Contributions to Operations Research: Proceedings of the by Jo van Nunen, Jacq Benders, Adrie Beulens (auth.), Prof. Dr.

By Jo van Nunen, Jacq Benders, Adrie Beulens (auth.), Prof. Dr. Klaus Neumann, Prof. Dr. Diethard Pallaschke (eds.)

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Read Online or Download Contributions to Operations Research: Proceedings of the Conference on Operations Research Held in Oberwolfach, West Germany February 26 – March 3, 1984 PDF

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Additional info for Contributions to Operations Research: Proceedings of the Conference on Operations Research Held in Oberwolfach, West Germany February 26 – March 3, 1984

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P2(z) > zED(f, g) 1\ ev11tz 1\ ~ = zJ"mgy ~ 91. '\ V ~, t -00, then there exists a z~ € D( ~, ~) such the t d2 (z*) in1' P2(z) • max zeD(f,g) Ie D(ti,g,) = d2 (zci). 4 are given in /12/ • • ) Cf. 3. 34 4. F§ Let V. c, v» then we obtain by the inequality +~ V (z,v)E Correspondingly we obtain for (p, -q) (ao+~ (0+Ez+B2v ,q> (401b) V(z, v)€ F, V(p,-q) € 11. In the following we consider only the speoial oase oharaoterized by E 5 0 (then E*.

Bounds for expectation and variance If the determination of distribution functions or bounding distribution is functions still too difficult some moments or bounds moments of the underlying random variables can be computed. ov In the 1 all needed information is yielded from the expec- special case m tation EtO ,v £ V(D ab ). For the here described generalization notice that i f Z is a discrete random variable with integer values from {O,l, ••• ,m} and distribution function FZ(T) then EZ = m EZ a m - m-l ~ T=O m-l ~ T=O FZIt) (2T+I) FZIt) holds.

N + VN(s) lO VN(s) = s /N + 1 f e -u (t) (Nt-s) dt. S+/N The equation cosh u(t) = etu(t) can be solved numerically. It turns out that t ~ p(t):= e-u(t) is decreasing and convex with p(O+) = 1 and p(1-) = O. Thus p can be easily estimated from above by a piecewise linear function p*. This has been implemented in a program. Estimating s+/N + f1 p*(t)Nt-Sdt ~ V~(s) from above, we got upper u* s+ /N 1 + bounds VN (s). Similarly, the lower boundsVN(s) = s /N were implemented. 586098. 2) bounds T *u for the optimal stopping time T* T *1 and have been calculated.

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