Discrete and Fractional Programming Techniques for Location Models

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Springer Science & Business Media, Apr 30, 1998 - Mathematics - 180 pages
At first sight discrete and fractional programming techniques appear to be two com pletely unrelated fields in operations research. We will show how techniques in both fields can be applied separately and in a combined form to particular models in location analysis. Location analysis deals with the problem of deciding where to locate facilities, con sidering the clients to be served, in such a way that a certain criterion is optimized. The term "facilities" immediately suggests factories, warehouses, schools, etc. , while the term "clients" refers to depots, retail units, students, etc. Three basic classes can be identified in location analysis: continuous location, network location and dis crete location. The differences between these fields arise from the structure of the set of possible locations for the facilities. Hence, locating facilities in the plane or in another continuous space corresponds to a continuous location model while finding optimal facility locations on the edges or vertices of a network corresponds to a net work location model. Finally, if the possible set of locations is a finite set of points we have a discrete location model. Each of these fields has been actively studied, arousing intense discussion on the advantages and disadvantages of each of them. The usual requirement that every point in the plane or on the network must be a candidate location point, is one of the mostly used arguments "against" continuous and network location models.
 

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Contents

Introduction
xvii
Discrete Location Models
3
22 Multilevel Uncapacitated Facility Location Problems
9
222 The 2echelon Uncapacitated Facility Location Problem
11
23 Submodularity
14
24 A General Uncapacitated Facility Depot Location Model
18
242 Formulations
20
243 Linear Relaxation
22
321 1level Fractional Location Problems
79
322 2level Fractional Location Problems
89
33 Conclusions
93
Generalized Fractional Programming
95
41 A Primal Approach
97
411 The Parametric Approach
98
412 An Allocation Model
106
413 A Nonstandard Class of Generalized Fractional Programs
110

244 Lagrangian Relaxation
25
245 Heuristics
41
246 Branch and Bound
43
247 Computational Results
47
25 Conclusions
56
Location Models and Fractional Programming
59
31 Fractional Programming
62
311 Continuous Fractional Programming
63
312 Integer Fractional Programming
76
32 Fractional Location Models
78
42 A Dual Approach
114
421 Solving the Standard Dual
115
422 A New Duality Approach
135
423 Computational Results
146
43 Conclusions
152
Summary and Remarks
155
Bibliography
157
Index
169
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