Some proposals for stochastic facility location models

The aim of this paper is to introduce stochastic features into a facility location model to describe both the total demand for facilities and the trip pattern of the customers. The usefulness of stochastic programming tools in formulating and solving problems of this type is explored. Numerical stochastic nondifferentiable optimization techniques are outlined, and optimality conditions and practical computations are discussed.     

A hierarchical location model for public facility planning

In this article, we present a discrete hierarchical location model for public facility planning. The main features of the model are: an accessibility maximization objective; several levels of demand and of facilities; a nested hierarchy of facilities (i.e. a facility of a given level can serve demand of equal and lower levels); maximum and minimum capacity constraints; and user-to-facility assignment constraints. The latter include single-assignment and closest-assignment constraints, as well as a new type of constraints called path-assignment constraints. Their purpose is to enforce some desirable properties for the spatial pattern of assignments. If they are not included, model solutions are difficult to interpret and to explain in a public facility planning context, therefore being less likely to be accepted by the users. The usefulness of the model is illustrated through a real-world application to school network planning.     

Forecast horizons and dynamic facility location planning

We consider a dynamic facility location model in which the objective is to find a planning horizon, *, and a first period decision,X ₁*, such thatX ₁* is a first period decision for at least one optimal policy for all problems with planning horizons equal to or longer than *. In other words, we seek a planning horizon, *, such that conditions after * do not influence the choice of the optimal initial decision,X ₁*. We call * aforecast horizon andX ₁* anoptimal initial decision. For the dynamic uncapacitated fixed charge location problem, we show that simple conditions exist such that the initial decision depends on the length of the planning horizon. Thus, a strictly optimal forecast horizon and initial policy may not exist. We therefore introduce the concepts ofe-optimal forecast horizons and -optimal initial solutions. Our computational experience inicates that such solutions can be found for practical problems. Although computing -optimal forecast horizons and initial decisions can be cumbersome, this approach offers the potential for making significantly better decisions than those generated by other approaches. To illustrate this, we show that the use of the scenario planning approach can lead to the adoption of the worst possible initial decision under conditions of future uncertainty. On the basis of our results, it appears that the forecast horizon approach offers an attractive tool for making dynamic location decisions.     

Facility location models for distribution planning

A strategic issue which is of interest to distribution planners is where to best site warehouses. Model formulations, and solution approaches, which address the issue vary widely in terms of mathematical and computational complexity. This paper reviews some of the significant contributions which have been made to the relevant and current state of knowledge.     

Facility location models for planning a transatlantic communications network

This paper presents two facility location models for the problem of determining how to optimally serve the requirements for communication circuits between the United States and various European and Middle Eastern countries. Given a projection of future requirements, the problem is to plan for the economic growth of a communications network to satisfy these requirements. Both satellite and submarine cable facilities may be used. The objective is to find an optimal placement of cables (type, location, and timing) and the routing of individual circuits between demand points (over both satellites and cables) such that the total discounted cost over a T-period horizon is minimized. This problem is cast as a multiperiod, capacitated facility location problem. Two mathematical models differing in their provisions for network reliability are presented. Solution approaches are outlined and compared by means of computational experience. Use of the models both in planning the growth of the network and in the economic evaluation of different cable technologies is also discussed.     

On models for continuous facility location with partial coverage

This paper presents a new concept of partial coverage distance, where demand points within a given threshold distance of a new facility are covered in the traditional sense, while non-covered demand points are penalized an amount proportional to their distance to the covered region. Two single facility location models, based on the minisum and minimax criteria, are formulated with the new distance function, and the structure of the models is analysed.     

A new bounding method for single facility location models

This paper develops a new lower bound for single facility location problems withl _p distances. We prove that the method produces superior results to other known procedures. The new bound is also computationally efficient. Numerical results are given for a range of examples with varying numbers of existing facilities andp values.     

Existence theory for spatially competitive network facility location models

Models for locating a firm's production facilities while simultaneously determining production levels at these facilities and shipping patterns so as to maximize the firm's profits are presented. In these models, existing firms, are assumed to act in accordance with an appropriate model of spatial equilibrium. A proof of existence of a solution to the combined location-equilibrium problem is provided.     

Uncertain models for single facility location problems on networks

In practical location problems on networks, the vertex demand is usually non-deterministic. This paper employs uncertainty theory to deal with this non-deterministic factor in single facility location problems. We first propose the concepts of satisfaction degree for both vertices and the whole network, which are used to evaluate products assignment. Based on different network satisfaction degree, two models are constructed. The solution to these models is based on Hakimi’s results, and some examples are given to illustrate these models.     

Corporate manpower planning: a review of models

Manpower planning has achieved maturity during the past decade. Personnel practitioners have become conversant with the analysis of manpower systems, the use of quantitative techniques, and have developed a sound approach to the whole question of manpower management. But, whilst they no longer rely on the management scientist for using those models and other techniques now widely available, there is a continued contribution to be made in advancing the field. This paper reviews the practical relecance of existing models. It concentrates on techniques for evaluating manpower supply and career management problems, distinguishing especially between the roles played by exploratory and normative models. The author hopes that this article will give management scientists a realistic appraisal of current practice and provide pointers as to where developments are most needed.     

Stochastic network optimization models for investment planning

We describe and compare stochastic network optimization models for investment planning under uncertainty. Emphasis is placed on multiperiod a sset allocation and active portfolio management problems. Myopic as well as multiple period models are considered. In the case of multiperiod models, the uncertainty in asset returns filters into the constraint coefficient matrix, yielding a multi-scenario program formulation. Different scenario generation procedures are examined. The use of utility functions to reflect risk bearing attitudes results in nonlinear stochastic network models. We adopt a newly proposed decomposition procedure for solving these multiperiod stochastic programs. The performance of the models in simulations based on historical data is discussed.Research partially supported by National Science Foundation Grant No. DCR-861-4057 and IBM Grant No. 5785. Also, support from Pacific Financial Companies is gratefully acknowledged.     

Outcomes of voting and planning in single facility location problems

For a given set of users located at the vertices of a network N, we consider the location of a single facility. Two different decision making procedures, voting among the users and minimizing total distance travelled by the users, are compared.Provided that a voting solution exists, it is shown that the two solutions sets coincide if N is a so-called cactus. For general networks, the outcomes of the two procedures are compared in terms of the cyclic structure of N and the number of users.     

Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study

In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs.     

Flow location (FlowLoc) problems: dynamic network flows and location models for evacuation planning

In this paper we combine two modeling tools to predict and evaluate evacuation plans: (dynamic) network flows and locational analysis. We present three exact algorithms to solve the single facility version 1-FlowLoc of this problem and compare their running times. After proving the $\mathcal{NP}$ -completeness of the multi facility q-FlowLoc problem, a mixed integer programming formulation and a heuristic for q-FlowLoc are proposed. The paper is concluded by discussing some generalizations of the FlowLoc problem, such as the multi-terminal problem, interdiction problem, the parametric problem and the generalization of the FlowLoc problem to matroids.     

Spatial competition facility location models: Definition,formulation and solution approach

Models are presented for locating a firm's production facilities and determining production levels at these facilities so as to maximize the firm's profit. These models take into account the changes in price at each of the spatially separated markets that would result from the increase in supply provided by the new facilities and also from the response of competing firms. Two different models of spatial competition are presented to represent the competitive market situation in which the firm's production facilities are being located. These models are formulated as variational inequalities; recent sensitivity analysis results for variational inequalities are used to develop derivatives of the prices at each of the spatially separated markets with respect to the production levels at each of the new facilities. These derivatives are used to develop a linear approximation of the implicit function relating prices to productions. A heuristic solution procedure making use of this approximation is proposed.     

Extensive facility location problems on networks: an updated review

Location problems with extensive facilities represent a challenging field of research. According to the specialized literature, a facility is called extensive if, for purposes of location, it is too large in relation to its environment to be considered a point. There are many examples of this type of structures that appear in real-world applications both in the continuous space (straight lines, circles, strips) and in networks (paths, cycles, trees). There exists a recent literature review on the location of dimensional facilities on continuous space (Díaz-Báñez et al. in TOP 154:22–44, 2004; Schöbel in Location of dimensional facilities in a continuous space, 2015) that does not cover similar problems on networks. The goal of this paper is to review the location of dimensional facilities in networks. We mainly concentrate on the location of paths and trees considering the most common objective functions in the location literature, namely median and center. However, we also consider some other alternative criteria generalizing them, as the ordered median objective function, or related to equity, reliability, and robustness. We include the basic tools and techniques that are applicable to develop algorithms for this kind of problems. Moreover, we present the best known complexity results for each of the considered problems. Finally, some suggestions are also made for possible directions of future research.     

Recent optimization models and trends in location,relocation, and dispatching of emergency medical vehicles

Over the past 10 years, a considerable amount of research has been devoted to the development of models to support decision making in the particular yet important context of Emergency Medical Services (EMS). More specifically, the need for advanced strategies to take into account the uncertainty and dynamism inherent to EMS, as well as the pertinence of socially oriented objectives, such as equity, and patient medical outcomes, have brought new and exciting challenges to the field. In this context, this paper summarizes and discusses modern modeling approaches to address problems related to ambulance fleet management, particularly those related to vehicle location and relocation, as well as dispatching decisions. Although it reviews early works on static ambulance location problems, this review concentrates on recent approaches to address tactical and operational decisions, and the interaction between these two types of decisions. Finally, it concludes on the current state of the art and identifies promising research avenues in the field.     

Statistical optimum estimation techniques for combinatorial optimization problems: a review and critique

Over the last several decades researchers have addressed the use of statistical techniques to estimate the optimal values of difficult optimization problems. These efforts have been developed in different communities with a wide range of different applications in mind. In this paper we review the theory and applications of these approaches and discuss their strengths and weaknesses. We conclude the paper with a discussion of issues to consider when using these methods in computational experiments, and suggest directions for future research.     

A D.C. optimization method for single facility location problems

The single facility location problem with general attraction and repulsion functions is considered. An algorithm based on a representation of the objective function as the difference of two convex (d.c.) functions is proposed. Convergence to a global solution of the problem is proven and extensive computational experience with an implementation of the procedure is reported for up to 100,000 points. The procedure is also extended to solve conditional and limited distance location problems. We report on limited computational experiments on these extensions.This research was supported in part by the National Science Foundation Grant DDM-91-14489.