Two-stage Capacitated Facility Location Problem Research Articles

A hybrid matheuristic for the Two-Stage Capacitated Facility Location problem

In the class of supply chain problems, the Two-Stage Capacitated Facility Location (TSCFL) is defined by optimal locations for installing factories and warehouses to meet the demand of customers. The problem aims to minimize operating costs: opening facilities and the flow of products from factories to customers, passing through warehouses, meeting the capacity constraints of factories and warehouses and customers’ demand. To solve this problem, a hybridization of Clustering Search (CS), Adaptive Large Neighborhood Search (ALNS) and Local Branching (LB) is proposed. This hybridization is a new and interesting approach which has found high quality solutions in low computational time. To show that, computational experiments were performed using benchmark instances. The results showed that the proposed method outperforms the current state-of-art for the TSCFL for 40 out of 50 instances.

An effective hybrid approach to the two-stage capacitated facility location problem

The two-stage capacitated facility location problem (TSCFLP) aims to simultaneously determine the locations of plants and depots with limited capacities and the product flows from plants to depots and then to single source customers minimizing the total facility opening and transportation costs. In this paper, based on a cut-and-solve strategy for tree searching, a hybrid approach combining cutting plane techniques, local branching and kernel search is proposed to optimally solve the TSCFLP. In each iteration of the approach, a three-stage cutting plane method is first applied to obtain a tight lower bound and a local branching method is adopted to partition the problem into two disjoint subproblems based on the corresponding lower bound solution. The subproblem with a relatively small solution space is then exactly solved and pruned with the help of a kernel search technique. To evaluate the efficiency and the effectiveness of the proposed approach, extensive experiments on benchmark and newly generated instances of TSCFLP, as well as instances of a single-source capacitated facility location problem that is a reduced TSCFLP, are conducted. The experimental results show that our proposed approach significantly outperforms existing methods in the literature.

A biased random-key genetic algorithm for the two-stage capacitated facility location problem

This paper presents a new metaheuristic approach for the two-stage capacitated facility location problem (TSCFLP), which the objective is to minimize the operation costs of the underlying two-stage transportation system, satisfying demand and capacity constraints. In this problem, a single product must be transported from a set of plants to meet customers demands passing out by intermediate depots. Since this problem is known to be NP-hard, approximated methods become an efficient alternative to solve real-industry problems. As far as we know, the TSCFLP is being solved in most cases by hybrid approaches supported by an exact method, and sometimes a commercial solver is used for this purpose. Bearing this in mind, a BRKGA metaheuristic and a new local search for TSCFLP are proposed. It is the first time that BRKGA had been applied to this problem and the computational results show the competitiveness of the approach developed in terms of quality of the solutions and required computational time when compared with those obtained by state-of-the-art heuristics. The approach proposed can be easily coupled in intelligent systems to help organizations enhance competitiveness by optimally placing facilities in order to minimize operational costs.

Formulation and solution of a two-stage capacitated facility location problem with multilevel capacities

In this paper, the multi-product facility location problem in a two-stage supply chain is investigated. In this problem, the locations of depots (distribution centres) need to be determined along with their corresponding capacities. Moreover, the product flows from the plants to depots and onto customers must also be optimised. Here, plants have a production limit whereas potential depots have several possible capacity levels to choose from, which are defined as multilevel capacities. Plants must serve customer demands via depots. Two integer linear programming (ILP) models are introduced to solve the problem in order to minimise the fixed costs of opening depots and transportation costs. In the first model, the depot capacity is based on the maximum number of each product that can be stored whereas in the second one, the capacity is determined by the size (volume) of the depot. For large problems, the models are very difficult to solve using an exact method. Therefore, a matheuristic approach based on an aggregation approach and an exact method (ILP) is proposed in order to solve such problems. The methods are assessed using randomly generated data sets and existing data sets taken from the literature. The solutions obtained from the computational study confirm the effectiveness of the proposed matheuristic approach which outperforms the exact method. In addition, a case study arising from the wind energy sector in the UK is presented.

Hybrid evolutionary algorithm with extreme machine learning fitness function evaluation for two-stage capacitated facility location problems

This paper considers the two-stage capacitated facility location problem (TSCFLP) in which products manufactured in plants are delivered to customers via storage depots. Customer demands are satisfied subject to limited plant production and limited depot storage capacity. The objective is to determine the locations of plants and depots in order to minimize the total cost including the fixed cost and transportation cost. However, the problem is known to be NP-hard. A practicable exact algorithm is impossible to be developed. In order to solve large-sized problems encountered in the practical decision process, an efficient alternative approximate method becomes more valuable. This paper aims to propose a hybrid evolutionary algorithm framework with machine learning fitness approximation for delivering better solutions in a reasonable amount of computational time. In our study, genetic operators are adopted to perform the search process and a local search strategy is used to refine the best solution found in the population. To avoid the expensive consumption of computational time during the fitness evaluating process, the framework uses extreme machine learning to approximate the fitness of most individuals. Moreover, two heuristics based on the characteristics of the problem is incorporated to generate a good initial population. Computational experiments are performed on two sets of test instances from the recent literature. The performance of the proposed algorithm is evaluated and analyzed. Compared with other algorithms in the literature, the proposed algorithm can find the optimal or near-optimal solutions in a reasonable amount of computational time. By employing the proposed algorithm, facilities can be positioned more efficiently, which means the fixed cost and the transportation cost can be decreased significantly, and organizations can enhance competitiveness by using the optimized facility location scheme.

Solving the robust two-stage capacitated facility location problem with uncertain transportation costs

In this study, we start from a multi-source variant of the two-stage capacitated facility location problem (TSCFLP) and propose a robust optimization model of the problem that involves the uncertainty of transportation costs. Since large dimensions of the robust TSCFLP could not be solved to optimality, we design a memetic algorithm (MA), which represents a combination of an evolutionary algorithm (EA) and a modified simulated annealing heuristic (SA) that uses a short-term memory of undesirable moves from previous iterations. A set of computational experiments is conducted to examine the impact of different protection levels on the deviation of the objective function value. We also investigate the impact of variations of transportation costs that may occur on both transhipment stages on the total cost for a fixed protection level. The obtained results may help in identifying a sustainable and efficient strategy for designing a two stage capacitated transportation network with uncertain transportation costs, and may be applicable in the design and management of similar transportation networks.

A simple and effective genetic algorithm for the two-stage capacitated facility location problem

This paper presents a simple and effective Genetic Algorithm (GA) for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem which arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying demand and capacity constraints of its agents. For this purpose, a GA is proposed and computational results are reported comparing the heuristic results with those obtained by two state-of-the-art Lagrangian heuristics proposed in the literature for the problem.

Lower and upper bounds for a two-stage capacitated facility location problem with handling costs

We study in this paper multi-product facility location problem in a two-stage supply chain in which plants have production limitation, potential depots have limited storage capacity and customer demands must be satisfied by plants via depots. In the paper, handling cost for batch process in depots is considered in a realistic way by a set of capacitated handling modules. Each module can be regards as alliance of equipment and manpower. The problem is to locate depots, choose appropriate handling modules and to determine the product flows from the plants, opened depots to customers with the objective to minimize total location, handling and transportation costs. For the problem, we developed a hybrid method. The initial lower and upper bounds are provided by applying a Lagrangean based on local search heuristic. Then a weighted Dantzig–Wolfe decomposition and path-relinking combined method are proposed to improve obtained bounds. Numerical experiments on 350 randomly generated instances demonstrate our method can provide high quality solution with gaps below 2%.

Lagrangian Heuristic for the Facility Location Problem

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 a Lagrangian relaxation is analyzed and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem

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, and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

Calculating the best dual bound for problems with multiple Lagrangian relaxations

There are often many ways in which a given problem can be relaxed in a Lagrangian fashion. It is not obvious a priori, which relaxation produces the best bound. Moreover, a bound may appear to be the best for a certain data set, while being among the worst for another problem instance. We consider here an optimization problem over the set of Lagrangian relaxations with the objective to indicate the relaxation producing the best dual bound. An iterative technique to solve this problem is proposed based on constraints generation scheme. The approach is illustrated by a computational study for a class of the two-stage capacitated facility location problem.

A Lagrangean relax-and-cut approach for the two-stage capacitated facility location problem

The two-stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand, the optimal assignment of customers to depots and the optimal product flow from plants to depots. In order to solve this problem, a Lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints. The resulting Lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch-and-bound methods. The best bound available from this relaxation is computed by means of a “weighted” Dantzig–Wolfe decomposition approach. Feasible solutions are constructed from those of the Lagrangean subproblems by applying simple reassignment procedures. Furthermore, the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program. Computational results and comparisons with some other bounds and heuristics for this problem are presented.

An LP-based heuristic for two-stage capacitated facility location problems

In this paper, a linear programming based heuristic is considered for a two-stage capacitated facility location problem with single source constraints. The problem is to find the optimal locations of depots from a set of possible depot sites in order to serve customers with a given demand, the optimal assignments of customers to depots and the optimal product flow from plants to depots. Good lower and upper bounds can be obtained for this problem in short computation times by adopting a linear programming approach. To this end, the LP formulation is iteratively refined using valid inequalities and facets which have been described in the literature for various relaxations of the problem. After each reoptimisation step, that is the recalculation of the LP solution after the addition of valid inequalities, feasible solutions are obtained from the current LP solution by applying simple heuristics. The results of extensive computational experiments are given.