Optimal Assignment tor a Random Sequence with an unknown Parameter
Tōru Nakai · Journal of Information and Optimization Sciences · 1980
Suppose that W is a random variable which takes values in the space Ω. Also, suppose that X is a random variable witb parameter ω(ω∈Ω), which takes values in the sample space S. Sequentially observe the realized value x of the random variable X and for each x assign the man with a probability p. If a “p” man is assigned to a job with the value x, It e expected reward is as, umed to be given by px. After a man is assigned to a job, he is unavailable for the future stages. We get the optimal strategy and its value, so as to maximize the total expected reward. In this paper we consider tbe sufficient conditions for obtaining the similar result of Derman, Lieberman and Ross [3]. If there are n–1 turning points and the optimal assignment in the initial stage oran n-stage problem is to use pi if x is contained in the i-th interval bttween (i–1)-th and i-th turning point, comprising the real line. These optimal strategy is characterized by the recursive equations which is obtained by the dynamic programming argument.