Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands

In this paper, the capacitated location-routing problem with fuzzy demands (CLRP-FD) is considered. In CLRP-FD, facility location problem (FLP) and vehicle routing problem (VRP) are observed simultaneously. Indeed, the vehicles and the depots have a predefined capacity to serve the customers that have fuzzy demands. To model this problem, a fuzzy chance constrained programming model of that is designed based upon the fuzzy credibility theory. To solve this problem, a greedy clustering method (GCM) including the stochastic simulation is proposed. To obtain the best value of the dispatcher preference index of the model and to analyze its influence on the final solution, numerical experiments are carried out. Finally, to show the performance of the greedy clustering method, associated results are compared with the lower bound of the solutions.     

Solving the capacitated location-routing problem

This is a summary of the main results presented in the author’s Ph.D thesis, available at http://prodhonc.free.fr/homepage. This thesis, written in French, was supervised by Christian Prins and Roberto Wolfler-Calvo, and defended on 16 October 2006 at the Université de Technologie de Troyes. Several new approaches are proposed to solve the capacitated location-routing problem (CLRP): heuristic, cooperative and exact methods. Their performances are tested on various kinds of instances with capacitated vehicles and capacitated or uncapacitated depots.      

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.     

Solving the capacitated location-routing problem by a GRASP complemented by a learning process and a path relinking

As shown in recent researches, the costs in distribution systems may be excessive if routes are ignored when locating depots. The location routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a new metaheuristic to solve the LRP with capacitated routes and depots. A first phase executes a GRASP, based on an extended and randomized version of Clarke and Wright algorithm. This phase is implemented with a learning process on the choice of depots. In a second phase, new solutions are generated by a post-optimization using a path relinking. The method is evaluated on sets of randomly generated instances, and compared to other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem. Furthermore, the algorithm is competitive with a metaheuristic published for the case of uncapacitated depots.     

A computational comparison of flow formulations for the capacitated location-routing problem

In this paper we present a computational comparison of four different flow formulations for the capacitated location-routing problem. We introduce three new flow formulations for the problem, namely a two-index two-commodity flow formulation, a three-index vehicle-flow formulation and a three-index two-commodity flow formulation. We also consider an existing two-index vehicle-flow formulation and extend it by considering new families of valid inequalities and separation algorithms. We introduce new branch-and-cut algorithms for each of the formulations and compare them on a wide number of instances. Our results show that compact formulations can produce tight gaps and solve many instances quickly, whereas three-index formulations scale better in terms of computing time.     

A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands

In this paper, the vehicle routing problem with fuzzy demands (VRPFD) is considered, and a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model. Moreover, the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation, and the best value of the dispatcher preference index is obtained.     

Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm

In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy β-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.     

A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands

This article introduces a new exact algorithm for the capacitated vehicle routing problem with stochastic demands (CVRPSD). The CVRPSD can be formulated as a set partitioning problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme. Computational experiments show promising results.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

Selective capacitated location-routing problem with incentive-dependent returns in designing used products collection network

This paper addresses a generalization of the capacitated location-routing problem (CLRP) arising in the design of a collection network for a company engaged in collecting used products from customer zones. The company offers customers a financial incentive per unit of used products. This incentive determines the quantity of used products which are returned by customers. Moreover, it is not necessary for the company to visit all customer zones or to collect all returns in each visited customer zone. The objective is to simultaneously find the location of collection centers, the routes of vehicles, the value of incentive offered and the amount of used products collected from customer zones, so as to maximize the company's overall profit. We develop two mixed integer linear programming formulations of the problem and a heuristic algorithm based on iterated local search. Extensive computational experiments on this problem demonstrate the effectiveness of the proposed algorithm.     

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.     

A multi-objective mathematical model for the industrial hazardous waste location-routing problem

Industrial hazardous waste management involves the collection, transportation, treatment, recycling and disposal of industrial hazardous materials that pose risk to their surroundings. In this paper, a new multi-objective location-routing model is developed, and implemented in the Marmara region of Turkey. The aim of the model is to help decision makers decide on locations of treatment centers utilizing different technologies, routing different types of industrial hazardous wastes to compatible treatment centers, locations of recycling centers and routing hazardous waste and waste residues to those centers, and locations of disposal centers and routing waste residues there. In the mathematical model, three criteria are considered: minimizing total cost, which includes total transportation cost of hazardous materials and waste residues and fixed cost of establishing treatment, disposal and recycling centers; minimizing total transportation risk related to the population exposure along transportation routes of hazardous materials and waste residues; and minimizing total risk for the population around treatment and disposal centers, also called site risk. A lexicographic weighted Tchebycheff formulation is developed and computed with CPLEX software to find representative efficient solutions to the problem. Data related to the Marmara region is obtained by utilizing Arcview 9.3 GIS software and Marmara region geographical database.     

Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm

In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.     

Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution

Hub and spoke networks are used to switch and transfer commodities between terminal nodes in distribution systems at minimum cost and/or time. The p-hub center allocation problem is to minimize maximum travel time in networks by locating p hubs from a set of candidate hub locations and allocating demand and supply nodes to hubs. The capacities of the hubs are given. In previous studies, authors usually considered only quantitative parameters such as cost and time to find the optimum location. But it seems not to be sufficient and often the critical role of qualitative parameters like quality of service, zone traffic, environmental issues, capability for development in the future and etc. that are critical for decision makers (DMs), have not been incorporated into models. In many real world situations qualitative parameters are as much important as quantitative ones. We present a hybrid approach to the p-hub center problem in which the location of hub facilities is determined by both parameters simultaneously. Dealing with qualitative and uncertain data, Fuzzy systems are used to cope with these conditions and they are used as the basis of this work. We use fuzzy VIKOR to model a hybrid solution to the hub location problem. Results are used by a genetic algorithm solution to successfully solve a number of problem instances. Furthermore, this method can be used to take into account more desired quantitative variables other than cost and time, like future market and potential customers easily.     

Entropy maximization model for the trip distribution problem with fuzzy and random parameters

Many trip distribution problems can be modeled as entropy maximization models with quadratic cost constraints. In this paper, the travel costs per unit flow between different zones are assumed to be given fuzzy variables and the trip productions at origins and trip attractions at destinations are assumed to be given random variables. For this case, an entropy maximization model with chance constraint is proposed, and is proved to be convex. In order to solve this model, fuzzy simulation, stochastic simulation and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, a numerical example is presented to demonstrate the application of the model and the algorithm.     

A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem

In this paper we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is a variation of the well-known Capacitated Vehicle Routing Problem (CVRP). In this problem, the traditional objective of minimizing total distance or time traveled by the vehicles is replaced by minimizing the sum of arrival times at the customers. We propose a branch-and-cut-and-price algorithm for obtaining optimal solutions to the problem. To the best of our knowledge, this is the first published exact algorithm for the CCVRP. We present computational results based on a set of standard CVRP benchmarks and investigate the effect of modifying the number of vehicles available.     

An artificial bee colony algorithm for the capacitated vehicle routing problem

This paper introduces an artificial bee colony heuristic for solving the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. An enhanced version of the artificial bee colony heuristic is also proposed to improve the solution quality of the original version. The performance of the enhanced heuristic is evaluated on two sets of standard benchmark instances, and compared with the original artificial bee colony heuristic. The computational results show that the enhanced heuristic outperforms the original one, and can produce good solutions when compared with the existing heuristics. These results seem to indicate that the enhanced heuristic is an alternative to solve the capacitated vehicle routing problem.     

Logistics distribution centers location problem and algorithm under fuzzy environment

Distribution centers location problem is concerned with how to select distribution centers from the potential set so that the total relevant cost is minimized. This paper mainly investigates this problem under fuzzy environment. Consequentially, chance-constrained programming model for the problem is designed and some properties of the model are investigated. Tabu search algorithm, genetic algorithm and fuzzy simulation algorithm are integrated to seek the approximate best solution of the model. A numerical example is also given to show the application of the algorithm.     

Solving the knapsack problem with imprecise weight coefficients using genetic algorithms

This paper investigates solving the knapsack problem with imprecise weight coefficients using genetic algorithms. This work is based on the assumption that each weight coefficient is imprecise due to decimal truncation or coefficient rough estimation by the decision-maker. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve this problem. We investigate the possibility of using genetic algorithms in solving the fuzzy knapsack problem without defining membership functions for each imprecise weight coefficient. The proposed approach simulates a fuzzy number by distributing it into some partition points. We use genetic algorithms to evolve the values in each partition point so that the final values represent the membership grade of a fuzzy number. The empirical results show that the proposed approach can obtain very good solutions within the given bound of each imprecise weight coefficient than the fuzzy knapsack approach. The fuzzy genetic algorithm concept approach is different, but gives better results than the traditional fuzzy approach.     

An iterative three-component heuristic for the team orienteering problem with time windows

This paper studies the team orienteering problem with time windows, the aim of which is to maximize the total profit collected by visiting a set of customers with a limited number of vehicles. Each customer has a profit, a service time and a time window. A service provided to any customer must begin in his or her time window. We propose an iterative framework incorporating three components to solve this problem. The first two components are a local search procedure and a simulated annealing procedure. They explore the solution space and discover a set of routes. The third component recombines the routes to identify high quality solutions. Our computational results indicate that this heuristic outperforms the existing approaches in the literature in average performance by at least 0.41%. In addition, 35 new best solutions are found.