Optimal Capacities in Discrete Facility Location Design Problem (original) (raw)

A combined facility location and network design problem with multi-type of capacitated links

This article presents a mixed-integer model to optimize the location of facilities and the underlying transportation network at the same time to minimize the total transportation and operating costs. In this problem, it is assumed that for connecting two nodes, there are several types of links in which their capacity, transportation and construction costs are different. The developed model has various applications in telecommunication, emergency , regional planning, pipeline network, energy management, distribution, to just name a few. To solve the model effectively, this paper also proposes a fix-and-optimize heuristic based on the evolutionary fire-fly algorithm. Finally, to validate the model and evaluate the algorithm's performance, a series of test instances with up to 100 nodes and 600 candidate links with three different levels of quality are reported.

A location model based on multiple metrics and multiple facility assignment

Transportation Research Part B: Methodological, 1986

Two of the most restrictive assumptions of classical network facility location models are that all customers are serviced by their closest facility and that the metric (distance, time or cost) between any two given points is always the same. A median location model based upon relaxations of both these assumptions is developed. This model retains many of the mathematical properties of the well known p-median problem. We show that an optimal solution exists at the nodes of the network, and formulate the problem as an integer linear program. Two very different potential applications are discussed. Solution procedures, optimal and heuristic, are described. The results from several different test data sets indicate that the solution of this new model does not require excessive computation times.

A discrete competitive facility location model with variable attractiveness

Journal of the Operational Research Society, 2011

We consider the discrete version of the competitive facility location problem in which new facilities have to be located by a new market entrant firm to compete against already existing facilities that may belong to one or more competitors. The demand is assumed to be aggregated at certain points in the plane and the new facilities can be located at predetermined candidate sites. We employ Huff 's gravity-based rule in modelling the behaviour of the customers where the probability that customers at a demand point patronize a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. The objective of the firm is to determine the locations of the new facilities and their attractiveness levels so as to maximize the profit, which is calculated as the revenue from the customers less the fixed cost of opening the facilities and variable cost of setting their attractiveness levels. We formulate a mixed-integer nonlinear programming model for this problem and propose three methods for its solution: a Lagrangean heuristic, a branch-and-bound method with Lagrangean relaxation, and another branch-and-bound method with nonlinear programming relaxation. Computational results obtained on a set of randomly generated instances show that the last method outperforms the others in terms of accuracy and efficiency and can provide an optimal solution in a reasonable amount of time.

Modeling Competitive Facility Location Problems: New Approaches and Results

Decision Technologies and Applications, 2009

The gravity model as applied to competitive facility location is described in this tutorial. The gravity model is used mainly by marketers to estimate the market share attracted by competing retail facilities. A demand area consists of potential customers who spend their discretionary buying power at competing retail facilities. We discuss the gravity model and issues related to the determination of the parameters of the models. The basic model is to find the best locations for new facilities that would attract the maximum buying power from customers in the area. Extensions to this basic model include modeling uncertainty about future market conditions, minimizing the probability that the attracted market share falls short of a certain target, demand generated by intercepting a flow of customers, market expansion and lost demand, and allocation of a given budget among one's facilities to improve their attractiveness. We describe special tools that are utilized in the solution procedures. These are the generalized Weiszfeld procedure, the big triangle small triangle global optimization approach, and the tangent line approximation.

A Generalized Model for Locating Facilities on a Network with Flow-Based Demand

2010

Flow-interception location problems identify good facility locations on a network with flow-based demand. Since the early 1990s, over 30 different flowinterception location models have appeared. In these publications, location researchers have developed new models by introducing changes in the objectives functions, constraints, and/or assumptions. These changes have led to many disparate models, each requiring a somewhat different solution method, and they have challenged the development of standardized software that would encourage widespread use in real-world, strategic decision-making processes. In this article, we formulate a generalized flowinterception location-allocation model (GFIM) which, with few exceptions, requires only simple modifications to its input data to effectively solve all current deterministic flow-interception problems. Additional flow-interception problems can be solved by simple model manipulation or the addition of constraints. Moreover, several critical considerations in flow-interception models-such as deviation from predetermined journeys, locational and proximity preferences, and capacity issues-can be handled within the proposed single framework. Two real-world examples reported in the literature (1989 morning and 2001 afternoon peak traffic for the city of Edmonton in Canada) show that a standard optimization engine such as ILOG-CPLEX optimally solves GFIM much more efficiently than it does the classic flow-interception location model.

Satisfying partial demand in facilities location

IIE Transactions, 2002

In this paper we consider the location of new facilities which serve only a certain proportion of the demand. The total weighted distances of the served demand is minimized. We consider the problem in the plane for the location of one facility and on a network for the location of m-facilities. Some computational experience with these models are reported. 0740-817X Ó 2002 ''IIE''

Facility location with adjacent units: a simple approximation scheme

International Journal of Information and Operations Management Education, 2013

In this paper, we provide a simple approximation scheme for the optimal objective value for a particular type of location problem. Typically, such problems are solved using the classic set covering formulation. Such a formulation automatically requires data for the constraint matrix and can get too large to implement or too difficult to solve to optimality. The scheme presented in this paper has minimal need for such data. Based on a simple count and with some basic and realistic assumptions about the geometry of the problem, we provide an algebraic formula that gives a close approximation to the optimal objective function value. Our formula can be easily implemented in a spreadsheet or hand-held calculator making it an effective planning tool for practice and also a good pedagogical aid. We illustrate by applying it to a location problem involving individual states in the continental US and collectively to the entire country.

A study on three different dimensional facility location problems

Economic Modelling, 2013

In supply chain strategy, designing a network is one of the most important part. This model deals with various dimensional facility location models. Initially, this paper begins with two echelon facility location model of dimension two. Then, it is extended to three dimensional model by adding commodity type and then, different types of transportation modes are added to make it four dimensional model. Delivery lead time and outside suppliers are assumed to meet the retailer's demand too. We construct some lemmas to compare the optimal solution for each of the problem. We also study the procedure of reducing the total cost of the supply chain network by applying a small change in constraint set. This is described by another lemma. Some numerical examples are allowed to illustrate the models.