Capacitated Facility Location Problem Research Articles

A 3-Approximation Algorithm for Uniform Capacitated Facility Location Problem with Penalties

We introduce an algorithm based on local search for “Uniform Capacitated Facility Location Problem with Penalties (UCFLPP)” and analyze the same. The algorithm is same as given by Korupolu et al. for the “Uniform Capacitated Facility Location Problem (UCFLP)”. Aggarwal et al. in their work proved that the algorithm given by Korupolu et al. is a 3-factor approximation algorithm for UCFLP. We extend idea of Aggarwal et al. to show that the same algorithm works for the problem with penalty incorporated. It has the same approximation guarantee for UCFLPP, as given by them. This improves upon the current best of 5.732 factor for the problem, which is an LP based algorithm by Lv and Wu.

Multi-neighborhood simulated annealing for the capacitated facility location problem with customer incompatibilities

We consider the Capacitated Facility Location Problem with Customer Incompatibilities, which is a recently -proposed variant of the classic facility location problem whose distinctive feature is to take into account incompatibilities between customers.We tackle this problem using local search and we propose a combination of neighborhoods and ad hoc techniques to reduce the size of the search space, in order to effectively deal with large instances. The resulting multi-neighborhood approach is guided by a simulated annealing procedure. Our method, suitably tuned in a statistically-principled way, has been able to outperform all previous techniques on the publicly available dataset, on both short and long running times.

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

Dynamic capacitated facility location problem in mobile renewable energy charging stations under sustainability consideration

The deployment of mobile renewable energy charging stations plays a crucial role in facilitating the overall adoption of electric vehicles and reducing reliance on fossil fuels. This study addresses the dynamic capacitated facility location problem in mobile charging stations from a sustainability perspective. This paper proposes Two-stage stochastic programming with recourse that performs well for this application, and the location of the mobile renewable energy charging station (MRECS) management addresses the complex dynamics of reusable items. To solve this problem, we suggested dealing with differential evolutionary (DE) and DE Q-learning (DEQL) algorithms, as two novel optimization and reinforcement learning approaches, are presented as solution approaches to validate their performance. Evaluation of the outcomes reveals a considerable disparity between the algorithms, and DEQL performs better in solving the presented problem. In addition, DEQL could minimize the total operation cost and carbon emission by 7% and 20%, respectively. In contrast, the DE could decrease carbon emissions and total operation costs by 5% and 2.5%, respectively.

Adaptive Supply Chain System Design for Fruit Crops under Climate Change

There is an urgent need for adaptive supply chain strategies that can mitigate the effects of climate change on the agricultural system. This study introduces a new mathematical model, Capacitated Facility Location Problems with Multi-Period (CFLP-MP), to respond to this challenge. Unlike existing models, the CFLP-MP framework is designed to optimize the supply chain system design of facility locations and transportation routes by accommodating changes in production and demand for multiple time periods. The proposed model can be extended to other time-sensitive agricultural foods, but in this research, it is applied to the U.S. apple industry as a case study. Despite varying conditions, the model demonstrates resilience in maintaining its operational efficiency, thereby offering a solution to the initial challenge of creating an adaptive agricultural supply chain system. In conclusion, this research offers a versatile toolset for enhancing resilience and sustainability in fruit crop production, precisely addressing the climate-induced challenges identified above.

Enhancing Branch-and-Bound for Multiobjective 0-1 Programming

In the biobjective branch-and-bound literature, a key ingredient is objective branching, that is, to create smaller and disjoint subproblems in the objective space, obtained from the partial dominance of the lower bound set by the upper bound set. When considering three or more objective functions, however, applying objective branching becomes more complex, and its benefit has so far been unclear. In this paper, we investigate several ingredients that allow us to better exploit objective branching in a multiobjective setting. We extend the idea of probing to multiple objectives for the 0-1 case, enhance it in several ways, and show that, when coupled with objective branching, it results in significant speedups in terms of CPU times. We also show how to adapt it to the general integer case. Furthermore, we investigate cut generation based on the objective branching constraints. Besides, we generalize the best bound idea for node selection to multiple objectives, and we show that the proposed rules outperform, in the multiobjective literature, the commonly employed depth-first and breadth-first strategies. We also analyze problem-specific branching rules. We test the proposed ideas on available benchmark instances for three problem classes with three and four objectives, namely, the capacitated facility location problem, the uncapacitated facility location problem, and the knapsack problem. Our enhanced multiobjective branch-and-bound algorithm outperforms the best existing branch-and-bound–based approach and is the first to obtain competitive and even slightly better results than a state-of-the-art objective space search method on a subset of the problem classes. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in whole, or in part, by the Austrian Science Fund [Grant P 31366]. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0299 .

Distributionally robust facility location with uncertain facility capacity and customer demand

This study explores a capacitated facility location problem where facility capacity and customer demand are subject to uncertainties simultaneously. This problem decides the subset of facilities to open at the system design phase to serve customers during the operational phase. The objective is to minimize the total cost, including the first-stage location cost and the second-stage recourse cost, and guarantee the system’s reliability, i.e., meeting demand as much as possible when uncertainties arise. A distributionally robust optimization (DRO) framework is utilized to model the problem. A scenario-wise ambiguity set with partial distributional information of random variables is constructed, which can capture uncertainties caused by different random events or different magnitudes of the same event type and explicitly represent the correlation between facilities’ uncertain capacity and customers’ uncertain demand. We apply an adaptation policy to the DRO model and reformulate it to a mixed-integer linear programming model, which is solvable by off-the-shelf solvers. Numerical results show that the scenario-wise DRO framework can provide a better trade-off between cost and service level than the stochastic programming model and the DRO model with a marginal moment-based ambiguity set, demonstrating that the proposed scenario-wise DRO model offers a practical decision-making tool for enhancing supply chain robustness via facility location.

Enhanced capacitated facility location problem for mental accounting management using partial resource concentration

Enhanced capacitated facility location problem for mental accounting management using partial resource concentration

Adjustable robust optimization with objective uncertainty

In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and involve mixed-integer variables, thus extending the existing literature to a much wider class of problems. We show how these problems can be reformulated using Fenchel duality, allowing to derive an enumerative exact algorithm, for which we prove asymptotic convergence in the general case, and finite convergence for cases where the first-stage variables are all integer.An implementation of the resulting algorithm, embedding a column generation scheme, is then computationally evaluated on a variant of the Capacitated Facility Location Problem with uncertain transportation costs, using instances that are derived from the existing literature. To the best of our knowledge, this is the first approach providing results on the practical solution of this class of problems.

Locker box location planning under uncertainty in demand and capacity availability

In this paper, we address the location of locker boxes in the last-mile delivery context under uncertainty in demand and capacity. The problem is modeled as an extension of the capacitated facility location problem, in which a fixed number of facilities has to be opened, choosing among a set of potential locations. Facilities are characterized by a homogeneous capacity, but a capacity reduction may occur with a given probability. The uncertainty in demand and capacity is incorporated through a set of discrete scenarios. Each customer can be assigned only to compatible facilities, i.e., to facilities located within a given radius from the individual location. The goal is to first maximize the total number of customers assigned to locker boxes, while, in case of a tie on this primary objective, a secondary objective intervenes aiming at minimizing the average distance covered by customers to reach their assigned locker box. A stochastic mathematical model as well as three matheuristics are presented. We provide an extensive computational study in order to analyze the impact of different parameters on the complexity of the problem. The importance of considering uncertainty in input data is discussed through the usage of general stochastic indicators from the literature as well as of problem specific indicators. A real-world case related to the City of Turin in Italy is analyzed in detail. The benefit achievable by optimizing locker box locations is discussed and a comparison with the current configuration is provided.

Benders-type branch-and-cut algorithms for capacitated facility location with single-sourcing

We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0–1 variables xj indicating whether faclility j is used or not and yij variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, the remaining problem is a transportation problem with single-sourcing. This structure suggest the use of a Benders’ type decomposition algorithm. Here we present three possible variants. Applied to CFLP-SS they are compared computationally with a commercial solver (CPLEX) on the original formulation, a CPLEX version of Benders and a recent cut-and-solve approach developed specifically for CFLP-SS. Our results show that for CFLP-SS, when the percentage of clients requiring single-sourcing is less equal than 25%, the Benders’ variants achieve speedups of between 1.2 and 3.7.

A Decision-Making Model for Remanufacturing Facility Location in Underdeveloped Countries: A Capacitated Facility Location Problem Approach

Underdeveloped countries are gradually opening remanufacturing facilities to recover end-of-life products (EOL). Locating these facilities in underdeveloped countries is quite challenging because many factors related to the environment, economics, and ethics have to be considered. This paper proposes a decision-making model for locating remanufacturing facilities, a critical factor in implementing remanufacturing in underdeveloped countries. Our principal objective is to obtain the capacity, number, and geographical locations for newly established remanufacturing facilities using a Capacitated Facility Location Problem (CFLP) approach. The mathematical model helps us find the number of facilities that will need to be opened to fully recover the EOL products and the total cost during the entire process. A case study on the establishment of SEVALO Remanufacturing Machinery Co., Ltd. in Cameroon is used to demonstrate the CFLP approach. The results and analyses show that the successful establishment of SEVALO in Cameroon will significantly help to reduce the quantity of construction machinery parts dumped into the environment.

Metaheuristic techniques for the capacitated facility location problem with customer incompatibilities

Metaheuristic techniques for the capacitated facility location problem with customer incompatibilities

A note on LP-based approximation algorithms for capacitated facility location problem

In the capacitated facility location problem, we are given a set F of potential facilities and a set D of clients, where each facility has a capacity and an open cost, and each client has a demand to be served by the facilities with service costs. The goal is to open some facilities in F and assign all clients in D to these open facilities such that the total cost is minimum. Based on the natural integer programming formulation, Levi et al. [8] presented an LP-based 5-approximation algorithm for this problem under the assumption that the facility costs are uniform. Based on the same integer programming formulation, we remove the uniformity assumption and present an (R+R2+8R2+3)-approximation algorithm for the capacitated facility location problem, where R is the upper bound of the ratio between facility costs. Our result is a slight extension of the corresponding result in [8], as when R=1 the worst-case ratio of our algorithm is R+R2+8R2+3=5.

LP-based approximation for uniform capacitated facility location problem

In this paper, we study uniform hard capacitated facility location problem. The standard LP for the problem is known to have an unbounded integrality gap. We present constant factor approximation by rounding a solution to the standard LP with a slight (1+ϵ) violation in the capacities.Our result shows that the standard LP is not too bad.Our algorithm is simple and more efficient as compared to the strengthened LP-based true approximation that uses the inefficient ellipsoid method with a separation oracle. True approximations are also known for the problem using local search techniques that suffer from the problem of convergence. Moreover, solutions based on standard LP are easier to integrate with other LP-based algorithms.The result is also extended to give the first approximation for uniform hard capacitated k-facility location problem violating the capacities by a factor of (1+ϵ) and breaking the barrier of 2 in capacity violation. The result violates the cardinality by a factor of 21+ϵ.

A hybridisation of linear programming and genetic algorithm to solve the capacitated facility location problem

This paper introduces a cooperative approach of a swarm intelligence algorithm and a linear programming solver to solve the capacitated facility location problem (CFLP). Given a set of potential locations to open facilities, the aim in CFLP is to find the minimum cost, which is the sum of facility opening costs and transportation costs. The developed solution strategy decomposes CFLP into two sub-problems. The former sub-problem has a binary domain. Although most of the swarm intelligence algorithms employ additional procedures such as sigmoid function to deal with binary domains, the proposed algorithm does not require for such methods. An adaptive mutation operator enhances this algorithm. The aim of the latter sub-problem is to generate a policy that optimally assigns customers to the opened facilities. In this regard, the generated binary vectors by the proposed algorithm are passed to a solver to optimise the generated linear model. Commonly used instances available in the literature are solved by the proposed strategy. Comprehensive experimental study includes comparisons with the sate-of-the-art. According to the statistically verified results, the proposed strategy is found as promising in solving CFLP.

Regionalization of primary health care units with multi-institutional collaboration

In this paper, the problem of locating and upgrading primary health care units within a multi-institutional public system is addressed. The problem is motivated by a real-world application in the Mexican Health Care System. Decisions also involve allocating customer demand to those facilities with the goal of minimizing the total travel distance in a capacitated facility location problem. The capacity is measured in units named basic kernels composed by a group of medical staff for outpatient services. A mixed-integer linear programming model is proposed. A computational study based on a real-world case in the State of Mexico is carried out. Test instances are successfully solved by branch and bound. The distribution of patient-to-health care unit distances and the variation of the capacity utilization rate of health care units are analyzed. Among the results, we found that the total travel distance had an average improvement of up to 32% when the capacity is shared between institutions. Some parameters such as the kernel capacity and the minimum allocated demand at each facility could help to balance the workload between health care units, but this outcome has a negative impact on the total travel distance. On average, 91% of demand travels less than 10 km to its health care units and 99% less than 20 km in the computed solutions. The results presented in this paper open the opportunity of using OR tools in the planning of health care resources in developing countries to face the challenges of the next decade in health care matters.

Algorithms for online data management problems considering the storage capacities

A mind-boggling amount of data will be generated every day. It is natural to consider clustering the data and putting each cluster into some place for storing. In reality, the arrival time of the data is unknown in advance and new data keep joining appropriate cluster upon arrival. This scenario can be captured as the online facility location problem. Usually, the places for storing the data have limited capacities. Therefore, the online capacitated facility location problem (O-CFLP) is proposed.Designing algorithms with bounded competitive ratios for the O-CFLP is impossible. This fact stimulates us to study special cases of the O-CFLP. We pay attention on the online soft capacitated facility location problem and its prize-collecting version, and we design dual-fitting competitive algorithms for them.

Robustness of solutions to the capacitated facility location problem with uncertain demand

Robustness of solutions to the capacitated facility location problem with uncertain demand

Mobility-Aware Controller Orchestration in Multi-Tier Service-Oriented Architecture for IoT

This work addresses the problem of controller orchestration in Internet of Things (IoT)-based Service-Oriented Architecture. It focuses on the fundamental issues of heterogeneity and dynamism of hybrid edge-cloud networks involving both static and mobile IoT devices for provisioning IoT-based services. Due to the limited capacity of IoT devices, IoT-cloud services require the support of edge networks, termed as ‘Service Edge,’ for meeting their ultra-low latency requirements. In such complex and dynamic networks, software-defined networking (SDN) paradigm is utilized for efficient resource utilization and service-oriented network management. A significant problem in SDN is the controller placement problem. Although researchers proposed several controller placement schemes for SDN, the problem of multi-tier controller placement in hybrid cloud-edge networks has not yet been addressed. In this work, this problem is formulated mathematically and shown to be a variant of the well-known <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two-level capacitated facility location problem</i> , which is NP-hard. Thereafter, COMET, a scheme based on coalitional game and social choice theory, is proposed to solve the problem in polynomial time. COMET is designed while considering varying loads on the switches due to the presence of mobile IoT devices. Simulations depict that COMET reduces network delay by 49.02% with a significant increase in resiliency compared to the state-of-the-art.