# zbMATH — the first resource for mathematics

Goal programming problems with interval coefficients and target intervals. (English) Zbl 0734.90056
Summary: In conventional goal programming, the coefficients of objective functions and constraints, and target values are determined as crisp values. However, it is not frequent that the coefficients and the target values are known precisely. In such cases, the coefficients and target values should be represented by intervals reflecting the imprecision. This paper treats goal programming problems in which coefficients and target values are given by intervals. It is shown that four formulations of the problems can be considered. The properties of the four formulated problems are investigated. An example is given to demonstrate the differences between the four formulations.

##### MSC:
 90C05 Linear programming 65G30 Interval and finite arithmetic
##### Keywords:
interval programming; goal programming
Full Text:
##### References:
  Ben-Israel, Adi; Robers, P.D., A decomposition method for interval linear programming, Management science, 16, 374-387, (1970) · Zbl 0191.48001  Bitran, G.R., Linear multiple objective problems with interval coefficient, Management science, 26, 694-706, (1980) · Zbl 0445.90076  Charnes, A.; Granot, Frieda; Phillips, F., An algorithm for solving interval linear programming problems, Operations research, 25, 688-695, (1977) · Zbl 0384.90081  Dubois, Didier, Linear programming with fuzzy data, (), 241-263 · Zbl 0657.90064  Ignizio, J.P., Linear programming in single- & multiple-objective systems, (1982), Prentice-Hall Englewood Cliffs · Zbl 0484.90068  Luhandjula, M.K., On possibilistic linear programming, Fuzzy sets and systems, 18, 15-30, (1986) · Zbl 0616.90038  Luhandjula, M.K., Linear programming with a possibilistic objective function, European journal of operational research, 31, 110-117, (1987) · Zbl 0635.90057  Moore, R.E., Methods and applications of interval analysis, (1979), SIAM Philadelphia · Zbl 0417.65022  Soyster, A.L., Convex programming with set-inclusive constraints and applications to inexact linear programming, Operations research, 21, 1154-1157, (1973) · Zbl 0266.90046  Soyster, A.L., Inexact linear programming with generalized resource sets, European journal of operational research, 3, 316-321, (1979) · Zbl 0405.90044  Steuer, R.E., Goal programming sensitivity analysis using interval penalty weights, Mathematical programming, 17, 16-31, (1979) · Zbl 0412.90063  Steuer, R.E., Algorithm for linear programming problems with interval objective function coefficients, Mathematics of operations research, 6, 333-348, (1981) · Zbl 0491.90059  Tanaka, H.; Asai, K., Fuzzy linear programming with fuzzy numbers, Fuzzy sets and systems, 13, 1-10, (1984) · Zbl 0546.90062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.