We propose and study the MpUFLP (universal facility location problem in the p-th power of metric space) in this paper, where the universal facility location problem (UFLP) extends several classical ...facility location problems like the uncapacitated facility location, hard-capacitated facility location, soft-capacitated facility location, incremental-cost facility location, concave-cost facility location, etc. In UFLP, a set of facilities, a set of clients, as well as the distances between them are given. Each facility has its specific cost function w.r.t. the amount of clients assigned to that facility. The goal is to assign the clients to facilities such that the sum of facility cost and service cost is minimized. In traditional facility location problems, the unit service cost is proportional to the distance between the client and its assigned facility and thus metric. However, in our work, this assumption is removed and a generalized version of universal facility location problem is proposed, which is the so-called MnUFLP. When p=2, it is also known as l22 measure considered by Jain and Vazirani J. ACM'01 and Fernandes et al. Math. Program.'15. Particularly in this case, we extend their work to include the aforementioned variants of facility location and a local search based (11.18+ε)-approximation algorithm is proposed. Furthermore, the reanalysis of the proposed algorithm gives a p-related performance guarantee for general p.
In the most single facility location problems, a set of points is given and the goal is to find the optimal location of a new facility with respect to given criteria such as minimizing time, cost, ...and distances between the clients and facilities. On the other side, the inverse single facility location problems try to modify the parameters of the problem with the minimum cost such that a given point becomes optimal. In this paper, we introduce a novel algorithm for the general case of the inverse single facility location problem with variable weights in the plane. The optimality conditions of the algorithm are presented. Then in the special cases the inverse minisum and minimax single facility location problems are considered and the algorithm is tested on some instances. The results indicate the efficiency of the algorithm on these instances.
•In this study we introduce an algorithm for the general inverse location models.•The algorithm can be applied for many kinds of inverse continuous location models.•The inverse minisum and minimax location problems are solved by the algorithm.
Max-Min 3-dispersion Problems HORIYAMA, Takashi; NAKANO, Shin-ichi; SAITOH, Toshiki ...
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences,
2021
Journal Article
Peer reviewed
Given a set P of n points on which facilities can be placed and an integer k, we want to place k facilities on some points so that the minimum distance between facilities is maximized. The problem is ...called the k-dispersion problem. In this paper, we consider the 3-dispersion problem when P is a set of points on a plane (2-dimensional space). Note that the 2-dispersion problem corresponds to the diameter problem. We give an O(n) time algorithm to solve the 3-dispersion problem in the L∞ metric, and an O(n) time algorithm to solve the 3-dispersion problem in the L1 metric. Also, we give an O(n2 log n) time algorithm to solve the 3-dispersion problem in the L2 metric.
► We review around 140 references on dynamic facility location problem. ► We classify all papers in terms of models, solutions, performance measures and applications. ► We suggest further researches ...and prospects in the area of dynamic facility location.
In order to modify the current facility or develop a new facility, the dynamics of facility location problems (FLPs) ought to be taken into account so as to efficiently deal with changing parameters such as market demand, internal and external factors, and populations. Since FLPs have a strategic or long-term essence, the inherited uncertainty of future parameters must be incorporated in relevant models, so these models can be considered applicable and ready to implement. Furthermore, due to largely capital outlaid, location or relocation of facilities is basically considered as a long-term planning. Hence, regarding the way in which relevant criteria will change over time, decision makers not only are concerned about the operability and profitability of facilities for an extended period, but also seek to robust locations fitting well with variable demands. Concerning this fact, a trade-off should be set between benefits brought by facility location changes and costs incurred by possible modifications. This review reports on literature pointing out some aspects and characteristics of the dynamics of FLPs. In fact, this paper aims not only to review most variants of these problems, but also to provide a broad overview of their mathematical formulations as well as case studies that have been studied by the literature. Finally, based on classified research works and available gaps in the literature, some possible research trends will be pointed out.
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.
Pre-positioning of emergency supplies is one mechanism of increasing preparedness for natural disasters. The goal of this research is to develop an emergency response planning tool that determines ...the location and quantities of various types of emergency supplies to be pre-positioned, under uncertainty about if, or where, a natural disaster will occur. The paper presents a two-stage stochastic mixed integer program (SMIP) that provides an emergency response pre-positioning strategy for hurricanes or other disaster threats. The SMIP is a robust model that considers uncertainty in demand for the stocked supplies as well as uncertainty regarding transportation network availability after an event. Due to the computational complexity of the problem, a heuristic algorithm referred to as the Lagrangian L-shaped method (LLSM) is developed to solve large-scale instances of the problem. A case study focused on hurricane threat in the Gulf Coast area of the US illustrates application of the model.
Electric vehicles are the key to facilitating the transition to low-carbon ‘green’ transport. However, there are concerns with their range and the location of the charging stations which delay a ...full-fledged adoption of their use. Hence, the electric charging infrastructure in a given region is critical to mitigating those concerns. In this study, an interval type-2 fuzzy set based multi-criteria decision-making method is introduced for selecting the best location for electric charging stations. This method is improved by Simulated Annealing obtaining the best configuration of the parameters of the interval type-2 membership functions along with two different aggregation operators; linguistic weighted sum and average. The proposed overall reusable multi-stage solution approach is applied to a real-world public transport problem of the municipal bus company in Istanbul. The results indicate that the approach indeed improves the model, capturing the associated uncertainties embedded in the interval type-2 membership functions better, leading to a more effective fuzzy system. The experts confirm those observations and that Simulated Annealing improved interval type-2 fuzzy method achieves more reliable results for selecting the best sites for the electric bus charging stations.
Two-stage robust facility location problem with drones Zhu, Tengkuo; Boyles, Stephen D.; Unnikrishnan, Avinash
Transportation research. Part C, Emerging technologies,
April 2022, 2022-04-00, Volume:
137
Journal Article
Peer reviewed
The past few years have witnessed the increasing adoption of drones in various industries such as logistics, agriculture, military, and telecommunications. This paper considers a short-term ...post-disaster unmanned aerial vehicle (UAV) humanitarian relief application where first-aid products need to be delivered to the customer demand points. The presented problem, two-stage robust facility location problem with drones (two-stage RFLPD), incorporates the demand uncertainty using demand scenarios. This problem aims to find a location–allocation-assignment plan that has minimal two-stage total cost in the worst-case scenario of all the possible demand outcomes. Three different models of the problem are proposed, two of which incorporate a realistic UAV electricity consumption model while the last one has greater operational flexibility. The column-and-constraint generation method and Benders decomposition are used to solve the two models, and a thorough comparison among the deterministic facility location problem with drones (FLPD) models and three proposed models are also presented. Numerical analysis results show that the proposed model has significantly less average cost in the simulation runs compared to the deterministic FLPD.
•This research considers an facility location problem with drones, which is one of the few researches that address FLP with drone operation.•This research uses an robust optimization approach to handle the uncertainty in customers’ demand.•The paper proposes multiple models that incorporates realistic drone’s electricity consumption function with various assumptions.•An exact column and constraints generation algorithm is proposed to solve the problem.
Determining the best location to serve companies’ profitability and sustainability is becoming more crucial every day, since the rivalry between companies is getting more intense. The transformation ...of economies from manufacturing orientation towards service based activities has resulted in a growing contribution of the service based economy in gross domestic product and workforce of developing countries. These recent changes in the economy are indicators that service facility related location science has received greater interest. Service location problems has been studied since the 1900s and interest on these types of problems has started to grow especially after the aforementioned economic transformation in the 2000s. A large number of problems have been investigated for different service facilities. However, there is a need for a survey that systematically classifies these papers in order to comprehend them thoroughly due to their prominence and complexity. This paper examines 90 papers that have been published on service facility location problems since 2000. The paper presents a classification based on 19 main characteristics including key features and descriptive dimensions of location problems in order to develop a taxonomy from an operations research perspective to assist the location scientists and practitioners who work on service facility location problems. Furthermore, service facility location problems are categorized according to their application fields and investigated in detail relating to each characteristic. We also draw interesting comparisons of characteristics between facility location problems in different application fields and highlight directions for future research.
In the history of sustainable development, logistics has been thought of as one of the key factors in the supply chain network. In the meantime, the issue of Closed-loop Supply Chain (CLSC) has ...received considerable attention as it ensures many diverse industries toward sustainability. But many industries including agricultural section often fail to address and fulfill these requirements. In this study, a new CLSC network is designed for the walnut industry as a part of agricultural crop by conducting a complete review of the past studies. Therefore, a new Mixed Integer Linear Programming (MILP) for the proposed network is developed minimizing the overall costs of the walnut industry. The designed network considers both forward and reverse flow not only to meet the demands of various markets, but also to prepare the returned products for the second use. In order to solve the proposed model, a set of exact, metaheuristics, and hybrid metaheuristics are employed. Finally, the best solutions are obtained by assessing the finest initial answers using Taguchi method. The results notoriously illustrated the excellent consistency between the proposed network and the employed algorithms along with its applicability and efficiency.
•Designing a sustainable closed-loop supply chain network for walnut industry.•Optimizing overall costs of the chain by using Mixed Integer Linear Programming.•Considering forward and reverse logistics to deliver goods and returned products.•Applying five tuned metaheuristic algorithms to identify the best solutions.•Conducting sensitivity analyses to study the model outcomes.
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