A Dual-Based Procedure for Dynamic Facility Location

In dynamic facility location problems, one desires to specify the time-staged establishment of facilities at different locations so as to minimize the total discounted costs for meeting demands specified over time at various customer locations. We formulate a particular dynamic facility location problem as a combinatorial optimization problem. The formulation permits both the opening of new facilities and the closing of existing ones. A branch-and-bound procedure incorporating a dual ascent method is presented and shown, in computational tests, to be superior to previously developed methods. The procedure is comparable to the most efficient methods for solving static (single-period) location problems. Problems with as many as 25 potential facility locations, 50 customer locations, and 10 time periods have been solved within one second of CPU time on an IBM 3033 computer. Extensions of the dynamic facility location problem that allow price-sensitive demands, linearized concave costs, interdependent projects, and multiple commodities can also be solved by the dual ascent method. The method can serve as a component of a solution process for more difficult capacitated problems

Facility location optimization model for emergency humanitarian logistics

Since the 1950s, the number of natural and man-made disasters has increased exponentially and the facility location problem has become the preferred approach for dealing with emergency humanitarian logistical problems. To deal with this challenge, an exact algorithm and a heuristic algorithm have been combined as the main approach to solving this problem. Owing to the importance that an exact algorithm holds with regard to enhancing emergency humanitarian logistical facility location problems, this paper aims to conduct a survey on the facility location problems that are related to emergency humanitarian logistics based on both data modeling types and problem types and to examine the pre- and post-disaster situations with respect to facility location, such as the location of distribution centers, warehouses, shelters, debris removal sites and medical centers. The survey will examine the four main problems highlighted in the literature review: deterministic facility location problems, dynamic facility location problems, stochastic facility location problems, and robust facility location problems. For each problem, facility location type, data modeling type, disaster type, decisions, objectives, constraints, and solution methods will be evaluated and real-world applications and case studies will then be presented. Finally, research gaps will be identified and be addressed in further research studies to develop more effective disaster relief operations

An Efficient Genetic Algorithm for Solving the Multi-Level Uncapacitated Facility Location Problem

In this paper a new evolutionary approach for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. Binary encoding scheme is used with appropriate objective function containing dynamic programming approach for finding sequence of located facilities on each level to satisfy clients' demands. The experiments were carried out on the modified standard single level facility location problem instances. Genetic algorithm (GA) reaches all known optimal solutions for smaller dimension instances, obtained by total enumeration and CPLEX solver. Moreover, all optimal/best known solutions were reached by genetic algorithm for a single-level variant of the problem

A Benders Based Rolling Horizon Algorithm for a Dynamic Facility Location Problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range

Robust mean absolute deviation problems on networks with linear vertex weights

This article deals with incorporating the mean absolute deviation objective function in several robust single facility location models on networks with dynamic evolution of node weights, which are modeled by means of linear functions of a parameter. Specifically, we have considered two robustness criteria applied to the mean absolute deviation problem: the MinMax criterion, and the MinMax regret criterion. For solving the corresponding optimization problems, exact algorithms have been proposed and their complexities have been also analyzed.Ministerio de Ciencia e Innovación MTM2007-67433-C02-(01,02)Ministerio de Ciencia e Innovación MTM2009-14243Ministerio de Ciencia e Innovación MTM2010-19576-C02-(01,02)Ministerio de Ciencia e Innovación DE2009-0057Junta de Andalucía P09-TEP-5022Junta de Andalucía FQM-584

Accelerated Benders Decomposition and Local Branching for Dynamic Maximum Covering Location Problems

The maximum covering location problem (MCLP) is a key problem in facility location, with many applications and variants. One such variant is the dynamic (or multi-period) MCLP, which considers the installation of facilities across multiple time periods. To the best of our knowledge, no exact solution method has been proposed to tackle large-scale instances of this problem. To that end, in this work, we expand upon the current state-of-the-art branch-and-Benders-cut solution method in the static case, by exploring several acceleration techniques. Additionally, we propose a specialised local branching scheme, that uses a novel distance metric in its definition of subproblems and features a new method for efficient and exact solving of the subproblems. These methods are then compared through extensive computational experiments, highlighting the strengths of the proposed methodologies

An Improved Genetic Algorithm for the Multi Level Uncapacitated Facility Location Problem

In this paper, an improved genetic algorithm (GA) for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. First improvement is achieved by better implementation of dynamic programming, which speeds up the running time of the overall GA implementation. Second improvement is hybridization of the genetic algorithm with the fast local search procedure designed specially for MLUFLP. The experiments were carried out on instances proposed in the literature which are modied standard single level facility location problem instances. Improved genetic algorithm reaches all known optimal and the best solutions from literature, but in much shorter time. Hybridization with local search improves several best-known solutions for large-scale MLUFLP instances, in cases when the optimal is not known. Overall running time of both proposed GA methods is signicantly shorter compared to previous GA approach

Dynamic Vehicle Scheduling for Working Service Network with Dual Demands

This study aims to develop some models to aid in making decisions on the combined fleet size and vehicle assignment in working service network where the demands include two types (minimum demands and maximum demands), and vehicles themselves can act like a facility to provide services when they are stationary at one location. This type of problem is named as the dynamic working vehicle scheduling with dual demands (DWVS-DD) and formulated as a mixed integer programming (MIP). Instead of a large integer program, the problem is decomposed into small local problems that are guided by preset control parameters. The approach for preset control parameters is given. By introducing them into the MIP formulation, the model is reformulated as a piecewise form. Further, a piecewise method by updating preset control parameters is proposed for solving the reformulated model. Numerical experiments show that the proposed method produces better solution within reasonable computing time