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Asymptotic Linear Programming
- Source :
- Operations Research. 21:1128-1141
- Publication Year :
- 1973
- Publisher :
- Institute for Operations Research and the Management Sciences (INFORMS), 1973.
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Abstract
- This paper studies the linear programming problem in which all coefficients (even those of the stipulations matrix) are rational functions of a single parameter t called “time,” and provides an algorithm that can solve problems of the following two types: (1) Steady-state behavior [the algorithm can be used to determine the functional form x(t) of the optimal solution as a function of t, this form being valid for all “sufficiently large” values of t], and (2) sensitivity analysis [if a value t0 of “time” is given, the algorithm can be used to determine the two possible functional forms of the optimal solution for all values of t “sufficiently close” to t0 (the first functional form valid for t < t0, the second for t < t0)]. In addition, the paper gives certain qualitative information regarding steady-state behavior, including the following result: If for some one of the properties of consistency, boundedness, or bounded constraint set, there exists a sequence tn ↗ +∞ such that the linear program at n has this property for all n, then the program has this property for all “sufficiently large” values of t.
Details
- ISSN :
- 15265463 and 0030364X
- Volume :
- 21
- Database :
- OpenAIRE
- Journal :
- Operations Research
- Accession number :
- edsair.doi...........6b520be4849c7c12ea5e9cab0f1249e2