A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones

A New Hybrid Algorithm to Optimize Stochastic-fuzzy Capacitated Multi-Facility Location-allocation Problem

Facility location-allocation models are used in a widespread variety of applications to determine the number of required facility along with the relevant allocation process. In this paper, a new mathematical model for the capacitated multi-facility location-allocation problem with probabilistic customer's locations and fuzzy customer’s demands under the Hurwicz criterion is proposed. This model is formulated as α-cost minimization model according to different criteria. Since our problem is strictly Np-hard, a new hybrid intelligent algorithm is presented to solve the stochastic-fuzzy model. The proposed algorithm is based on a vibration damping optimization (VDO) algorithm which is combined with the simplex algorithm and fuzzy simulation (SFVDO). Finally, a numerical example is presented to illustrate the capability of the proposed solving methodologies

Simulation and Optimization Of Ant Colony Optimization Algorithm For The Stochiastic Uncapacitated Location-Allocation Problem

This study proposes a novel methodology towards using ant colony optimization (ACO) with stochastic demand. In particular, an optimizationsimulation-optimization approach is used to solve the Stochastic uncapacitated location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. ACO is modeled using discrete event simulation to capture the randomness of customers’ demand, and its objective is to optimize the costs. On the other hand, the simulated ACO’s parameters are also optimized to guarantee superior solutions. This approach’s performance is evaluated by comparing its solutions to the ones obtained using deterministic data. The results show that simulation was able to identify better facility allocations where the deterministic solutions would have been inadequate due to the real randomness of customers’ demands

Enhanced cell-based algorithm with dynamic radius in solving capacitated multi-source weber problem

Capacitated Multi-source Weber Problem (CMSWP) is a type of Location Allocation Problem (LAP) which have been extensively researched because they can be applied in a variety of contexts. Random selection of facility location in a Cell-based approach may cause infeasible or worse solutions. This is due to the unprofitable cells are not excluded and maybe selected for locating facilities. As a result, the total transportation cost increases, and solution quality is not much improved. This research finds the location of facilities in a continuous space to meet the demand of customers which minimize the total cost using Enhanced Cell-based Algorithm (ECBA). This method was derived from previous study that divides the distribution of customers into smaller cells of promising locations. The methodology consists of three phases. First, the profitable cells were constructed by applying ECBA. Second, initial facility configuration was determined using fixed and dynamic radius. Third, Alternating Transportation Problem (ATL) was applied to find a new location. The algorithm was tested on a dataset of three sizes which are 50, 654 and 1060 customers. The computational results of the algorithm prove that the results are superior in terms of total distance compared to the result of previous studies. This study provides useful knowledge to other researchers to find strategic facilities locations by considering their capacities

A Hybrid Multi-Criteria Analysis Model for Solving the Facility Location–Allocation Problem: a Case Study of Infectious Waste Disposal

Choosing locations for infectious waste disposal (IWD) is one of the most significant issues in hazardous waste management due to the risk imposed on the environment and human life. This risk can be the result of an undesirable location of IWD facilities. In this study a hybrid multi-criteria analysis (Hybrid MCA) model for solving the facility location–allocation (FLA) problem for IWD was developed by combining two objectives: total cost minimization and weight maximization. Based on an actual case of forty-seven hospitals and three candidate municipalities in the northeastern region of Thailand, first, the Fuzzy AHP and Fuzzy TOPSIS techniques were integrated to determine the closeness of the coefficient weights of each candidate municipality. After that, these weights were converted to weighting factors and then these factors were taken into the objective function of the FLA model. The results showed that the Hybrid MCA model can help decision makers to locate disposal centers, hospitals and incinerator size simultaneously. Besides that the model can be extended by incorporating additional selection criteria/objectives. Therefore, it is believed that it can also be useful for addressing other complex problems

A queuing location-allocation model for a capacitated health care system

International audienceThe aim of the present paper is to propose a location-allocation model for a capacitated health care system. This paper develops a discrete modeling framework to determine the optimal number of facilities among candidates and optimal allocations of the existing customers to operating health centers in a coverage distance. In doing so, the total sum of customer and operating facility costs is minimized. Our goal is to create a model that is more practical in the real world. Therefore, setup costs of hospitals are based on the costs of customers, xed costs of establishing health centers, and costs based on the available resources in each level of hospitals. In this paper, the idea of hierarchical structure has been used. There are two levels of service in hospitals, including low and high levels, and sections at diierent levels that provide diierent types of services. The patients refer to diierent sections of the hospital according to their requirements. To solve the model, two meta-heuristic algorithms, including genetic and simulated annealing algorithms and their combination, are proposed. To evaluate the performance of the three algorithms, some numerical examples are produced and analyzed using the statistical test in order to determine which algorithm works better

A new local search for . . .

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulatio

Mathematical Model and Stochastic Multi-Criteria Acceptability Analysis for Facility Location Problem

This paper studies a real-life public sector facility location problem. The problem fundamentally originated from the idea of downsizing the number of service centres. However, opening of new facilities is also considered in case the current facilities fail to fulfil general management demands. Two operation research methodologies are used to solve the problem and the obtained results are compared. First, a mathematical programming model is introduced to determine where the new facilities will be located, and which districts get service from which facilities, as if there were currently no existing facilities. Second, the Stochastic Multi-criteria Acceptability Analysis-TRI (SMAA-TRI) method is used to select the best suitable places for service centres among the existing facilities. It is noted that the application of mathematical programming model and SMAA-TRI integration approach on facility location problem is the first study in literature. Compression of outcomes shows that mixed integer linear programming (MILP) model tries to open facilities in districts which are favoured by SMAA-TRI solution.</span