CAPACITATED FACILITY LOCATION PROBLEM WITH GENERAL OPERATING AND BUILDING COSTS (original) (raw)
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Applied Mathematical Modelling, 2014
This paper considers the multi level uncapacitated facility location problem (MLUFLP). A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on instances known from literature. The results achieved by CPLEX and Gurobi solvers, based on the proposed MILP formulation, are compared to the results obtained by the same solvers on the already known formulations. The results show that CPLEX and Gurobi can optimally solve all small and medium sized instances and even some large-scale instances using the new formulation.
Robust capacitated facility location problem: Optimization model and solution algorithms
In this article, we propose an extension of the capacitated facility location problem under uncertainty, where uncertainty may appear in the model's key parameters such as demands and costs. In this model, it is assumed that facilities have hard constraint on the amount of demand they can serve and, as a result, some customers may not be fully satisfied. Unfortunately, traditional models ignore this situation and if facilities do not serve all demands, the model becomes infeasible. Accordingly, we develop the mathematical formulation in order to allow partial satisfaction by introducing penalty costs for unsatisfied demands. In general, this model optimizes location for predefined number of capacitated facilities in such a way that minimizes total expected costs of transportation, construction, and penalty costs of uncovered demands, while relative regret in each scenario must be no greater than a positive number (0 p ). The developed model is NP-hard and very challenging to solve. Therefore, an efficient heuristic solution algorithm based on the variable neighborhood search is developed to solve the problem. The algorithm's efficiency is compared with the simulated annealing algorithm and CPLEX solver by solving variety of test problems.Computational experiments show that the proposed algorithm is more effective and efficient in terms of CPU time and solutions quality.
Two Stage Capacitated Facility Location Problem
Meta-Heuristics Optimization Algorithms in Engineering, Business, Economics, and Finance, 2013
In the two-stage capacitated facility location problem, a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work two different mixed integer linear programming formulations are considered for the problem. Several Lagrangian relaxations are analyzed and compared, a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.
WSEAS Transactions on Mathematics, 2009
The Osorio and Glover (2003) use of dual surrogate analysis is exploited to fix variables in capacitated facility location problems (CFLP). The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the LP relaxation. A known solution is used to convert the objective function in a constraint that forces the solution to be less or equal to it. The surrogate constraint is paired with the objective function to obtain a combined constraint where negative variables are replaced by complemented variables and the resulting constraint used to fix binary variables in the model.
A two-stage method for the capacitated multi-facility location-allocation problem
International Journal of Operational Research, 2019
This paper examines the capacitated planar multi-facility location-allocation problem, where the number of facilities to be located is specified and each of which has a capacity constraint. A two-stage method is put forward to deal with the problem where in the first stage a technique that discretises continuous space into discrete cells is used to generate a relatively good initial facility configurations. In Stage 2, a Variable Neighbourhood Search (VNS) is implemented to improve the quality of solution obtained by the previous stage. The performance of the proposed method is evaluated using benchmark data sets from the literature. The numerical experiments show that the proposed method yields competitive results when compared to the best known results from the literature. In addition, some future research avenues are also suggested.
An effective heuristic for large-scale capacitated facility location problems
Journal of Heuristics, 2008
The Capacitated Facility Location Problem (CFLP) consists of locating a set of facilities with capacity constraints to satisfy the demands of a set of clients at the minimum cost. In this paper we propose a simple and effective heuristic for largescale instances of CFLP. The heuristic is based on a Lagrangean relaxation which is used to select a subset of "promising" variables forming the core problem and on a Branch-and-Cut algorithm that solves the core problem. Computational results on very large scale instances (up to 4 million variables) are reported.
A heuristic for BILP problems: The Single Source Capacitated Facility Location Problem
European Journal of Operational Research, 2014
In the Single Source Capacitated Facility Location Problem (SSCFLP) each customer has to be assigned to one facility that supplies its whole demand. The total demand of customers assigned to each facility cannot exceed its capacity. An opening cost is associated with each facility, and is paid if at least one customer is assigned to it. The objective is to minimize the total cost of opening the facilities and supply all the customers. In this paper we extend the Kernel Search heuristic framework to general Binary Integer Linear Programming (BILP) problems, and apply it to the SSCFLP. The heuristic is based on the solution to optimality of a sequence of subproblems, where each subproblem is restricted to a subset of the decision variables. The subsets of decision variables are constructed starting from the optimal values of the linear relaxation. Variants based on variable fixing are proposed to improve the efficiency of the Kernel Search framework. The algorithms are tested on benchmark instances and new very large-scale test problems. Computational results demonstrate the effectiveness of the approach. The Kernel Search algorithm outperforms the best heuristics for the SSCFLP available in the literature. It found the optimal solution for 165 out of the 170 instances with a proven optimum. The error achieved in the remaining instances is negligible. Moreover, it achieved, on 100 new very large-scale instances, an average gap equal to 0.64% computed with respect to a lower bound or the optimum, when available. The variants based on variable fixing improved the efficiency of the algorithm with minor deteriorations of the solution quality.
Mathematical Problems in Engineering
In this paper, we incorporate an efficiency criterion using data envelopment analysis into the single-source and multi-source capacitated facility location problems. We develop two bi-objective integer programs to find optimal and efficient location patterns, simultaneously. The proposed models for these capacitated facility location problems have fewer variables and constraints compared to existing models presented in the literature. We use the LP-metric procedure to solve the proposed models on two numerical examples. Results show that new models give better solutions, based on cost and efficiency criteria.
A Lagrangean Approach to the Facility Location Problem with Concave Costs
Journal of the Operations Research Society of Japan
We consider'the concave cost capacitated facility location pTo])lem, and develop a, composite algorithm Qf lower and upper bounding procedures. Computational results for several instarices with up to 100 customers and 25 candidate facility iocations are also presented, Our numerical experiments show that the proposed algorithm generates good selutions, The gaps between upper and lower bounds are within 1 percent fbr al1 test problems.