Location problem

A plant location problem has arisen. Two possible sites exist for building a new plant, A and B, and two customer locations are to be supplied, C and D. Demands and pro-duction/supply costs are listed as follows. 

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-... 

Canel C, Khumawala BM (1996) A mixed-integer programming approach for the international facilities location problem. International Journal of Operations Production Management 16 49-68... 

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... 

Chardaire P, Sutter A, Costa M-C (1996) Solving the Dynamic Facility Location Problem. Networks 28 117-124... 

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. 

Hindi KS, Pienkosz K (1999) Efficient solution of large scale, singlesource, capacitated plant location problems. Journal of the Operational Research Society 50 268-274... 

Hines Jr. JR (1999) Lessons from Behavioral Responses to International Taxation. National Tax Journal 52 305-322 Hinojosa Y, Puerto J, Fernandez FR (2000) A multiperiod two-echelon multicommodity capacitated plant location problem. European Journal of Operational Research 123 271-291 Hinterhuber HH, Lauda K, Matzler K, Schatz D (1994) Strategische Standortplanung - Eine Fallstudie aus der Bekleidungsbranche. Journal fur Betriebswirtschaft 44 102-113... 

Kathawala Y, Gholamnezhad H (1987) New approach to facility location decisions. International Journal of Systems Science 18 389-402 Kaufman L, Vanden Eede M (1977) A Plant and Warehouse Location Problem. Operational Research Quarterly 28 547-554 Keeney RL (1992) Value-Focused Thinking. Harvard University Press, Cambridge, Massachusetts... 

Keeney RL, Raiffa H (1976) Decisions with Multiple Objectives Preferences and Value Tradeoffs. John Wiley Sons, New York et al. Kelly DL, Marucheck AS (1984) Planning Horizon Results For the Dynamic Warehouse Location Problem. Journal of Operations Management 4 279-294... 

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... 

Shulman A (1991) An Algorithm for Solving Dynamic Capacitated Plant Location Problems with Discrete Expansion Sizes. Operations Research 39 423-436... 

Sridharan R (1995) The capacitated plant location problem. European Journal of Operational Research 87 203-213... 

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... 

Wu JA, Wu NL (1984) Analysing Multi-Dimensional Attributes for the Single Plant Location Problem via an Adaptation of the Analytical Hierarchy Process. International Journal of Operations Production Management 4 13-21... 

We will start by reviewing the wetted surface from reservoir to flow cell output. I will discuss the minimum tools and spare parts you should have on hand and when to use them as well as a strange-sounding technique to cut your solvent usage. A systematic approach to locating problems will be presented next. Then we ll look at how to get the most out of data acquisition hardware. 

In an HPLC system, problems can arise from many sources. Malfunction can be allocated to various points. Chromatographers should use not only their experience to locate problems but also aU their senses (obviously, except taste) to identify LC problems. For example, a leak can be noticed by smeU before it is actually seen. A strange noise indicates some kind of malfunction and a hot smell indicates an overheating module. Most problems, however, are identified by sight, and they can mainly be observed as changes in the chromatogram. As soon as the problem has been defined, actions should be taken to correct the malfunctioning component. The incident should be recorded, in a log book kept for this purpose, to help with further failure problems at a later time. 

Electronics. —> Locate problem. Get servicing. Isolate detector and recorder electronically. Use a voltage stabilizer for the LC system or use an independent electrical circuit for the chromatography equipment. 

A. Marin and B. Pelegrin, "The Return Plant Location Problem Modelling and Resolution, European Journal of Operational Research, 104, 375-392 (1998). 

Children will be helped to develop their creative faculties—their imagination and independent thinking for locating problems, suggesting solutions and trying out their ideas. 

The optimal source location problem is then to choose (X, 7) (assuming that the stack height Z is fixed) to minimize E subject to the constraint that (X, 7) lies in the region. Carry through the solution for the optimal location X of a ground-level cross-wind line source (parallel to the y axis) on a region 0 < x < L. Let Po uj) and Pi (Uj) be the fractions of time that the wind blows in the +x and -x directions, respectively. Show that the value of X to minimize E subject to 0 < X < L is... 

The optimal source location problem is then Choose (X, Y) (assuming the stack height Z is fixed) to minimize E subject to the constraint that (X, K) lies in the region. 

The above presentation shows that a great deal of experience and knowledge is required to make a realistic plant location study. The next sections of this chapter present a more detailed discussion of the primary and specific plant location factors so that the student can gain some knowledge in this area. An actual plant location problem is then worked out at the end of the chapter. It is impossible to Include a very complete compilation of specific information for a plant location study in this type of textbook. A listing of useful sources of information is presented in Table 7-1. 

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. 

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