Allocation of an indivisible resource: Optimal control and prices
- 32 Downloads
Under study is a dynamical system of economics with discrete time whose states at each moment correspond to nonnegative integer points of a two-dimensional vector space. There are two types of products and two facilities each of which can change the state of the system by random integer vectors with different collections of probabilities. By a control we understand the choice at each moment of time of one available collection of probabilities. The goal of control is to minimize the probability of leaving the positive quadrant. The question is considered of the existence of some prices that agree with an optimal control.
Key wordsoptimal control prices Markov chain
Unable to display preview. Download preview PDF.
- 3.E. O. Rapoport, “About a Stochastic Model of Allocation of an Indivisible Resource,” in Proceedings of the Siberian Conference on Applied and Industrial Mathematics (Inst. Mat., Novosibirsk, 1997), pp. 197–206.Google Scholar
- 7.W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2 (John Wiley and Sons, New York, 1966; Mir, Moscow, 1984).Google Scholar