A SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM
STANFORD UNIV CA
Pagination or Media Count:
Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a p man is assigned to an X x job, the expected reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p1 or p2 or ... or pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith non-overlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the ps. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the expected reward if a p man is assigned to an x job is given by a function rp,x.
- Operations Research