Single Source Capacitated Facility Location Problem Research Articles

A branch-and-price algorithm for the robust single-source capacitated facility location problem under demand uncertainty

We consider the robust single-source capacitated facility location problem with uncertainty in customer demands. A cardinality-constrained uncertainty set is assumed for the robust problem. To solve it efficiently, we propose an allocation-based formulation derived by Dantzig–Wolfe decomposition and a branch-and-price algorithm. The computational experiments show that our branch-and-price algorithm outperforms CPLEX in many cases, which solves the ordinary robust reformulation. We also examine the trade-off relationship between the empirical probability of infeasibility and the additional costs incurred and observe that the robustness of solutions can be improved significantly with small additional costs.

Smooth and Flexible Dual Optimal Inequalities

We address the problem of accelerating column generation (CG) for set-covering formulations via dual optimal inequalities (DOIs). We study two novel classes of DOIs, which are referred to as Flexible DOIs (F-DOIs) and Smooth-DOIs (S-DOIs), respectively (and jointly as SF-DOIs). F-DOIs provide rebates for covering items more than necessary. S-DOIs describe the payment of a penalty to permit the undercoverage of items in exchange for the overinclusion of other items. Unlike other classes of DOIs from the literature, the S-DOIs and F-DOIs rely on very little problem-specific knowledge and, as such, have the potential to be applied to a vast number of problem domains. In particular, we discuss the application of the new DOIs to three relevant problems: the single-source capacitated facility location problem, the capacitated p-median problem, and the capacitated vehicle-routing problem. We provide computational evidence of the strength of the new inequalities by embedding them within a column-generation solver for these problems. Substantial speedups can be observed as when compared with a nonstabilized variant of the same CG procedure to achieve the linear-relaxation lower bound on problems with dense columns and structured assignment costs.

A Study on the Logistics Network Resign using An Algorithm for the Single-Source Capacitated Facility Location Problem

A Study on the Logistics Network Resign using An Algorithm for the Single-Source Capacitated Facility Location Problem

Uplink/downlink decoupled energy efficient user association in heterogeneous cloud radio access networks

Heterogeneous Cloud Radio Access Networks (H−CRAN) is a network architecture that combines Macro Base Stations (MBS)s and Small Base Stations (SBS)s with cloud infrastructures. The dense deployment of SBSs in H-CRAN is needed to provide high data rates to User Equipments (UEs) but causes high energy consumption. Unrealistic power models lead to inefficient UE association schemes in terms of energy. In this paper, we study the joint optimization of Uplink (UL) and Downlink (DL) decoupled UE association and switching on/off the SBSs in H-CRAN by incorporating a realistic power model with the objective of minimizing the power consumption in H-CRAN. The power model encompasses static and the dynamic power consumption of MBS, the static power consumption of SBS, the power consumption of transmission links to cloud infrastructure and the power consumption of UEs. The problem is transformed into Single Source Capacitated Facility Location Problem (SSCFLP) which is NP-Hard. We then propose a heuristic algorithm based on the use of LP relaxation and solving many-to-one assignment problem with generalized assignment problem heuristics. Extensive simulations demonstrate that the proposed heuristic algorithm performs very close to optimal and achieves significant improvements in minimizing total power consumption compared to coupled UE association algorithm and algorithms utilizing the power consumption models that do not encompass MBS dynamic power consumption and the power consumption of transmission links to cloud infrastructure for various scenarios.

A biased-randomised algorithm for the capacitated facility location problem with soft constraints

This paper analyzes the single-source capacitated facility location problem (SSCFLP) with soft capacity constraints. Hence, the maximum capacity at each facility can be potentially exceed by incurring in a penalty cost, which increases with the constraint-violation gap. In some realistic scenarios, this penalty cost can be modelled as a piecewise function. As a result, the traditional cost-minimization objective becomes a non-smooth function that is difficult to optimise using exact methods. A mathematical model of this non-smooth SSCFLP is provided, and a biased-randomized iterated local search metaheuristic is proposed as a solving method. A set of computational experiments is run to illustrate our algorithm and test its efficiency.

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.

Revisiting Lagrangian relaxation for network design

We consider a general network design model for which we compare theoretically different Lagrangian relaxations. Fairly general assumptions on the model are proposed, allowing us to generalize results obtained for special cases. The concepts are illustrated on two classical network design problems, the fixed-charge multicommodity capacitated network design problem and the single-source capacitated facility location problem. We also show that, even though our assumptions might not be verified, it is often possible to derive extended reformulations that satisfy them. We study the impact of such extended reformulations on Lagrangian relaxations, by focusing on two particular cases, the hop-constrained fixed-charge multicommodity capacitated network design problem and the multicommodity capacitated network design problem.

A hypergraph multi-exchange heuristic for the single-source capacitated facility location problem

In this paper, we introduce a large-scale neighborhood search procedure for solving the single-source capacitated facility location problem (SSCFLP). The neighborhood structures are induced by innovative split multi-customer multi-exchanges, where clusters of customers assigned to one facility can be moved simultaneously to multiple destination facilities and vice versa. To represent these exchanges, we use two types of improvement hypergraphs. The improvement hypergraphs are built dynamically and the moving customers associated with each hyperedge are selected by solving heuristically a suitably defined mixed-integer program. We develop a hypergraph search framework, including forward and backward procedures, to identify improving solutions efficiently. Our proposed algorithm can obtain improving moves more quickly and even find better solutions than a traditional multi-exchange heuristic (Ahuja, Orlin, Pallottino, & Scuttellà, 2004). In addition, when compared with the Kernel Search algorithm (Guastaroba & Speranza, 2014), which at present is the most effective for solving SSCFLP, our algorithm is not only competitive but can find better solutions or even the best known solution to some very large scale benchmark instances from the literature.

An improved cut-and-solve algorithm for the single-source capacitated facility location problem

In this paper, we present an improved cut-and-solve algorithm for the single-source capacitated facility location problem. The algorithm consists of three phases. The first phase strengthens the integer program by a cutting plane algorithm to obtain a tight lower bound. The second phase uses a two-level local branching heuristic to find an upper bound, and if optimality has not yet been established, the third phase uses the cut-and-solve framework to close the optimality gap. Extensive computational results are reported, showing that the proposed algorithm runs 10–80 times faster on average compared to state-of-the-art problem-specific algorithms.

A hybrid algorithm for stochastic single-source capacitated facility location problem with service level requirements

A hybrid algorithm for stochastic single-source capacitated facility location problem with service level requirements

An iterated tabu search heuristic for the Single Source Capacitated Facility Location Problem

This paper discusses the Single Source Capacitated Facility Location Problem (SSCFLP) where the problem consists in determining a subset of capacitated facilities to be opened in order to satisfy the customers’ demands such that total costs are minimized. The paper presents an iterated tabu search heuristic to solve the SSCFLP. The iterated tabu search heuristic combines tabu search with perturbation operators to avoid getting stuck in local optima. Experimental results show that this simple heuristic is capable of generating high quality solutions using small computing times. Moreover, it is also competitive with other metaheuristic approaches for solving the SSCFLP.

A heuristic for BILP problems: The Single Source Capacitated Facility Location Problem

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.

A cutting plane algorithm for the Capacitated Connected Facility Location Problem

We consider a network design problem that arises in the cost-optimal design of last mile telecommunication networks. It extends the Connected Facility Location problem by introducing capacities on the facilities and links of the networks. It combines aspects of the capacitated network design problem and the single-source capacitated facility location problem. We refer to it as the Capacitated Connected Facility Location Problem. We develop a basic integer programming model based on single-commodity flows. Based on valid inequalities for the capacitated network design problem and the single-source capacitated facility location problem we derive several (new) classes of valid inequalities for the Capacitated Connected Facility Location Problem including cut set inequalities, cover inequalities and combinations thereof. We use them in a branch-and-cut framework and show their applicability and efficacy on a set of real-world instances.

A cut-and-solve based algorithm for the single-source capacitated facility location problem

In this paper, we present a cut-and-solve (CS) based exact algorithm for the Single Source Capacitated Facility Location Problem (SSCFLP). At each level of CS’s branching tree, it has only two nodes, corresponding to the Sparse Problem (SP) and the Dense Problem (DP), respectively. The SP, whose solution space is relatively small with the values of some variables fixed to zero, is solved to optimality by using a commercial MIP solver and its solution if it exists provides an upper bound to the SSCFLP. Meanwhile, the resolution of the LP of DP provides a lower bound for the SSCFLP. A cutting plane method which combines the lifted cover inequalities and Fenchel cutting planes to separate the 0–1 knapsack polytopes is applied to strengthen the lower bound of SSCFLP and that of DP. These lower bounds are further tightened with a partial integrality strategy. Numerical tests on benchmark instances demonstrate the effectiveness of the proposed cutting plane algorithm and the partial integrality strategy in reducing integrality gap and the effectiveness of the CS approach in searching an optimal solution in a reasonable time. Computational results on large sized instances are also presented.

물류 센터 위치 선정 및 대리점 할당 모형에 대한 휴리스틱 해법

시설물 입지 선정 문제(FLP)는 전통적인 최적화 문제중에 하나이다. FLP에 공급제약과 하나의 고객은 하나의 시설물에서만 제품을 공급받을 수 있다는 제약을 추가하면 단일 시설물 공급제약을 가지는 시설물 위치 설정 문제(SSFLP)가 된다. SSFLP는 NP-hard 문제로 알려져 있으며 진화 알고리즘과 같은 휴리스틱 알고리즘을 사용하여 해결하는 것이 일반적이다. 본 논문에서는 SSFLP를 위한 효율적인 진화 알고리즘을 제안한다. 제안하는 알고리즘은 적응형 링크 조절 진화 알고리즘과 3가지 휴리스틱 해 개선 방법을 조합하여 고안되었다. 제안하는 알고리즘을 벤치마크 문제에 적용하여 다른 알고리즘과 성능을 비교분석해 본 결과, 제안하는 알고리즘은 중간 크기의 문제에서 대부분 최적해를 찾았으며 큰 문제에서도 안정된 결과를 보여주었다. The facility location problem is one of the traditional optimization problems. In this paper, we deal with the single source capacitated facility location problem (SSCFLP) and it is known as an NP-hard problem. Thus, it seems to be natural to use a heuristic approach such as evolutionary algorithms for solving the SSCFLP. This paper introduces a new efficient evolutionary algorithm for the SSCFLP. The proposed algorithm is devised by incorporating a general adaptive link adjustment evolutionary algorithm and three heuristic local search methods. Finally we compare the proposed algorithm with the previous algorithms and show the proposed algorithm finds optimum solutions at almost all middle size test instances and very stable solutions at larger size test instances.

Stochastic single-source capacitated facility location model with service level requirements

A stochastic version of single-source capacitated facility location problem is considered. A set of capacitated facilities is to be selected to provide service to demand points with stochastic demand at the minimal total cost. The facilities have service level requirements modeled by chance constraints. For Poisson demand, the problem is proved equivalent to a known solvable deterministic problem. For Normally distributed demand, it is equivalent to a deterministic mixed integer non-linear programming problem. A hybrid heuristic of Lagrangean relaxation with a single-customer-multi-exchange heuristic is embedded within a branch-and-bound framework to find upper and lower bounds for this problem. From test instances created from benchmark problems (10–20 facilities and 50 demand nodes) and real-life data on the deterministic problem, the gap between the bounds is within 6.5% with an average of 2.5%.

Combining Lagrangian heuristic and Ant Colony System to solve the Single Source Capacitated Facility Location Problem

The facility location problems have been applied extensively in practice. We describe a Multiple Ant Colony System (MACS) to solve the Single Source Capacitated Facility Location Problem (SSCFLP). Lagrangian heuristics have been shown to produce good solutions for the SSCFLP. A hybrid algorithm, which combines Lagrangian heuristic and Ant Colony System (ACS), LH–ACS, is developed for the SSCFLP. The performance of the proposed methods are tested on two sets of benchmark instances and compared with other heuristic algorithms in the literature. The computational results indicate that both MACS and LH–ACS are effective and efficient for the SSCFLP and competitive with other well-known algorithms.

Scatter search for the single source capacitated facility location problem

This paper considers the Single Source Capacitated Facility Location Problem (SSCFLP). We propose a Scatter Search approach to provide upper bounds for the optimal solution of the problem. The proposed approach uses GRASP to initialize the Reference Set. Solutions of the Reference Set are combined using a procedure that consists of two phases: (1) the initialization phase and (2) the improvement phase. During the initialization phase each client is assigned to an open facility to obtain a solution that is then improved with the improvement phase. Also, a tabu search algorithm is applied. In order to evaluate the proposed approach we use different sets of test problems. According to the results obtained we observe that the method provides good quality solutions with reasonable computational effort.

A Multi-Exchange Heuristic for the Single-Source Capacitated Facility Location Problem

We present a very large-scale neighborhood (VLSN) search algorithm for the capacitated facility location problem with single-source constraints. The neighborhood structures are induced by customer multi-exchanges and by facility moves. We consider both traditional single-customer multi-exchanges, detected on a suitably defined customer improvement graph, and more innovative multicustomer multi-exchanges, detected on a facility improvement graph dynamically built through the use of a greedy scheme. Computational results for some benchmark instances are reported that demonstrate the effectiveness of the approach for solving large-scale problems. A further test on real data involving an Italian factory is also presented.

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.