An entropy-based algorithm to solve the facility layout design problem

This paper presents a new design approach used in order to solve the facility layout problem. The layout problem is viewed from the general perspective as a problem of the arrangement of elements within a system. The main attributes and relationships among the elements of the system are analyzed.     

Applied p-median and p-center algorithms for facility location problems

Facility location problems with the objective to minimize the sum of the setup cost and transportation cost are studied in this paper. The setup and transportation costs are considered as a function of the number of opened facilities. Three methods are introduced to solve the problem. The facility location model with bounds for the number of opened facility is constructed in this work. The relationship between setup cost and transportation cost is studied and used to build these methods based on greedy algorithm, p-median algorithm and p-center algorithm. The performance of the constructed methods is tested using 100 random data sets. In addition, the networks representing the road transportation system of Chiang Mai city and 5 provinces in Northern Thailand are illustrated and tested using all presented methods. Simulation results show that the method developed from greedy algorithm is suitable for solving problems when the setup cost is higher than transportation cost while the opposite cases are more efficiently solved with the method developed by the p-median problem.     

A simple filter-and-fan approach to the facility location problem

The design of effective neighborhood search procedures is a primary issue for the performance of local search and advanced metaheuristic algorithms. Several recent studies have focused on the development of variable depth neighborhoods that generate sequences of interrelated elementary moves to create more complex compound moves. These methods are chiefly conceived to produce an adaptive search as the number of elementary moves in a compound move may vary from one iteration to another depending on the state of the search. The objective is to achieve this goal with modest computational effort. Although ejection chain methods are currently the most advanced methods in this domain, they usually require more complex implementations. The filter-and-fan (F&F) method appears as an alternative to ejection chain methods allowing for the creation of compound moves based on an effective tree search design.     

Covering problems in facility location: A review

In this study, we review the covering problems in facility location. Here, besides a number of reviews on covering problems, a comprehensive review of models, solutions and applications related to the covering problem is presented after Schilling, Jayaraman, and Barkhi (1993). This survey tries to review all aspects of the covering problems by stressing the works after Schilling, Jayaraman, and Barkhi (1993). We first present the covering problems and then investigate solutions and applications. A summary and future works conclude the paper.     

A study on a probabilistic two-echelon location system for deteriorating items

A special case of the probabilistic multi-locationproblem is studied for deteriorating items. The objective of this study is to determine the location of the minimum number of supply centres among a discrete set of location sites of supply centres under the condition that the probability of each retailer being covered by one of the supply centres is not less than a specified value. A logistic cost function including the deterioration rate is developped for a performance measure of the system.

We have formulated a probabilistic set-covering programming which can be solved by a 0–1 programming. The result of a set of numerical examples well shows the impact of deteriorating rate on the location problems. And also this study will provide a method of a useful guidelines for the location decisions.     

Competitive facility location: the Voronoi game

We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second player, where the arena is a circle or a line segment. We permit variations where players can play more than one point at a time, and show that the first player can ensure that the second player wins by an arbitrarily small margin.     

An LP rounding algorithm for approximating uncapacitated facility location problem with penalties

In this paper, we consider an interesting variant of the facility location problem called uncapacitated facility location problem with penalties (UFLWP, for short) in which each client can be either assigned to some opened facility or rejected by paying a penalty. Existing approaches [M. Charikar, S. Khuller, D. Mount, G. Narasimhan, Algorithms for facility location problems with outliers, in: Proc. Symposium on Discrete Algorithms, 2001, p. 642] and [K. Jain, M. Mahdian, E. Markakis, A. Saberi, V. Vazirani, Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP, J. ACM 50 (2003) 795] for this variant of facility location problem are all based on primal-dual method. In this paper, we present an efficient linear programming (LP) rounding based approach to show that LP rounding techniques are equally capable of solving this variant of facility location problem. Our algorithm uses a two-phase filtering technique (generalized from Lin and Vitter's [?-approximation with minimum packing constraint violation, in: Proc. 24th Annual ACM Symp. on Theory of Computing, 1992, p. 771]) to identify those to-be-rejected clients and open facilities for the remaining ones. Our approach achieves an approximation ratio of 2+2/e (≈2.736) which is worse than the best approximation ratio of 2 achieved by the much more sophisticated dual fitting technique [K. Jain, M. Mahdian, E. Markakis, A. Saberi, V. Vazirani, Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP, J. ACM 50 (2003) 795], but better than the approximation ratio of 3 achieved by the primal-dual method [M. Charikar, S. Khuller, D. Mount, G. Narasimhan, Algorithms for facility location problems with outliers, in: Proc. Symposium on Discrete Algorithms, 2001, p. 642]. Our algorithm is simple, natural, and can be easily integrated into existing LP rounding based algorithms for facility location problem to deal with outliers.     

Use of distributed data sources in facility location

Facility location decisions are usually determined by cost and coverage related factors although empirical studies show that such factors as infrastructure, labor conditions and competition also play an important role in practice. The objective of this paper is to develop a multi-objective facility location model accounting for a wide range of factors affecting decision-making. The proposed model selects potential facilities from a set of pre-defined alternative locations according to the number of customers, the number of competitors and real-estate cost criteria. However, that requires large amount of both spatial and non-spatial input data, which could be acquired from distributed data sources over the Internet. Therefore, a computational approach for processing input data and representation of modeling results is elaborated. It is capable of accessing and processing data from heterogeneous spatial and non-spatial data sources. Application of the elaborated data gathering approach and facility location model is demonstrated using an example of fast food restaurants location problem.     

An ontology change management approach for facility management

Facility management (FM) or technical property management is an approach to operate, maintain, improve and adapt buildings and infrastructures of organizations. A FM project requires the cooperation of many actors from different domains so it has to be automated in a constrained collaborative environment. This paper proposes a new approach for ontology change management applied on facility management of such projects. The industrial challenge is, firstly, to ensure consistency of a FM project knowledge from the construction phase to the technical property management phase (after delivery). Secondly, it has to provide to each actor of the project a personal up-to-date “view” of the building knowledge related to its business profile and allow its evolution. The scientific approach, called OntoVersionGraph, is a change management methodology for managing ontology life cycle including ontology evolution and versioning features, in conjunction with contextual view modeling. Its contribution is the impact management of changes between the ontology and its different views.     

Planar geometric location problems

We present anO(n ² log³ n) algorithm for the two-center problem, in which we are given a setS ofn points in the plane and wish to find two closed disks whose union containsS so that the larger of the two radii is as small as possible. We also give anO(n ² log⁵ n) algorithm for solving the two-line-center problem, where we want to find two strips that coverS whose maximum width is as small as possible. The best previous solutions of both problems requireO(n ³) time.Pankaj Agarwal has been supported by DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), an NSF Science and Technology Center, under Grant STC-88-09648. Micha Sharir has been supported by the Office of Naval Research under Grants N00014-89-J-3042 and N00014-90-J-1284, by the National Science Foundation under Grant CCR-89-01484, by DIMACS, and by grants from the US-Israeli Binational Science Foundation, the Fund for Basic Research administered by the Israeli Academy of Sciences, and the G.I.F., the German-Israeli Foundation for Scientific Research and Development. A preliminary version of this paper has appeared inProceedings of the Second Annual ACM-SIAM Symposium on Discrete Algorithms, 1991, pp. 449–458.     

Capacitated facility location problem with general setup cost

This paper presents an extension of the capacitated facility location problem (CFLP), in which the general setup cost functions and multiple facilities in one site are considered. The setup costs consist of a fixed term (site setup cost) plus a second term (facility setup costs). The facility setup cost functions are generally non-linear functions of the size of the facility in the same site. Two equivalent mixed integer linear programming (MIP) models are formulated for the problem and solved by general MIP solver. A Lagrangian heuristic algorithm (LHA) is also developed to find approximate solutions for this NP-hard problem. Extensive computational experiments are taken on randomly generated data and also well-known existing data (with some necessary modifications). The detailed results are provided and the heuristic algorithm is shown to be efficient.     

Solving the uncapacitated facility location problem using tabu search

A tabu search heuristic procedure is developed to solve the uncapacitated facility location problem. Tabu search is used to guide the solution process when evolving from one solution to another. A move is defined to be the opening or closing of a facility. The net cost change resulting from a candidate move is used to measure the attractiveness of the move. After a move is made, the net cost change of a candidate move is updated from its old value. Updating, rather than re-computing, the net cost changes substantially reduces computation time needed to solve a problem when the problem is not excessively large. Searching only a small subset of the feasible solutions that contains the optimal solution, the procedure is computationally very efficient. A computational experiment is conducted to test the performance of the procedure and computational results are reported. The procedure can easily find optimal or near optimal solutions for benchmark test problems from the literature. For randomly generated test problems, this tabu search procedure not only obtained solutions completely dominating those obtained with other heuristic methods recently published in the literature but also used substantially less computation time. Therefore, this tabu search procedure has advantage over other heuristic methods in both solution quality and computation speed.     

Multi-dimensional dynamic facility location and fast computation at query points

We present O(nlogn) time algorithms for the minimax rectilinear facility location problem in R¹ and R². The algorithms enable, once they terminate, computing the cost of any given query point in O(logn) time. Based on these algorithms, we develop a preprocessing procedure which enables solving the following two problems: Fast computation of the cost of any query point in Rd, and fast solution for the dynamic location problem in R² (namely, in the presence of an additional facility). Finally, we show that the preprocessing always gives a bound on the optimal value, which allows us in many cases to find the optimum fast (for both the traditional and the dynamic location problems in Rd for any d).     

Modeling health care facility location for moving population groups

Locating public services for nomadic population groups is a difficult challenge as the locations of the targeted populations seasonally change. In this paper, the population groups are assumed to occupy different locations according to the time of the year, i.e., winter and summer. A binary integer programming model is formulated to determine the optimal number and locations of primary health units for satisfying a seasonally varying demand. This model is successfully applied to the actual locations of 17 seasonally varying nomadic groups in the Middle East. Computational tests are performed on different versions of the model in order analyze the tradeoffs among different performance measures.     

A new optimization model to support a bottom-up approach to facility design

The facility layout problem is typically solved in what is referred to as a “top-down approach” of block layout design followed by detailed layout determination. However, a number of research efforts recently have challenged this approach, producing a reformulated bottom-up approach to the facility layout problem. In this paper we consider the bottom-up approach, applying a tighter formulation than prior efforts and investigating the solvability limits of the new model. Empirical testing of the new bottom-up layout model indicates that although this model produces more usable output, as judged by industry experts, it is approximately three times harder to solve. Valid inequalities and special cases are identified to help improve the formulation's solvability.     

The heuristic concentration-integer and its application to a class of location problems

We propose a new metaheuristic called heuristic concentration-integer (HCI). This metaheuristic is a modified version of the heuristic concentration (HC), oriented to find good solutions for a class of integer programming problems, composed by problems in which p   elements must be selected from a larger set, and each element can be selected more than once. These problems are common in location analysis. The heuristic is explained and general instructions for rewriting integer programming formulations are provided, that make the application of HCI to these problems easier. As an example, the heuristic is applied to the maximal availability location problem (MALP), and the solutions are compared to those obtained using linear programming with branch and bound (LP+B&B)$(\mathrm{LP}+\mathrm{B}\&\mathrm{B})$. For one-third of the instances of MALP, LP+B&B$\mathrm{LP}+\mathrm{B}\&\mathrm{B}$ can be allowed to run until the computer is out of memory without termination, while HCI can find good solutions to the same instances in a reasonable time. In one such case, LP-IP was allowed to run for nearly 100 times longer than HCI and HCI still found a better solution. Furthermore, HCI found the optimal solution in 33.3% of cases and had an objective value gap of less than 1% in 76% of cases. In 18% of the cases, HCI found a solution that is better than LP+B&B. Therefore, in cases where LP+B&B$\mathrm{LP}+\mathrm{B}\&\mathrm{B}$ is unreasonable due to time or memory constraints, HCI is a valuable tool.     

Risk management in uncapacitated facility location models with random demands

In this paper we consider a location-optimization problem where the classical uncapacitated facility location model is recast in a stochastic environment with several risk factors that make demand at each customer site probabilistic and correlated with demands at the other customer sites. Our primary contribution is to introduce a new solution methodology that adopts the mean–variance approach, borrowed from the finance literature, to optimize the “Value-at-Risk” (VaR) measure in a location problem. Specifically, the objective of locating the facilities is to maximize the lower limit of future earnings based on a stated confidence level. We derive a nonlinear integer program whose solution gives the optimal locations for the p facilities under the new objective. We design a branch-and-bound algorithm that utilizes a second-order cone program (SOCP) solver as a subroutine. We also provide computational results that show excellent solution times on small to medium sized problems.     

Simultaneous location of a service facility and a rapid transit line

This paper presents a location problem on the plane where a single service facility and a rapid transit line have to be simultaneously located. The rapid transit line represents an alternative transportation line which can be used by clients whenever it provides a cost-saving or time-saving service, and it is given by a segment with fixed and known length. This type of problems has not previously been considered in the Location Theory literature, as we are only aware of the existence of models that consider the location of service facilities in the presence of an already located alternative transportation system or models dealing with the location of rapid transit lines to minimize the travelling time among a set of points. To solve this problem we will develop an algorithm based on some characterizations of the objective function behavior.