Capacitated Facility Research Articles

Approximation Scheme for the Single-Client Capacitated Facility Location Problem With Operational Cost Budget Constraint

Approximation Scheme for the Single-Client Capacitated Facility Location Problem With Operational Cost Budget Constraint

Impact of mistriages in on-scene injury assessment on trauma network and patient safety

An accurate on-scene assessment of a trauma patient’s injury by emergency medical service providers is critical to determining the right hospital for prompt care delivery. However, literature and anecdotal evidence from trauma professionals in the Midwestern U.S. suggest that mistriages (i.e., an error in assessing a severely injured patient as having non-severe injuries, and vice versa) often occur in practice. Due to a lack of approaches that consider such mistriages while designing the trauma network, we propose a stochastic nested multi-level, multi-transportation capacitated facility location model, which explicitly considers mistriages in injury assessment, to maximize patient safety by determining the number and locations of major trauma centers (MTCs). Assessment-related mistriages are modeled using a Bernoulli random variable for each of the two injury groups, moderate (ISS 9–15) and severe (ISS>15). We propose a Simheuristic approach that integrates Monte Carlo Simulation with a genetic algorithm. We convert infeasible solutions into feasible ones during offspring generation and maintain a superior population pool to balance quality against computational time. Our findings based on a realistic data set suggest that assessment-related mistriages in the ISS>15 group can substantially decrease patient safety and may lead to a clustering of MTCs, while mistriages in the ISS 9–15 group tend to have a dispersed distribution of MTCs in the resulting network. Our case study using actual 2019 data from a midwestern state of the U.S. resulted in an over 20% reduction in the mistriages, further providing evidence for incorporating injury assessment-related mistriages in trauma network design.

Facility Location Problem: Modeling Joint Disruptions Using Subordination

We study the facility location problem with disruptions where the objective is to choose a set of locations that minimizes the sum of expected servicing and setup costs. Disruptions can affect multiple locations simultaneously and are caused by multiple factors like geography, supply chain characteristics, politics, and ownership. Accounting for the various factors when modeling disruptions is challenging due to a large number of required parameters, the lack of calibration methodologies, the sparsity of disruption data, and the number of scenarios to be considered in the optimization. Because of these reasons, existing models neglect dependence or prespecify the dependence structures. Using partially subordinated Markov chains, we present a comprehensive approach that starts from disruption data, models dependencies, calibrates the disruption model, and optimizes location choices. We construct a metric and a calibration algorithm that learns from the data the strength of dependence, the number of necessary factors (subordinators), and the locations each subordinator affects. We prove that our calibration approach yields consistent estimates of the model parameters. Then, we introduce a variant of the standard approach to the underlying optimization problem, which leverages partially subordinated Markov chains to solve it quickly and precisely. Finally, we demonstrate the efficacy of our approach using twelve different disruption data sets. Our calibrated parameters are robust, and our optimization algorithm performs better than the simulation-based algorithm. The solutions from our model for disruptions have lower costs than those from other disruption models. Our approach allows for better modeling of disruptions from historical data and can be adapted to other problems in logistics, like the hub location, capacitated facility location, and so on., with joint disruptions. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0103 .

A Lagrangian relaxation approach for resource allocation problem with capacity constraints

AbstractThis study evaluates a capacitated facility location model enhanced with distance constraints for an emergency response problem, ensuring certain neighborhoods remain within an accessible range from facilities following a hurricane. The proposed model takes into account the capacity constraints for drones and vehicles. The model determines optimal locations for facilities and the distribution of supplies across the city. It also specifies which facilities should support the needs of each neighborhood and decides on the appropriate mode of transportation—ground vehicles if possible, or drones if roadways are obstructed. To solve the problem, a Lagrangian relaxation technique is employed, relaxing the constraints related to facility capacity and distance. The numerical results confirm the quality and efficiency of the solutions. The findings indicate that ground transportation is more frequently utilized than drones at each operational facility. A comprehensive set of sensitivity analyses is conducted to examine the impact of various variables and parameters on the solution.

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.

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 Two-Stage Optimization Approach for Healthcare Facility Location- Allocation Problems With Service Delivering Based on Genetic Algorithm.

Objective: This study assesses a multi-period capacitated maximal-covering location-allocation model for healthcare services, taking interservice referral as well as equity access into account. Methods: A two-stage optimization strategy is used to formulate the model. In the first stage, facilities are located to maximize covered demand, and in the second stage, patients are allocated to capacitated facilities based on their radius of coverage over multiple time periods. The problem, which belongs to the NP-hard class of optimization problems, is solved using a linear mixed-integer programming (MILP) model. Results: A numerical example is presented to evaluate the efficiency of the proposed model. In addition, to identify near-optimal solutions for large instances, a hybrid genetic-sequential quadratic programming approach (GA-SQP) is developed. To examine the performance and efficiency of the GA-SQP, we employed several randomly generated test instances of various sizes and compared them to those obtained using the exact method. Conclusion: The proposed model has demonstrated an excellent ability in locating healthcare facilities and allocating health services while taking shortage and equity into account during each time period.

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 meta heuristic approach for reliable capacitated facility joint inventory-location problem with round-trip transportation under imperfect information of disruption in a Fuzzy environment

In today’s systems and networks, disruption is inevitable. Designing a reliable system to overcome probable facility disruptions plays a crucial role in planning and management. This article proposes a reliable capacitated facility joint inventory-location problem where location-independent disruption may occur in facilities. The system tries to satisfy customer’s demands and considers penalty costs for unmet customer demand. The article aims to minimize total costs such as establishing inventory, uncovered demand’s penalty, and transportation costs. While many articles in this area only use exact methods to solve the problem, this article uses a metaheuristic algorithm, the red deer algorithm, and the exact methods. Various numerical examples have shown the outstanding performance of the red deer algorithm compared to exact methods. Sensitivity analyses show the impacts of various parameters on the objective function and the optimal facility layouts. Lastly, managerial insights will be proposed based on sensitivity analysis.

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.