A hybrid evolutionary algorithm for the periodic location-routing problem

The well-known vehicle routing problem (VRP) has been studied in depth over the last decades. Nowadays, generalizations of VRP have been developed for tactical or strategic decision levels of companies but not both. The tactical extension or periodic VRP (PVRP) plans a set of trips over a multiperiod horizon, subject to frequency constraints. The strategic extension is motivated by interdependent depot location and routing decisions in most distribution systems. Low-quality solutions are obtained if depots are located first, regardless of the future routes. In the location-routing problem (LRP), location and routing decisions are tackled simultaneously. Here for the first time, except for some conference papers, the goal is to combine the PVRP and LRP into an even more realistic problem covering all decision levels: the periodic LRP or PLRP. A hybrid evolutionary algorithm is proposed to solve large size instances of the PLRP. First, an individual representing an assignment of customers to combinations of visit days is randomly generated. The evolution operates through an Evolutionary Local Search (ELS) on visit day assignments. The algorithm is hybridized with a heuristic based on the Randomized Extended Clarke and Wright Algorithm (RECWA) to create feasible solutions and stops when a given number of iterations is reached. The method is evaluated over three sets of instances, and solutions are compared to the literature on particular cases such as one-day horizon (LRP) or one depot (PVRP). This metaheuristic outperforms the previous methods for the PLRP.     

A survey of recent research on location-routing problems

The design of distribution systems raises hard combinatorial optimization problems. For instance, facility location problems must be solved at the strategic decision level to place factories and warehouses, while vehicle routes must be built at the tactical or operational levels to supply customers. In fact, location and routing decisions are interdependent and studies have shown that the overall system cost may be excessive if they are tackled separately. The location-routing problem (LRP) integrates the two kinds of decisions. Given a set of potential depots with opening costs, a fleet of identical vehicles and a set of customers with known demands, the classical LRP consists in opening a subset of depots, assigning customers to them and determining vehicle routes, to minimize a total cost including the cost of open depots, the fixed costs of vehicles used, and the total cost of the routes. Since the last comprehensive survey on the LRP, published by Nagy and Salhi (2007), the number of articles devoted to this problem has grown quickly, calling a review of new research works. This paper analyzes the recent literature (72 articles) on the standard LRP and new extensions such as several distribution echelons, multiple objectives or uncertain data. Results of state-of-the-art metaheuristics are also compared on standard sets of instances for the classical LRP, the two-echelon LRP and the truck and trailer problem.     

A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

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.     

Vehicle routing considerations in distribution system design

In Distribution System Design, one minimizes total costs related to the number, locations and sizes of warehouses, and the assignment of warehouses to customers. The resulting system, while optimal in a strategic sense, may not be the best choice if operational aspects such as vehicle routing are also considered.We formulate a multicommodity, capacitated distribution planning model as anon-linear, mixed integer program. Distribution from factories to customers is two-staged via depots (warehouses) whose number and location must be chosen. Vehicle routes from depots to customers are established by considering the “fleet size and mix” problem, which also incorporates strategic decisions on fleet makeup and vehicle numbers of each type. This problem is solved as a generalized assignment problem, within an algorithm for the overall distribution/routing problem that is based on Benders decomposition. We furnish two version of our algorithm denoted Technique I and II. The latter is an enhaancement of the former and is employed at the user's discretion. Computer solution of test problems is discussed.     

2-Facility manifold location routing problem

The location routing problem (LRP), known to be the combination of the facility location and vehicle routing problems, is solved in the literature by either assuming planar or spherical surfaces. In this work, the manifold location routing problem (MLRP), that is an LRP on Riemannian manifold surfaces, is explained for the 2-facility (2-MLRP) case with the corresponding heuristic algorithm solution. The 2-MLRP problem is a mixed integer non-linear programming problem that is determined to be NP-hard. Special cases of MLRP include LRP on planar surfaces, when the manifold’s curvature is 0, and LRP on spherical surfaces when the curvature of the manifold is 1.     

Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia

In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant).     

A two-phase tabu search approach to the location routing problem

In many distribution systems, the location of the distribution facilities and the routing of the vehicles from these facilities are interdependent. Although this interdependence has been recognized by academics and practitioners alike, attempts to integrate these two decisions have been limited. The location routing problem (LRP), which combines the facility location and the vehicle routing decisions, is NP-hard. Due to the problem complexity, simultaneous solution methods are limited to heuristics. This paper presents a two-phase tabu search architecture for the solution of the LRP. First introduced in this paper, the two-phase approach offers a computationally efficient strategy that integrates facility location and routing decisions. This two-phase architecture makes it possible to search the solution space efficiently, thus producing good solutions without excessive computation. An extensive computational study shows that the TS algorithm achieves significant improvement over a recent effective LRP heuristic.     

Local search for the undirected capacitated arc routing problem with profits

This paper deals with a recently introduced routing problem variant called the undirected capacitated arc routing problem with profits (UCARPP). The UCARPP model considered in the present study is primarily aimed at generating the route set which maximizes the profit collected from a set of potential customers, represented by edges of the examined transportation network. The secondary objective is to minimize the total route travel time. The generated routes are subject both to capacity and travel time constraints. To tackle the examined problem, we propose a local search metaheuristic development which explores two solution neighborhood structures. The conducted search is effectively diversified by means of the promises concept which is based on the aspiration criteria used in tabu search approaches. The proposed algorithm was tested on UCARPP benchmark instances taken from the literature. It efficiently produced high-quality results, improving several previously best known solutions.     

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%).     

Local improvement in planar facility location using vehicle routing

In physical distribution the location of depots and vehicle routes are interdependent problems, but they are usually treated independently. Location-routing is the study of solving locational problems such that routing considerations are taken into account. We present an iterative heuristic for the location-routing problem on the plane. For each depot the Weber problem is solved using the end-points of the routes found previously as input nodes to the Weiszfeld procedure. Although the improvements found are usually small they show that it pays not to ignore the routing aspects when solving continuous location problems. Possible research avenues in continuous location-routing will also be suggested.     

Combination of geographical information system and efficient routing algorithms for real life distribution operations

This paper presents a decision support system (DSS) employing a metaheuristic algorithm called BoneRoute, for solving the open vehicle routing problem (OVRP). The OVRP deals with the problem of finding a set of vehicle routes, for a fleet of capacitated vehicles to satisfy the delivery requirements of customers, without returning to the distribution centre. The computational performance of the BoneRoute algorithm for the OVRP was found to be very efficient, producing new best solutions over a set of well-known published case studies examined. Technical and managerial issues aroused from the ad hoc connections between the geographical information system (GIS), the routing technique used for calculating shortest paths and the BoneRoute algorithm for finding the optimal sequence of customers, were faced successfully.     

A metaheuristic based on a pool of routes for the vehicle routing problem with multiple trips and time windows

This paper studies the vehicle routing problem with multiple trips and time windows, in which vehicles are allowed to perform multiple trips during a scheduling period and each customer must be served within a given time interval. The problem is of particular importance for planning fleets of hired vehicles in common practices, such as e-grocery distributions, but this problem has received little attention in the literature. As a result of the multi-layered structure characteristic of the problem solution, we propose a pool-based metaheuristic in which various routes are first constructed to fill a pool, following which some of the routes are selected and combined to form vehicle working schedules. Finally, we conduct a series of experiments over a set of benchmark instances to evaluate and demonstrate the effectiveness of the proposed metaheuristic.     

High-Level Relay Hybrid Metaheuristic Method for Multi-Depot Vehicle Routing Problem with Time Windows

This paper presents an efficient hybrid metaheuristic solution for multi-depot vehicle routing with time windows (MD-VRPTW). MD-VRPTW involves the routing of a set of vehicles with limited capacity from a set of depots to a set of geographically dispersed customers with known demands and predefined time windows. The present work aims at using a hybrid metaheuristic algorithm in the class of High-Level Relay Hybrid (HRH) which works in three levels and uses an efficient genetic algorithm as the main optimization algorithm and tabu search as an improvement method. In the genetic algorithm various heuristics incorporate local exploitation in the evolutionary search. An operator deletion- retrieval strategy is executed which shows the efficiency of the inner working of the proposed method. The proposed algorithm is applied to solve the problems of the standard Cordeau??s Instances. Results show that proposed approach is quite effective, as it provides solutions that are competitive with the best known in the literature.     

An exact algorithm for solving a capacitated location-routing problem

In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem in which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints, generalized subtour elimination constraints, and chain barring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations.     

An exact algorithm for a single-vehicle routing problem with time windows and multiple routes

This paper describes an exact algorithm for solving a problem where the same vehicle performs several routes to serve a set of customers with time windows. The motivation comes from the home delivery of perishable goods, where vehicle routes are short and must be combined to form a working day. A method based on an elementary shortest path algorithm with resource constraints is proposed to solve this problem. The method is divided into two phases: in the first phase, all non-dominated feasible routes are generated; in the second phase, some routes are selected and sequenced to form the vehicle workday. Computational results are reported on Euclidean problems derived from benchmark instances of the classical vehicle routing problem with time windows.     

Integer linear programming models for a cement delivery problem

We consider a cement delivery problem with an heterogeneous fleet of vehicles and several depots. The demands of the customers are typically larger than the capacity of the vehicles which means that most customers are visited several times. This is a split delivery vehicle routing problem with additional constraints. We first propose a two phase solution method that assigns deliveries to the vehicles, and then builds vehicle routes. Both subproblems are formulated as integer linear programming problems. We then show how to combine the two phases in a single integer linear program. Experiments on real life instances are performed to compare the performance of the two solution methods.     

Routing and scheduling in a flexible job shop by tabu search

A hierarchical algorithm for the flexible job shop scheduling problem is described, based on the tabu search metaheuristic. Hierarchical strategies have been proposed in the literature for complex scheduling problems, and the tabu search metaheuristic, being able to cope with different memory levels, provides a natural background for the development of a hierarchical algorithm. For the case considered, a two level approach has been devised, based on the decomposition in a routing and a job shop scheduling subproblem, which is obtained by assigning each operation of each job to one among the equivalent machines. Both problems are tackled by tabu search. Coordination issues between the two hierarchical levels are considered. Unlike other hierarchical schemes, which are based on a one-way information flow, the one proposed here is based on a two-way information flow. This characteristic, together with the flexibility of local search strategies like tabu search, allows to adapt the same basic algorithm to different objective functions. Preliminary computational experience is reported.     

Solving routing problems with pairwise synchronization constraints

Pairwise route synchronization constraints are commonly encountered in the field of service technician routing and scheduling and in the area of mobile care. Pairwise route synchronization refers to constraints that require that two technicians or home care workers visit the same location at exactly the same time. We consider constraints of this type in the context of the well-known vehicle routing problem with time windows and a generic service technician routing and scheduling problem. Different approaches for dealing with the problem of pairwise route synchronization are compared and several ways of integrating a synchronization component into a metaheuristic algorithm tailored to the original problems are analyzed. When applied to benchmark instances from the literature, our algorithm matches almost all available optimal values and it produces several new best results for the remaining instances.

     

A multi-depot period vehicle routing problem arising in the utilities sector

This paper considers the resource planning problem of a utility company that provides preventive maintenance services to a set of customers using a fleet of depot-based mobile gangs. The problem is to determine the boundaries of the geographic areas served by each depot, the list of customers visited each day and the routes followed by the gangs. The objective is to provide improved customer service at minimum operating cost subject to constraints on frequency of visits, service time requirements, customer preferences for visiting on particular days and other routing constraints. The problem is solved as a Multi-Depot Period Vehicle Routing Problem (MDPVRP). The computational implementation of the complete planning model is described with reference to a pilot study and results are presented. The solution algorithm is used to construct cost-service trade-off curves for all depots so that management can evaluate the impact of different customer service levels on total routing costs.