Single Source Capacitated Facility Location Research Articles

A hybrid iterated local search matheuristic for large-scale single source capacitated facility location problems

A hybrid iterated local search matheuristic for large-scale single source capacitated facility location problems

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

A dual RAMP algorithm for single source capacitated facility location problems

A dual RAMP algorithm for single source capacitated facility location problems

A novel facility location problem for taxi hailing platforms

PurposeMotivated by a problem in the context of DiDi Travel, the biggest taxi hailing platform in China, the purpose of this paper is to propose a novel facility location problem, specifically, the single source capacitated facility location problem with regional demand and time constraints, to help improve overall transportation efficiency and cost.Design/methodology/approachThis study develops a mathematical programming model, considering regional demand and time constraints. A novel two-stage neighborhood search heuristic algorithm is proposed and applied to solve instances based on data sets published by DiDi Travel.FindingsThe results of this study show that the model is adequate since new characteristics of demand can be deduced from large vehicle trajectory data sets. The proposed algorithm is effective and efficient on small and medium as well as large instances. The research also solves and presents a real instance in the urban area of Chengdu, China, with up to 30 facilities and demand deduced from 16m taxi trajectory data records covering around 16,000 drivers.Research limitations/implicationsThis study examines an offline and single-period case of the problem. It does not consider multi-period or online cases with uncertainties, where decision makers need to dynamically remove out-of-service stations and add other stations to the selected group.Originality/valuePrior studies have been quite limited. They have not yet considered demand in the form of vehicle trajectory data in facility location problems. This study takes into account new characteristics of demand, regional and time constrained, and proposes a new variant and its solution approach.

Optimal Distributed Generator Placement in Utility-Based Microgrids During a Large-Scale Grid Disturbance

Microgrids are localized electric grids that can operate independent of the main grid and help strengthen grid resiliency by working alongside backup generators to maintain electricity supply in the event of a large-scale grid disturbance. This research proposes a single-source capacitated facility location coverage problem (SS-CFLCP) to optimize the location, assignment and number of renewable distributed generators (DGs) within a utility-based microgrid during a large-scale grid disturbance, where the microgrid is operating independent of the main grid. Traditional analytical techniques for DG placement within microgrids tend to focus on minimizing power losses, minimizing electric energy losses, improving voltage profile and maximizing cost savings. To deter from these traditional techniques, the proposed SS-CFLCP combines the facility location and location coverage problems, with an aim to minimize the following: total investment costs, total operation and maintenance cost, the distance traveled for electricity distribution, the power outage levels (unmet electricity demand) experienced due to a large-scale grid disturbance, and the levels of excess renewable penetration, which can cause reverse power flow issues that damage the main grid, within a network. Additionally, the proposed SS-CFLCP is modeled with a budgetary constraint for installing the DGs, making it a more practical and applicable model for a utility company. A case study using solar/photovoltaic-based DGs is used to show the effectiveness of the proposed model.

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.

On single-source capacitated facility location with cost and fairness objectives

We consider a location problem where a planner has to decide where to open facilities which have to be reached by customers at their own cost. The planner has two objectives: cost minimization and customer satisfaction. We argue that performance and fairness, as structural components of customer satisfaction, are both captured by an equity measure called conditional β-mean. We thus formulate the Fair Single-Source Capacitated Facility Location (F-SSCFL) problem, where the cost minimization objective is paired with the conditional β-mean minimization objective. The resulting formulation is a bi-objective mixed-integer linear program. A weighted sum method is developed to generate a small representative set of efficient solutions to the F-SSCFL problem, and a Benders decomposition approach is implemented to handle large-scale instances. On small/medium-scale instances, we analyse the trade-off between cost and conditional β-mean, showing that the model may be used as a managerial tool to balance direct costs and customer service. We also compare the quality of the solutions obtained with those obtained using alternative equity measures. On large-scale instances, we test Benders decomposition, showing that it is able to find good quality solutions in a relatively short computing time.

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.

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.

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

A note on the facility location problem with stochastic demands

In this research note that the single source capacitated facility location problem with general stochastic identically distributed demands is studied. The demands considered are independent and identically distributed random variables with arbitrary distribution. The unified a priori solution for the locations of facilities and for the allocation of customers to the operating facilities is found. This solution minimizes the objective function which is the sum of the fixed costs and the value of one of two different recourse functions. For each case the recourse function is given in closed form and a deterministic equivalent formulation of the model is presented. Some numerical examples are also given.

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.

Combining very large scale and ILP based neighborhoods for a two-level location problem

In this paper we tackle a generalization of the Single Source Capacitated Facility Location Problem in which two sets of facilities, called intermediate level and upper level facilities, have to be located; the dimensioning of the intermediate set, the assignment of clients to intermediate level facilities, and of intermediate level facilities to upper level facilities, must be optimized, as well. Such problem arises, for instance, in telecommunication network design: in fact, in hierarchical networks the traffic arising at client nodes often have to be routed through different kinds of facility nodes, which provide different services. We propose a heuristic approach, based on very large scale neighborhood search to tackle the problem, in which both ad hoc algorithms and general purpose solvers are applied to explore the search space. We report on experimental results using datasets from the capacitated location literature. Such results show that the approach is promising and that Integer Linear Programming based neighborhoods are significantly effective.