Abstract
The problem analysed in this work is a particular parametric integer linear programming problem (PILP) and more precisely the problem to determine the behaviour of the optimal solution of an integer linear programming problem (ILP) when a resource varies in a given interval. The PILP is tackled with the following hypotheses:
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-the ILP problem is solved via a classical branch and bound algorithm, by far the most common approach in integer linear programming;
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-the interest is concentrated on approximate solutions of the PILP and on the set of ILP problems that can be usefully approached with approximate techniques.
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References
U.J.JR.BOWMAN: Sensitivity Analysis in Linear Integer Programming. In AIIE Technical Papers (1972).
J.M. FLEISHER, R.R. MEYER: New Sufficient Conditions for Integer Programming and their Application. Cpmputer Sciences Technical Report, University of Wisconsin, Madison (Jan. 1976).
C.R.JR.FRANK: Parametric Programming in Integers. In operations Research Verfahren, vol. III (1967).
A.M.GEOFFRION, R.NAUSS: Parametric and Postoptimality Analysis in Integer Linear Programming. In Management Science, vol. 23, n. 5 (1977).
M.LUCERTINI, A.MARCHETTI SPACCAMELA: Approximate Solutions of a Parametric Integer Linear Programming Problem: The Right-Hand-Side Case. Rapporto Ist. di Automatica e CSSCCA del CNR, Roma, Aprile 1978.
A.M.MARSTEN, T.L.MORIN: Parametric Integer Programming: The Right-Hand-Side.Case. In Hammer, Johnson, Korte and Nemhauser (eds), Studies in Integer Programming North-Holland Publishing Company.
R. NAUSS: Parametric Integer Programming. Published as Working Paper n.226,Western Management Science Institute, UCLA (Jan.1975).
H.NOLTEMEIER: Sensitivitalsanalyse bei distreten linearen Optimie r ungsproblem. In M.Beckman and H.P.Kunzi, eds. “Lecture Notes in Operations Research and Mathematical Systems, Springer-Verlag N.Y. (1970).
C.J.PIPER, A.A.ZOTNERS: Some easy Postoptimality Analysis for Zero-One Programming. In Management Science, vol. 22 n.7 (1976).
C.J.PIPER, A.A.ZOLTNERS: Implicit Enumeration Based Algorithm for Postoptimizing Zero-One Programs. In Management Sciences Research Report n. 313, Graduate School of Industrial Administration, Carnegie-Mellon University (March 1973).
G.M.ROODMAN: Postoptimality Analysis in Zero-One Programming by Implicit Enumeration. In Naval Research Logistics Quarterly, vol. 19 (1972).
G.M.ROODMAN: Postoptimality Analysis by Implicit Enumeration: The Mixed Integer Case. Report of the Amos Tuck School of Business Administration, Dartmouth College (Oct. 1973).
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© 1979 Springer-Verlag
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Lucertini, M., Spaccamela, A.M. (1979). Approximate solutions of an integer linear programming problem with resource variations. In: Marchuk, G.I. (eds) Modelling and Optimization of Complex System. Lecture Notes in Control and Information Sciences, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004165
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DOI: https://doi.org/10.1007/BFb0004165
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