A two-stage method for the capacitated multi-facility location-allocation problem

This is the author accepted manuscript. The final version is available from Inderscience via the DOI in this recordThis 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 datasets 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

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

The continuous single source location problem with capacity and zone-dependent fixed cost: Models and solution approaches

The continuous capacitated single-source multi-facility Weber problem with the presence of facility fixed cost is investigated. A new mathematical model which incorporates multi-level type capacity (or design) and facility fixed cost that is capacity-based and zone-dependent is introduced. As no data set exists for this new location problem, a new data set based on convex polygons using triangular shape is constructed. A generalised two stage heuristic scheme that combines the concept of aggregation, an exact method, and an enhanced Cooper’s alternate location-allocation method is put forward. A framework that embeds Variable Neighbourhood Search is also proposed. Computational experiments show that these matheuristics produce encouraging results for this class of location problems. The proposed approaches are also easily adapted to cater for a recently studied variant namely the single-source capacitated multi-facility Weber problem where they outperform those recently published solution method

The continuous single-source capacitated multi-facility Weber problem with setup costs: formulation and solution methods

The continuous single-source capacitated multi-facility Weber problem (SSCMFWP) where setup cost of opening facilities is taken into account is investigated. The aim is to locate a set of facilities on the plane, to define their respective capacities which can be linked to the configuration of the processing machines used, and to allocate customers to exactly one facility with the objective being the minimisation of the total transportation and setup costs. A new nonlinear mathematical model based on the SSCMFWP is introduced where Rectilinear and Euclidean distances are used. Efficient metaheuristic approaches based on Variable Neighbourhood Search and Simulated Annealing are also developed. The proposed metaheuristics incorporate an exact method and the commonly used Cooper’s alternate location-allocation method. We also constructed a new data set to reflect the characteristic of this particular location problem as no data set is available in the literature. Computational experiments show that the proposed metaheuristics generate interesting results for this class of continuous location problems

The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances

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

Hybrid Cell Selection-based Heuristic for capacitated multi-facility Weber problem with continuous fixed costs

This is the final version. Available on open access from EDP Sciences via the DOI in this recordLocation-allocation problem (LAP) has attracted much attention in facility location field. The LAP in continuous plane is well-known as Weber problem. This paper assessed this problem by considering capacity constraints and fixed costs as each facility has different setup cost and capacity limit to serve customers. Previous studies considered profitable areas by dividing continuous space into a discrete number of equal cells to identify optimal locations from a smaller set of promising locations. Unfortunately, it may lead to avoid choosing good locations because unprofitable areas are still considered while locating the facilities. Hence, this allows a significant increment in the transportation costs. Thus, this paper intelligently selected profitable area through a hybridization of enhanced Cell Selection-based Heuristic (CSBH) and Furthest Distance Rule (FDR) to minimize total transportation and fixed costs. The CSBH divides customer distribution into smaller set of promising locations and intelligently selected profitable area to increase possibility of finding better locations, while FDR aims to forbid the new locations of the facilities to be close to the previously selected locations. Numerical experiments tested on well-known benchmark datasets showed that the results of hybrid heuristic outperformed single CSBH and FDR, while producing competitive results when compared with previously published results, apart from significantly improving total transportation cost. The new hybrid heuristic is simple yet effective in solving LAP

Solving the Capacitated Multifacility Weber Problem approximately

In this study, we consider the capacitated multifacility Weber problem which is concerned with locating m facilities in the plane, and allocating their limited capacities to n customers at minimum total cost. In this group of location-allocation problems, the only cost dealt with is the transportation cost that is proportional to the distance between the facility and the customer. The capacities of each facility and the demands and the locations of each customer are predetermined and given as parameters. This problem is an intractable non-convex optimization problem and difficult to solve. Therefore, using approximation strategies to compute efficient and accurate lower and upper bounds for the capacitated multifacility Weber problem can be a good approach. We first concentrate on the alternating location allocation heuristics. Then we continue with the discretization strategies and the Lagrangean relaxations of the approximating models. Some specific lower bounding algorithms are also defined by using the special properties of some of the distance functions. In addition to them, the relaxation of the main model is investigated and a Lagrangean heuristic is devised. In this heuristic, either a linear relaxation or exact solution of the Lagrangean subproblem is found by using column generation and branch and price algorithms combined with concave minimization. Although an exact solution methodology is not found, the approximation methods give accurate results. The tight bounds calculated by using these algorithms can be convenient in searching the exact solutions for this group of problems

The optimal location of facilities on a network

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