The Facility Location Problem

The nature of the basic problem the company faced was that no one in the company knew what the true cost of the current facilities was, or what the financial benefits of moving were. The following is a summary of some of the problems encountered. 

Organizational. The facility was leased from a parent company, at a lease rate that might not have reflected the market or tme costs. 

Accounting. Cost elements were scattered throughout the company and its parent s accounting statements, so there was the aspect of transfer pricing and sorting out of where the costs and benefits show up on the balance sheet and income statement. 

Political. There were factions within the company who were perfectly happy staying where they were others wished to move, but not all to the same city location. The city where the DC was located favored manufacturers over distributors because they hired more personnel per square foot and generated more taxes to the dty s coffers. 

Individuals who worked at the facility lived in different cities, and commute time changes could be onerous with a new facility. 

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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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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... 

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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... 

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) ... 

We will save the discussion of production planning models, however, for Chapter 5, based on the similarity of that problem to the facility location and location-allocation problems discussed in that chapter. Also in Chapter 5, we introduce the notion of risk pooling, which is a means of reducing the safety stock required to support a target service level by aggregating demands across multiple sources, for example across multiple customers or customer regions supported by a single facility. 

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. 

In this chapter, we will address the plant location problem, that is, where to place a chemical facility considering cost and demand data. This problem is quite common in chemical engineering and lies in the interface between chemical engineering itself and operations research. We will provide a basic general formulation and then give some additional references to other similar models. 

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. 

The first step is to enter the problem data as shown in cells B5 F12. Next, we set the decision variables (x, y) corresponding to the location of the new facility in cells B16 and B17, respectively. In cells G5 G12, we then calcnlate the distance from the facility location (x, y) to each source or market, using Equation 5.4. The total TC is then calculated in cell B19 using Equation 5.5. 

The air pollution problems associated with combustion of coal are of major concern. These problems generally occur away from the coal mine. The problems of atmospheric emissions due to mining, cleaning, handling, and transportation of coal from the mine to the user are of lesser sigruficance as far as the overall air pollution problems are concerned. Whenever coal is handled, particulate emission becomes a problem. The emissions can be either coal dust or inorganic inclusions. Control of these emissions can be relatively expensive if the coal storage and transfer facilities are located near residential areas. 

Although transformers suitable for other industrial installations are generally suitable for producing applications, certain options may be desirable— primarily due to environmental considerations. At locations subject to harsh environmental conditions, and particularly at locations subject to washdown with high-pressure hoses, non-ventilated enclosures are desirable, if not necessary. Likewise, at locations subjected to salt water and salt-laden air, it often is desirable to specify copper windings and lead wires. Most manufacturers provide standard units with aluminum windings and lead wires. Even if aluminum coils are used, it is almost always desirable to require stranded copper lead wires. This will lessen corrosion and loose terminal problems when transformers arc interconnected to the facility electrical system with copper conductors. If the transformers are to be installed outdoors in corrosive environments, cases should be of corrosion-resistant material (e.g., stainless steel) or be provided with an exterior coating suitable for the location. 

Quench liquid selection The choice of the appropriate quench liquid depends on a number of factors. Water is usually the first quench liquid to consider. If water is selected as the quench liquid, the tank should be located indoors, if possible, to avoid freezing problems if the facility is in a cold climate. If the tank has to be located outdoors in a cold climate, the addition of antifreeze is preferable to heat-tracing the tank, since overheating of the tank can result from tracing, thus reducing its effectiveness. 

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