Facility location models

Aikens CH (1985) Facility location models for distribution planning. European Journal of Operational Research 22 263-279... 

A large class of facility location models assumes that fadlities can be located on a network composed of nodes and Unks. Travel can occur only on the links of this network. This is to be contrasted with planar models, which can locate fadlities anywhere on the plane. Often, facilities are characterized by capacities (e.g., warehouses) or throughput (e.g., transfer terminals). We present next a qualitative overview of some useful network location models, drawing primarily from Daskin (1995). 

Church, R. L. (1974), Synthesis of a Class of Public Facilities Location Models, Ph.D. Dissertation, Johns Hopkins University. 

The models and arguments in this section are mostly based on Watson et al. (2013) s book [4]. Location problem are very diverse. American Mathematical Society (AMS) has specific codes for location problems (90B80 for discrete location and assignment, and 90B85 for continuous location) [2]. General location problems include customers and facilities to satisfy customer demands. Facility locations problems are classified as discrete and continuous ones. Here, we are interested in discrete facility location problems. Also problem distinction is based on being capacitated or not. Melo et al. [2] identify four core features to be included in a facility location model to use in supply chain decisions ... 

Brimberg, J. andRevelle,C., 1999. A multi-facility location model with partial, satisfaction of demand. Studies in Locational Analysis, 13,91-101. 

Love, R.F., Morris, J.G., and Wesolowsky, G.O. (1988) Facilities Location Models and Methods, North-Holland Publishing Co., New York. 

The DSS was basically a MILP model, similar to the capacitated facility location model we discussed in Section 5.2.3 (Example 5.5). The MILP model determined the best locations for the telemarketing centers from a set of candidate locations, and the volume of customer traffic from different regions handled by each center. The objective was to minimize the total cost of labor, fixed facility, and conununication. For example, in 1988, the model helped 46 AT T telemarketing customers with their site location decisions. AT T got business worth 375M in annual communication revenues and 31M in equipment sales. 

We then presented the basics of the "continuous location" models. We presented the "gravity model" for single facility location and the iterative algorithm for its solution. Extensions to the multiple facility location models were... 

The model-solving algorithm is responsible for solving the facility location model using the provided input data. The geographical information system is used to represent the modeling results. The representation is created by combining spatial data layers provided by different external data sources. 

This constraint is similar to constraints often used in traditional facility location models assigning each demand point exclusively to a single facility. In order to avoid nonlinearity, multiplication XjXj is replaced by the following constraints ... 

The proposed facility location model can be expanded to include additional criteria subject to data availability. While majority of existing facility locatimi models focus on optimizing facility location costs or travel time related measures, the proposed model attempts to locate facilities according to a wide range of contextual characteristics. 

Amin, S. H., and Zhang, G. A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return. Applied Mathematical Modelling 37, no. 6 (2013b) 4165-4176. 

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. 

While the underlying mathematical optimization problem, also referred to as Steiner-Weber-problem or minisum problem, is one of the classical models discussed in operations research literature on facility location (cf. Drezner et al. 2001), it is much too abstract to be of real value to actual industrial location decisions (cf. Gotze 1995, p. 56). A general criticism of Weber s theory can be found in Behrens (1971, pp. 15-19) and Meyer-Lindemann (1951, pp. 55-67). 

ReVelle (2001, p. 459) defines location analysis as "the development of formulations and algorithms/methodologies to site facilities of diverse kinds in a spatial or geographic environment". In the following, the facilities to be located are further specified to possess point characteristics excluding models dealing with the location of area objects. The latter are employed to support facility layout and hence are not relevant in the context of this work (cf. Domschke and Krispin (1997) or Francis et al. (1992) for further references on facility layout models). 

Figure 16 contains the most important criteria to classify facility location problems. Regarding solution space, as Francis et al. (1983, pp. 221, 240) explain, discrete location models are the most realistic (especially be-... 

Categorization schemes have been suggested both for facility location (e.g., Hamacher and Nickel 1998 Ballou 1992, pp. 323-324 Brandeau and Chiu 1989, pp. 647-650) and supply chain optimization models (e.g., Bankhofer 2003, pp. 27-34 Bestmann 2001, pp. 46-47) and many literature reviews contain classifications of the models they review. The following criteria (the abbreviations in brackets are used in Table 4), extending the classification introduced by Melo et al. (2005, p. 198), are used to classify the models from literature contained in Table 4 ... 

Canel C, Das SR (2002) Modeling global facility location decisions integrating marketing and manufacturing decisions. Industrial Management Data Systems 102 110-118... 

Eiselt HA (1992) Location modeling in practice. American Journal of Mathematical and Management Sciences 12 3-18 Eiselt HA, Laporte G (1995) Objectives in Location Problems. In Drezner Z (ed) Facility Location. Springer, Berlin et al., pp 151-180 Eiteman DK, Stonehill AI, Moffett MH (2006) Multinational Business Finance, 11th edn. Pearson Education, Boston et al. 

Hunt JR, Koulamas CP (1989) A Model for Evaluating Potential Facility Locations on a Global Basis. S.A.M. Advanced Management Journal 54 19-23... 

Melo MT, Nickel S, Saldanha da Gama F (2005) Dynamic multi-commodity capacitated facility location a mathematical modeling framework for strategic supply chain planning. Computers Operations Research 33 181-208... 

Yang J, Lee H (1997) An AHP decision model for facility location selection. Facilities 15 241-254... 

In this paper we have drawn on analyses carried out as part of the Maya Jade and Ceramics Project, a collaborative program of the Museum of Fine Arts, Boston and Brookhaven National Laboratory during 1977-1983. Work at Brookhaven was conducted under the auspices of the U.S. Department of Energy. Exploration into the interface between archaeological objectives, compositional variation and statistical modeling is an endeavor of the Smithsonian Archaeometric Research Collections and Records (SARCAR) facility located at the Smithsonian s Conservation Analytical Laboratory. Neffs participation in this research is made possible by a Smithsonian Institution Materials Analysis Postdoctoral Fellowship. 

Neutralization or Demilitarization Hazardous items may be neutralized by detonation in place, or they may be removed to a demilitarization facility located on, or at some distance from, the site undergoing remediation. Detonation in place, which is often the only safe method for neutralization of explosive items, carries with it concerns for blast, noise, and vapor containment. Blast containment coverings tend to be heavy, bulky, and difficult to position. Sand tamping for noise control is labor intensive and time consuming, and it creates problems with dust. Reliable mathematical models for predicting the noise impact on neighboring communities do not appear to be available, although their development should not be particularly difficult. 

The problems presented above can be extended further when the facilities are not aU similar but are organized hierarchically, resulting in hierarchical facility-location problems. Similarly, when multiple, and sometimes conflicting, objectives are present, multiobjective facility-location problems are obtained. Finally, many models exist that deal with the location of undesirable facilities (e.g., hazardous waste dumps) where instead of wanting to minimize, we want to maximize some measure of the distance between the demand nodes (e.g., population centers) and the facilities. 

Abstract Transportation and facility location decisions are crucial in strategic supply chain design. Optimization models guide location decisions giving the optimal site selection under certain assumptions and constraints. It is an art to decide which model to use and how to modify the results based on the needs of a company. This chapter presents some of the important optimization models in supply chain. Mathematical formulations and solution procedures are also given. The models can be expanded for multi-echelon supply chains and/or include multiple products. 

In Chap. 2, we dealt with topics in supply chain management. Supply chain management comprises decision making about facility location, production, transportation, and inventory control. Many companies employ optimization as a decision making tool. Here, we will introduce important and core optimization models and solution strategies for some important supply chain problems. 

---