses a new strategy to update the increased pheromone, called ant-weight strategy, and a mutation operation, to solve VRP. The computational results for fourteen benchmark problems are reported and compared to those of other metaheuristic approaches.     

A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem

The fleet size and mix vehicle routing problem consists of defining the type, the number of vehicles of each type, as well as the order in which to serve the customers with each vehicle when a company has to distribute goods to a set of customers geographically spread, with the objective of minimizing the total costs. In this paper, a heuristic algorithm based on tabu search is proposed and tested on several benchmark instances. The computational results show that the proposed algorithm produces high quality results within a reasonable computing time. Some new best solutions are reported for a set of test problems used in the literature.