Methods of Games theory in problems of optimal production planning

Аuthors

Kobzar A. I.^*, Tikmenov V. N.^**, Tikmenova I. V.^***

STC ELINS, 4/1, Panfilovsky av., Moscow, 124460, Russia

*e-mail: kobzar@elins.ru
**e-mail: tikmenov@elins.ru
***e-mail: jasmin@elins.ru

Abstract

Uncertain demand for output products forces a manufacturer to make planned decisions under conditions of uncertainty and risk.

An efficient tool for enhancing the quality of planned solutions is implementation of the games theory methods. The article analyses the task of searching for an optimal decision in a situation, where the volume of government-guaranteed orders is a source of uncertainty and risk.

A search for optimal decisions comes down to the game with nature, in which one player — companys management — acts consciously and the second player — nature (state customer) — makes decisions regardless of the companys management and is guided only by changing of external economic and political conditions.

The article considers also methodological issues related to making a decision on optimization of a Government order performance plan by the example of a defense industry enterprise.

The article describes the key elements of payoff matrix related to the game with nature. The companys profit maximization is a criterion of optimal planning decision.

The maximax criteria advanced by Wald, Hurwitz and Savage under conditions of uncertainty is applied.

Applying an expert probability estimate of the state of nature (a volume of government orders) makes it possible to calculate the risk criteria by Bayes, Laplace, Hodges-Lehmann. The opinion consistency within a group of experts is estimated by Kendalls and Babington Smiths coefficient of concordance.

A comprehensive comparison of total calculated criteria allowed developing an optimal strategy for preparation of government order performance plan ensuring the companys maximum average profit provided that it is fulfilled within the established time limits.

Keywords:

decision optimality, game with the nature, complete uncertainty criteria, risk criteria, production plan

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