Mathematical Methods of Operations Research

Pintér, J.

doi: 10.1007/BF01423332pmid: N/A

A simple general framework for derivingexplicit deterministic approximations of probability inequalities of the formP(ξ⩾a) ⩽ α is presented. These approximations are based on limited parametric information about the involved random variables (such as their mean, variance, range or upper bound values). First the case of a single random variableξ is analysed, followed by the cases of independent and dependent summands $$\xi = \mathop \sum \limits_1^n \xi _i $$ . As examples of possible applications, a stochastic extension of the “knapsack problem” and the stochastic linear programming problem with separate chance-constraints are investigated: we provide approximate deterministic surrogates for these problems.

Schwarze, J.

doi: 10.1007/BF01423333pmid: N/A

Singer, I.

doi: 10.1007/BF01423334pmid: N/A

Distinguishing between a problem and its instances, we redefine the perturbational dual problem corresponding to an unperturbational dual problem, by means of explicit formulas, instead of “the scheme” of “formal replacements” of [15]. We show the relations between some main perturbational dual problems and the perturbational dual problems corresponding to some main unperturbational dual problems.

Chun, Y.

doi: 10.1007/BF01423335pmid: N/A

We analyze bargaining situations in which the feasible set is known but the disagreement point is uncertain. By requiring that all agents, generally, be affected by the uncertainty in the same way, we characterize thelexicographic egalitarian solution.

Gallisch, E.

doi: 10.1007/BF01423336pmid: N/A

We present a model for manpower planning which describes the dependence between stocks, flows and age distributions. An unbalanced age distribution results in the following conflict: either a recruitment is chosen which produces minimal deviations from a given stock. Then the unbalanced age distribution will be reproduced. Or a recruitment is selected which produces a balanced age distribution, but then oscillations of the stock will occur until a stationary age distribution will be reached. A mixture of these two recruitment policies is possible.

Becker, H.; Dowling, M.; Palmer, E.

doi: 10.1007/BF01423337pmid: N/A

Schmidt, G.; Engl, Heinz

doi: 10.1007/BF01423338pmid: N/A

doi: 10.1007/BF01423339pmid: N/A