Facility Location Problems

Problem formulations [ 1-3 ] for designing lead-generation library under different constraints belong to a class of combinatorial resource allocation problems, which have been widely studied. They arise in many different applications such as minimum distortion problems in data compression (11), facility location problems (12), optimal quadrature rules and discretization of partial differential equations (13), locational optimization problems in control theory (9), pattern recognition (14), and neural networks... 

A. M. Geoffrion and R. McBride. Lagrangian relaxation applied to capacitated facility location problems. AIIE Trans., 10 40,1978. 

Uncapacitated Facility Location Problem Upper Partial Mean... 

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-... 

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Canel C, Khumawala BM, Law J, Loh A (2001) An algorithm for the capacitated, multi-commodity multi-period facility location problem. Computers Operations Research 28 411-427... 

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Industrial Marketing Management 29 65-83 Lee CY (1991) An optimal algorithm for the multiproduct capacitated facility location problem with a choice of facility type. Computers Operations Research 18 167-182... 

Mazzola JB, Neebe AW (1999) Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type. European Journal of Operational Research 115 285-299... 

Tcha DW, Lee BI (1984) A branch-and-bound algorithm for the multilevel uncapacitated facility location problem. European Journal of Operational Research 18 35-43... 

Wirtschaftswissenschaftliches Studium 1 388-393 Tong H-M, Walter CK (1980) An Empirical Study of Plant Location Decisions of Foreign Manufacturing Investors in the United States. Columbia Journal of World Business 15 66-73 Tragantalerngsak S, Holt J, Ronnqvist M (2000) An exact method for the two-echelon, single-source, capacitated facility location problem. European Journal of Operational Research 123 473-489 Triantaphyllou E (2001) Two New Cases of Rank Reversals when the AHP and Some of its Additive Variants are Used that do not Occur with the Multiplicative AHP. Journal of Multi-Criteria Decision Analysis 10 11-25... 

Wallace SW (1988) A two-stage stochastic facility-location problem with time-dependent supply. In Ermoliev Y, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin et al., pp 489-513... 

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. 

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 ... 

They reveal that facility location problems mostly include inventory and production decisions as well while routing, transportation mode selection, and procurement integrated location decision problems receive less attention in the literature. Facility location decisions are strategic in supply chain design since a company supply chain will need to adapt to changing market needs migrating to new locations for example. They also state that most of the facility location studies consider minimization of costs as the objective. 

Another model for single facility layout problem has an objective of minimizing the summation of weighted distances between the new facility and existing ones (also known as minimum facility location problems, also minimax problems exist in the literature) ... 

Facility Location Problems Table 4.11 Customers (demand points) are sorted in ascending order of x- 55 -coordinates... 

Snyder and Multi-objective Facflity disruption Considers facility location problems... 

The sample facility location problem considered in this paper deals with locating fast food restaurants. There are a number of preselected potential facility location sites and the total number of facilities to be open is limited. It is aimed to locate restaurants at sites having the largest number of customers and the smallest number of competitors in its proximity and having acceptable real estate costs. 

Each depot can be linked to a single hub, called single-allocation, or it can be linked to more than one hub, called multiple-allocation. Both situations occur in practice. As seen in Fig. 5.7, LTL trucking networks have each depot assigned to a single break bulk terminal (hub) for load consolidation. Passenger airline networks, on the other hand, have flights scheduled from many non-hub cities to a few hubs. Also note that capacity limitations at hubs may force multiple-allocation, as seen in many facility location problems. 

Prepositioned supplies (in a general delivery warehouse) are used only when a disaster strikes. Therefore, the length of storage needed at such warehouses is uncertain. Balcik and Beamon (2008) discuss a facility location problem for humanitarian relief that integrates facility location with inventory decisions, and considers multiple items with different criticalities and response time requirements. 

The concept of level r facility is introduced in Snyder and Daskin (2005) to handle sequential allocation of facilities to customers in an incapacitated facility location problem. In the model presented here, a level 1 supplier is responsible of supplying the products as long as there is no disruption and is named as a primary supplier. In case of a disruption, a backup supplier replaces the failed primary supplier. A buyer can have only one primary supplier for a given product. Remaining suppliers are then assigned as backups at the m levels, where m < m. Other parameters used in the sequential supplier assignment (SSA) model are given in Table 10.2. 

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