An approach to postoptimality and sensitivity analysis of zero-one goal programs. (English) Zbl 0645.90055
This article presents an approach to postoptimality and sensitivity analysis of zero-one goal programs based on the set of k-best solutions. The set of k-best solutions is generated by using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problems. In a single-parameter sensitivity analysis bounds on the increase and the decrease in a goal coefficient, a relative weight of a goal, or a right-hand side are determined such that the optimal solution still resides in the original k-best set. A multiple-parameter postoptimality analysis is presented which gives a sufficiency condition for whether the new solution resides in the original k-best set.
Reviewer: J.Terno
MSC:
| 90C10 | Integer programming |
| 90C31 | Sensitivity, stability, parametric optimization |
| 65K05 | Numerical mathematical programming methods |
Keywords:
postoptimality; sensitivity analysis; zero-one goal programs; k-best solutions; branch and bound; implicit enumeration; multiple objective problemsReferences:
| [1] | Crowder, Operations Research 31 pp 803– (1983) |
| [2] | Geoffrion, Management Science 23 pp 453– (1977) |
| [3] | Geoffrion, Management Science 18 pp 465– (1972) |
| [4] | Goal Programming and Extensions, Lexington Books, Lexington, MA, 1976. |
| [5] | Linear Programming in Single and Multiple Objective Systems, Prentice-Hall, Englewood Cliffs, NJ, 1982. |
| [6] | , and , ”Multiple Criteria Decision Making Approach to MIS Planning,” working paper, Management Research Center, University of Wisconsin-Milwaukee, 1984. |
| [7] | Kochenberger, Operations Research Letters 1 pp 182– (1982) |
| [8] | Goal Programming for Decision Analysis, Auerback, Philadelphia, PA, 1972. |
| [9] | and , ”Project Proposals Evaluation: Zero-One Integer Goal Programming Approach,” Proceedings of the Midwest AIDS Annual Meeting, Detroit, April 16–17, 1981, pp. 241–243. |
| [10] | Piper, Naval Research Logistics Quarterly 22 pp 791– (1976) |
| [11] | Piper, Management Science 22 pp 759– (1976) |
| [12] | Roodman, Naval Research Logistics Quarterly 19 pp 435– (1972) |
| [13] | ”Multiple Criteria Project Selection Models: Zero-One Integer Goal Programming with Sensitivity Features,” working paper, Department of Industrial Engineering, Lehigh University, 1980. |
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