Lasso solution strategies for the vehicle routing problem with pickups and deliveries

This paper considers the vehicle routing problem with pickups and deliveries (VRPPD) where the same customer may require both a delivery and a pickup. This is the case, for instance, of breweries that deliver beer or mineral water bottles to a set of customers and collect empty bottles from the same customers. It is possible to relax the customary practice of performing a pickup when delivering at a customer, and postpone the pickup until the vehicle has sufficient free capacity. In the case of breweries, these solutions will often consist of routes in which bottles are first delivered until the vehicle is partly unloaded, then both pickup and delivery are performed at the remaining customers, and finally empty bottles are picked up from the first visited customers. These customers are revisited in reverse order, thus giving rise to lasso shaped solutions. Another possibility is to relax the traditional problem even more and allow customers to be visited twice either in two different routes or at different times on the same route, giving rise to a general solution. This article develops a tabu search algorithm capable of producing lasso solutions. A general solution can be reached by first duplicating each customer and generating a Hamiltonian solution on the extended set of customers. Test results show that while general solutions outperform other solution shapes in term of cost, their computation can be time consuming. The best lasso solution generated within a given time limit is generally better than the best general solution produced with the same computing effort.     

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.     

Vehicle routing problem with simultaneous deliveries and pickups

The vehicle routing problem with backhauls involves the delivery and pickup of goods at different customer locations. In many practical situations, however, the same customer may require both a delivery of goods from the distribution centre and a pickup of recycled items simultaneously. In this paper, an insertion-based procedure to generate good initial solutions and a heuristic based on the record-to-record travel, tabu lists, and route improvement procedures are proposed to resolve the vehicle routing problems with simultaneous deliveries and pickups. Computational characteristics of the insertion-based procedure and the hybrid heuristic are evaluated through computational experiments. Computational results show that the insertion-based procedure obtained better solutions than those found in the literature. Computational experiments also show that the proposed hybrid heuristic is able to reduce the gap between initial solutions and optimal solutions effectively and is capable of obtaining optimal solutions very efficiently for small-sized problems.     

A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem

We present a variable neighborhood search approach for solving the one-commodity pickup-and-delivery travelling salesman problem. It is characterized by a set of customers such that each of the customers either supplies (pickup customers) or demands (delivery customers) a given amount of a single product, and by a vehicle, whose given capacity must not be exceeded, that starts at the depot and must visit each customer only once. The objective is to minimize the total length of the tour. Thus, the considered problem includes checking the existence of a feasible travelling salesman’s tour and designing the optimal travelling salesman’s tour, which are both NP-hard problems. We adapt a collection of neighborhood structures, k-opt, double-bridge and insertion operators mainly used for solving the classical travelling salesman problem. A binary indexed tree data structure is used, which enables efficient feasibility checking and updating of solutions in these neighborhoods. Our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best-known algorithms in terms of both the solution quality and computational efforts. Moreover, we improve the best-known solutions of all benchmark instances from the literature (with 200 to 500 customers). We are also able to solve instances with up to 1000 customers.     

An iterated local search algorithm for the Travelling Salesman Problem with Pickups and Deliveries

The Travelling Salesman Problem with Pickups and Deliveries (TSPPD) consists in designing a minimum cost tour that starts at the depot, provides either a pickup or delivery service to each of the customers and returns to the depot, in such a way that the vehicle capacity is not exceeded in any part of the tour. In this paper, the TSPPD is solved by considering a metaheuris-tic algorithm based on Iterated Local Search with Variable Neighbourhood Descent and Random neighbourhood ordering. Our aim is to propose a fast, flexible and easy to code algorithm, also capable of producing high quality solutions. The results of our computational experience show that the algorithm finds or improves the best known results reported in the literature within reasonable computational time.     

考虑客户满意度的同时收发车辆路径问题

当客户要求车辆一次性完成发送以及收集货物的任务时, 只需考虑车辆的路径安排即可.但若客户进一步提出在时间窗内完成的话,就必须考虑客户的等待时间--客户的满意度的衡量标准,等待时间越短满意度越高.因此问题的目标为最小化车辆路径总长度、最小化所有客户等待时间之和.本文通过加权转变为单目标函数,由最邻近法及最廉价插入法得到初始解后经过禁忌搜索算法可得到改进算法,解并通过实例对不同权参数的情况进行了比较.     

Notes on the single route lateral transhipment problem

Previous research has analyzed deterministic and stochastic models of lateral transhipments between different retailers in a supply chain. In these models the analysis assumes given fixed transhipment costs and determines under which situations (magnitudes of excess supply and demand at various retailers) the transhipment is profitable. However, in reality, these depend on aspects like the distance between retailers or the transportation mode chosen. In many situations, combining the transhipments may save transportation costs. For instance, one or more vehicle routes may be used to redistribute the inventory of the potential pickup and delivery stations. This can be done in any sequence as long as the vehicle capacity is not violated and there is enough load on the vehicle to satisfy demand. The corresponding problem is an extension of the one-commodity pickup and delivery traveling salesman and the pickup and delivery vehicle routing problem. When ignoring the routing aspect and assuming given fixed costs, transhipment is only profitable if the quantities are higher than a certain threshold. In contrast to that, the selection of visited retailers is dependent on the transportation costs of the tour and therefore the selected retailers are interrelated. Hence the problem also has aspects of a (team) orienteering problem. The main contribution is the discussion of the tour planning aspects for lateral transhipments which may be valuable for in-house planning but also for price negotiations with external contractors. A mixed integer linear program for the single route and single commodity version is presented and an improved LNS framework to heuristically solve the problem is introduced. Furthermore, the effect of very small load capacity on the structure of optimal solutions is discussed.     

General solutions to the single vehicle routing problem with pickups and deliveries

The single vehicle routing problem with pickups and deliveries (SVRPPD) is defined on a graph in which pickup and delivery demands are associated with the customer vertices. The problem consists of designing a least cost route for a vehicle of capacity Q. Each customer is allowed to be visited once for a combined pickup and delivery, or twice if these two operations are performed separately. This article proposes a mixed integer linear programming model for the SVRPPD. It introduces the concept of general solution which encompasses known solution shapes such as Hamiltonian, double-path and lasso. Classical construction and improvement heuristics, as well as a tabu search heuristic, are developed and tested over several instances. Computational results show that the best solutions generated by the heuristics are frequently non-Hamiltonian and may contain up to two customers visited twice.     

Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery

In this paper, we consider a variant of the many-to-many location-routing problem, where hub facilities have to be located and customers with either pickup or delivery demands have to be combined in vehicle routes. In addition, several commodities and inter-hub transport processes are taken into account. A practical application of the problem can be found in the timber-trade industry, where companies provide their services using hub-and-spoke networks. We present a mixed-integer linear model for the problem and use CPLEX 12.4 to solve small-scale instances. Furthermore, a multi-start procedure based on a fix-and-optimize scheme and a genetic algorithm are introduced that efficiently construct promising solutions for medium- and large-scale instances. A computational performance analysis shows that the presented methods are suitable for practical application.     

Real-time split-delivery pickup and delivery time window problems with transfers

In this research we present the design and implementation of heuristics for solving split-delivery pickup and delivery time window problems with transfer (SDPDTWP) of shipments between vehicles for both static and real-time data sets. In the SDPDTWP each shipment is constrained with the earliest possible pickup time from the origin and the latest acceptable delivery time to a destination. Split-deliveries occur when two or more vehicles service the same origin or destination. The proposed heuristics were applied to both static and real-time data sets. The heuristics computed a solution, in a few seconds, for a static problem from the literature, achieving an improvement of 60% in distance in comparison to the published solution. In the real-time SDPDTWP problems, requests for pickup and delivery of a package, breakdown of a truck or insertion of a truck can occur after the vehicle has left the origin and is enroute to service the customers. Thirty data sets, each consisting of one to seven real-time customer or truck events, were used to test the efficiency of the heuristics. The heuristics obtained solutions to real-time data sets in under five seconds of CPU time.      

A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery

This paper addresses a location-routing problem with simultaneous pickup and delivery (LRPSPD) which is a general case of the location-routing problem. The LRPSPD is defined as finding locations of the depots and designing vehicle routes in such a way that pickup and delivery demands of each customer must be performed with same vehicle and the overall cost is minimized. We propose an effective branch-and-cut algorithm for solving the LRPSPD. The proposed algorithm implements several valid inequalities adapted from the literature for the problem and a local search based on simulated annealing algorithm to obtain upper bounds. Computational results, for a large number of instances derived from the literature, show that some instances with up to 88 customers and 8 potential depots can be solved in a reasonable computation time.     

Planning and approximation models for delivery route based services with price-sensitive demands

Classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services. Existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers. This paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent. Such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services. These models seek to maximize profit from delivery service, where price determines demand for deliveries as well as the total revenue generated by satisfying demand. We consider a variant of the model in which each customer’s delivery volume is price sensitive, as well as the case in which customer delivery volumes are fixed, but the total number of customers who select the delivery service provider is price sensitive. A third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit.     

A multi-commodity, capacitated pickup and delivery problem: The single and two-vehicle cases

We explore dynamic programming solutions for a multi-commodity, capacitated pickup and delivery problem. Cargo flows are given by an origin/destination matrix which is not necessarily symmetric. This problem is a generalization of several known pickup and delivery problems, as regards both problem structure and objective function. Solution approaches are developed for the single-vehicle and two-vehicle cases. The fact that for each cargo that goes from a node i to another node j there may be a cargo going in the opposite direction provides the motivation for the two-vehicle case, because one may conceivably consider solutions where no cargoes that travel in opposite directions between node pairs are carried by the same vehicle. Yet, it is shown that such scenarios are generally sub-optimal. As expected, the computational effort of the single vehicle algorithm is exponential in the number of cargoes. For the two-vehicle case, said effort is of an order of magnitude that is not higher than that of the single-vehicle case. Some rudimentary examples are presented or both the single-vehicle and two-vehicle cases so as to better illustrate the method.     

A unified heuristic for a large class of Vehicle Routing Problems with Backhauls

The Vehicle Routing Problem with Backhauls is a generalization of the ordinary capacitated vehicle routing problem where goods are delivered from the depot to the linehaul customers, and additional goods are brought back to the depot from the backhaul customers. Numerous ways of modeling the backhaul constraints have been proposed in the literature, each imposing different restrictions on the handling of backhaul customers. A survey of these models is presented, and a unified model is developed that is capable of handling most variants of the problem from the literature. The unified model can be seen as a Rich Pickup and Delivery Problem with Time Windows, which can be solved through an improved version of the large neighborhood search heuristic proposed by Ropke and Pisinger [An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Technical Report, DIKU, University of Copenhagen, 2004]. The results obtained in this way are comparable to or improve on similar results found by state of the art heuristics for the various variants of the problem. The heuristic has been tested on 338 problems from the literature and it has improved the best known solution for 227 of these. An additional benefit of the unified modeling and solution method is that it allows the dispatcher to mix various variants of the Vehicle Routing Problem with Backhauls for the individual customers or vehicles.     

An algorithm for the traveling salesman problem with pickup and delivery customers

The paper extends the branch and bound algorithm of Little, Murty, Sweeney, and Karel to the traveling salesman problem with pickup and delivery customers, where each pickup customer is required to be visited before its associated delivery customer. The problems considered include single and multiple vehicle cases as well as infinite and finite capacity cases. Computational results are reported.     

A greedy look-ahead heuristic for the vehicle routing problem with time windows

In this paper we consider the problem of physically distributing finished goods from a central facility to geographically dispersed customers, which pose daily demands for items produced in the facility and act as sales points for consumers. The management of the facility is responsible for satisfying all demand, and promises deliveries to the customers within fixed time intervals that represent the earliest and latest times during the day that a delivery can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns such as vehicle capacity, delivery time intervals and all relevant costs. The model, which is a case of the vehicle routing problem with time windows, is solved using a new heuristic technique. Our solution method, which is based upon Atkinson's greedy look-ahead heuristic, enhances traditional vehicle routing approaches, and provides surprisingly good performance results with respect to a set of standard test problems from the literature. The approach is used to determine the vehicle fleet size and the daily route of each vehicle in an industrial example from the food industry. This actual problem, with approximately two thousand customers, is presented and solved by our heuristic, using an interface to a Geographical Information System to determine inter-customer and depot–customer distances. The results indicate that the method is well suited for determining the required number of vehicles and the delivery schedules on a daily basis, in real life applications.     

A stochastic dynamic traveling salesman problem with hard time windows

Just-in-time (JIT) trucking service, i.e., arriving at customers within specified time windows, has become the norm for freight carriers in all stages of supply chains. In this paper, a JIT pickup/delivery problem is formulated as a stochastic dynamic traveling salesman problem with time windows (SDTSPTW). At a customer location, the vehicle either picks up goods for or delivers goods from the depot, but does not provide moving service to transfer goods from one location to another. Such routing problems are NP-hard in deterministic settings, and in our context, complicated further by the stochastic, dynamic nature of the problem. This paper develops an efficient heuristic for the SDTSPTW with hard time windows. The heuristic is shown to be useful both in controlled numerical experiments and in applying to a real-life trucking problem.     

Comparing backhauling strategies in vehicle routing using Ant Colony Optimization

In the Vehicle Routing Problem with Backhauls and Time Windows (VRPBTW) customers either receive goods from the depot or send goods to the depot and pickup or delivery at a customer has to occur within a pre-specified time window. The main objective is to minimize the total required fleet size for serving all customers. Secondary objectives are to minimize the total distance travelled or to minimize the total route duration of all vehicles. In this paper we consider a variant of the mixed VRPBTW where backhauls may be served before linehauls on any given route. Besides the modelling aspect of this variant we will study its performance implications when compared to the standard VRPBTW using a heuristic algorithm based on Ant Colony Optimization.     

A new VRPPD model and a hybrid heuristic solution approach for e-tailing

We analyze a business model for e-supermarkets to enable multi-product sourcing capacity through co-opetition (collaborative competition). The logistics aspect of our approach is to design and execute a network system where “premium” goods are acquired from vendors at multiple locations in the supply network and delivered to customers. Our specific goals are to: (i) investigate the role of premium product offerings in creating critical mass and profit; (ii) develop a model for the multiple-pickup single-delivery vehicle routing problem in the presence of multiple vendors; and (iii) propose a hybrid solution approach. To solve the problem introduced in this paper, we develop a hybrid metaheuristic approach that uses a Genetic Algorithm for vendor selection and allocation, and a modified savings algorithm for the capacitated VRP with multiple pickup, single delivery and time windows (CVRPMPDTW). The proposed Genetic Algorithm guides the search for optimal vendor pickup location decisions, and for each generated solution in the genetic population, a corresponding CVRPMPDTW is solved using the savings algorithm. We validate our solution approach against published VRPTW solutions and also test our algorithm with Solomon instances modified for CVRPMPDTW.     

A branch-and-price algorithm for the multi-depot heterogeneous-fleet pickup and delivery problem with soft time windows

The growing cost of transportation and distribution pushes companies, especially small and medium transportation enterprises, to form partnership and to exploit economies of scale. On the other hand, to increase their competitiveness on the market, companies are asked to consider preferences of the customers as well. Therefore, tools for logistics management need to manage collective resources, as many depots and heterogeneous fleets, providing flexible preference handling at the same time. In this paper we tackle a pickup and delivery vehicle routing problem involving such aspects; customers place preferences on visiting time (represented as soft time windows), and their violation is allowed at a price. Our interest in this problem stems from an ongoing industrial project. First we propose an exact branch-and-price algorithm, having as a core advanced dynamic programming techniques. Then we analyze through a computational campaign the impact of soft time windows management on the optimal solution in terms of both routing and overall distribution costs. Our experiments show that our approach can solve instances of real size, and clarify the practical usefulness of soft time windows management.