A heuristic solution method for node routing based solid waste collection problems

This paper considers a real world waste collection problem in which glass, metal, plastics, or paper is brought to certain waste collection points by the citizens of a certain region. The collection of this waste from the collection points is therefore a node routing problem. The waste is delivered to special sites, so called intermediate facilities (IF), that are typically not identical with the vehicle depot. Since most waste collection points need not be visited every day, a planning period of several days has to be considered. In this context three related planning problems are considered. First, the periodic vehicle routing problem with intermediate facilities (PVRP-IF) is considered and an exact problem formulation is proposed. A set of benchmark instances is developed and an efficient hybrid solution method based on variable neighborhood search and dynamic programming is presented. Second, in a real world application the PVRP-IF is modified by permitting the return of partly loaded vehicles to the depots and by considering capacity limits at the IF. An average improvement of 25% in the routing cost is obtained compared to the current solution. Finally, a different but related problem, the so called multi-depot vehicle routing problem with inter-depot routes (MDVRPI) is considered. In this problem class just a single day is considered and the depots can act as an intermediate facility only at the end of a tour. For this problem several instances and benchmark solutions are available. It is shown that the algorithm outperforms all previously published metaheuristics for this problem class and finds the best solutions for all available benchmark instances.     

Emergency Logistics Planning in Natural Disasters

Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes. In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand. The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.     

Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints

When vehicle routing problems with additional constraints, such as capacity or time windows, are solved via column generation and branch-and-price, it is common that the pricing subproblem requires the computation of a minimum cost constrained path on a graph with costs on the arcs and prizes on the vertices. A common solution technique for this problem is dynamic programming. In this paper we illustrate how the basic dynamic programming algorithm can be improved by bounded bi-directional search and we experimentally evaluate the effectiveness of the enhancement proposed. We consider as benchmark problems the elementary shortest path problems arising as pricing subproblems in branch-and-price algorithms for the capacitated vehicle routing problem, the vehicle routing problem with distribution and collection and the capacitated vehicle routing problem with time windows.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

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 meta-heuristic algorithm for heterogeneous fleet vehicle routing problems with two-dimensional loading constraints

The two-dimensional loading heterogeneous fleet vehicle routing problem (2L-HFVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles. These vehicles have different capacities, fixed and variable operating costs, length and width in dimension, and two-dimensional loading constraints. The objective of this problem is to minimize transportation cost of designed routes, according to which vehicles are used, to satisfy the customer demand. In this study, we proposed a simulated annealing with heuristic local search (SA_HLS) to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints in 2L-HFVRP. To speed up the search process, a data structure was used to record the information related to loading feasibility. The effectiveness of SA_HLS was tested on benchmark instances derived from the two-dimensional loading vehicle routing problem (2L-CVRP). In addition, the performance of SA_HLS was also compared with three other 2L-CVRP models and four HFVRP methods found in the literature.     

A worst-case analysis for the split delivery vehicle routing problem with minimum delivery amounts

In the vehicle routing problem (VRP), a fleet of vehicles must service the demands of customers in a least-cost way. In the split delivery vehicle routing problem (SDVRP), multiple vehicles can service the same customer by splitting the deliveries. By allowing split deliveries, savings in travel costs of up to 50 % are possible, and this bound is tight. Recently, a variant of the SDVRP, the split delivery vehicle routing problem with minimum delivery amounts (SDVRP-MDA), has been introduced. In the SDVRP-MDA, split deliveries are allowed only if at least a minimum fraction of a customer’s demand is delivered by each visiting vehicle. We perform a worst-case analysis on the SDVRP-MDA to determine tight bounds on the maximum possible savings.     

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.     

Integrated service network design for a cross-docking supply chain network

This paper considers an integrated service network design problem for a given set of freight demands that is concerned with integration of locating cross-docking (CD) centers and allocating vehicles for the associated direct (transportation) services from origin node to a CD center or from a CD center to the destination node. For the vehicle allocation, direct services (sub-routes) should be determined for the given freight demands, and then the vehicle allocation has to be made in consideration of routing for the associated direct service fulfillment subject to vehicle capacity and service time restriction. The problem is modeled as a path-based formulation for which a tabu-search-based solution algorithm is proposed. To guarantee the performance of the proposed solution algorithm, strong valid inequalities are derived based on the polyhedral characteristics of the problem domain and an efficient separation heuristic is derived for identifying any violated valid inequalities. Computational experiments are performed to test the performance of the proposed solution algorithm and also that of a valid-inequality separation algorithm, which finds that the solution algorithm works quite well and the separation algorithm provides strengthened lower bounds. Its immediate application may be made to strategic (integrated) service network designs and to tactical service network planning for the CD network.     

A heuristic method for the capacitated arc routing problem with refill points and multiple loads

We describe a solution procedure for a capacitated arc routing problem with refill points and multiple loads. This problem stems from the road network marking in Quebec, Canada. Two different types of vehicles are used: the first type (called servicing vehicle—SV) with a finite capacity to service the arcs and the other (called refilling vehicle—RV) to refill the SV vehicle.The RV can deliver multiple loads, which means that it meets the SV several times before returning to the depot. The problem consists of simultaneously determining the vehicle routes that minimize the total cost of the two vehicles.We present an integer formulation and a route first-cluster second heuristic procedure. Computational results are provided.     

An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls

In this article, a visual interactive approach based on a new greedy randomised adaptive memory programming search (GRAMPS) algorithm is proposed to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) and a new extension of the HFFVRP, which is called heterogeneous fixed fleet vehicle routing problem with backhauls (HFFVRPB). This problem involves two different sets of customers. Backhaul customers are pickup points and linehaul customers are delivery points that are to be serviced from a single depot by a heterogeneous fixed fleet of vehicles, each of which is restricted in the capacity it can carry, with different variable travelling costs.     

成品油配送多车舱车辆指派及路径优化问题研究

针对成品油配送中多车型、多车舱的车辆优化调度难题,综合考虑多车型车辆指派、多车舱车辆装载及路径安排等决策,以派车成本与油耗成本之和的总成本最小为目标,建立了多车型多车舱的车辆优化调度模型。为降低模型求解的复杂性,本文提出一种基于C-W节约算法的“需求拆分→合并装载”的车辆装载策略,并综合利用Relocate和Exchange算子进行并行邻域搜索改进,获得优化的成品油配送方案。最后,通过算例验证了本文提出的模型与算法用于求解大规模成品油配送问题的有效性。并通过数据实验揭示了以下规律:1)多车舱车辆相对于单车舱车辆在运营成本上具有优越性;2)大型车辆适合远距离配送,小型车辆适合近距离配送;3)多车型车辆混合配送相对于单车型车辆配送在运营成本上具有优越性。这些规律可为成品油配送公司的车辆配置提供决策参考。     

Using clustering analysis in a capacitated location-routing problem

The location routing problem (LRP) appears as a combination of two difficult problems: the facility location problem (FLP) and the vehicle routing problem (VRP). In this work, we consider a discrete LRP with two levels: a set of potential capacitated distribution centres (DC) and a set of ordered customers. In our problem we intend to determine the set of installed DCs as well as the distribution routes (starting and ending at the DC). The problem is also constrained with capacities on the vehicles. Moreover, there is a homogeneous fleet of vehicles, carrying a single product and each customer is visited just once. As an objective we intend to minimize the routing and location costs.     

A primal-dual approximation algorithm for a two depot heterogeneous traveling salesman problem

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. We consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we consider a routing problem where there are two heterogeneous vehicles that start from distinct initial locations and a set of targets. The objective is to find a tour for each vehicle such that each of the targets is visited at least once by a vehicle and the sum of the distances traveled by the vehicles is minimal. We consider an important special case of this routing problem where the travel costs satisfy the triangle inequality and the following monotonicity property: the first vehicle’s cost of traveling between any two targets is at most equal to the second vehicle’s cost of traveling between the same targets. We present a primal-dual algorithm for this case that provides an approximation ratio of 2.     

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.     

Design of a recovery network for WEEE collection: the case of Galicia,Spain

This research aims to optimize the design of the reverse logistic network for the collection of Waste of Electric and Electronic Equipment (WEEE), in the Spanish region of Galicia. As a basis for our study a three-phase hierarchical approach is proposed. In the first phase a facility location problem is formulated and solved by means of a mixed integer linear programming; in the second phase a new integer programming formulation for the corresponding heterogeneous fleet vehicle routing problem is presented, and a savings-based heuristic algorithm is developed to efficiently solve the related collection routing problems; in the third phase a simulation study is performed on the collection routes in order to assess the overall performance of the recovery system. The results show a good performance of the proposed procedure, and an improved configuration of the recovery network compared to the one currently in use (particularly transportation costs are reduced by 29.2%).     

Minimizing waiting times in a route design problem with multiple use of a single vehicle

In this study we introduce a routing problem with multiple use of a single vehicle and service time in demand points (clients) with the aim of minimizing the sum of clients waiting time to receive service. This problem is relevant in the distribution of aid, in disaster stricken communities, in the recollection and/or delivery of perishable goods and personnel transportation, among other situations, where reaching clients to perform service, fast and fair, is a priority. We consider vehicle capacity and travel distance constraints which force multiple use of the vehicle in the planning horizon. This paper presents and compares two mixed integer formulations for this problem, based on a multi–level network.     

Synchronized routing of seasonal products through a production/distribution network

This paper presents a multi-period vehicle routing problem for a large-scale production and distribution network. The vehicles must be routed in such a way as to minimize travel and inventory costs over a multi-period horizon, while also taking retailer demands and the availability of products at a central production facility into account. The network is composed of one distribution center and hundreds of retailers. Each retailer has its demand schedule representing the total number of units of a given product that should have been received on a given day. Many high value products are distributed. Product availability is determined by the production facility, whose production schedule determines how many units of each product must be available on a given day. To distribute these products, the routes of a heterogeneous fleet must be determined for a multiple period horizon. The objective of our research is to minimize the cost of distributing products to the retailers and the cost of maintaining inventory at the facility. In addition to considering product availability, the routing schedule must respect many constraints, such as capacity restrictions on the routes and the possibility of multiple vehicle trips over the time horizon. In the situation studied, no more than 20 product units could be carried by a single vehicle, which generally limited the number of retailers that could be supplied to one or two per route. This article proposes a mathematical formulation, as well as some heuristics, for solving this single-retailer-route vehicle routing problem. Extensions are then proposed to deal with the multiple-retailer-route situation.     

A customer-centric routing problem with multiple trips of a single vehicle

In this study, we introduce a routing problem with multiple uses of a single vehicle and service time in demand points, minimizing the sum of clients’ waiting time to receive service. This problem is relevant in the distribution of aid in disaster-stricken communities, in the recollection and/or delivery of perishable goods and personnel transportation, among other situations, where reaching clients to perform service, fast and fair, is a priority. We consider vehicle capacity and travel distance constraints, forcing multiple use of the vehicle during the planning horizon. This paper presents two mixed integer formulations for this problem, based on a multi-level network, as well as a metaheuristic algorithm. The proposed models can solve to optimality instances with up to 30 clients. The proposed metaheuristic algorithm obtains high-quality solutions in short computational times.     

Modeling inventory routing problems in supply chains of high consumption products

Given a distribution center and a set of sales-points with their demand rates, the objective of the inventory routing problem (IRP) is to determine a distribution plan that minimizes fleet operating and average total distribution and inventory holding costs without causing a stock-out at any of the sales-points during a given planning horizon. We propose a new model for the long-term IRP when demand rates are stable and economic order quantity-like policies are used to manage inventories of the sales-points. The proposed model extends the concept of vehicle routes (tours) to vehicle multi-tours. To solve the nonlinear mixed integer formulation of this problem, a column generation based approximation method is suggested. The resulting sub-problems are solved using a savings-based approximation method. The approach is tested on randomly generated problems with different settings of some critical factors to compare our model using multi-tours as basic constructs to the model using simple tours as basic constructs.