A Sequential Stochastic Assignment Problem
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 p 1 \leqq p 2 \leqq \cdots \leqq p n the optimal choice in the initial stage of an n stage assignment problem is to use p i if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. 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 r(p, x).
Volume (Year): 18 (1972)
Issue (Month): 7 (March)
|Contact details of provider:|| Postal: |
Web page: http://www.informs.org/Email:
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:349-355. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc)
If references are entirely missing, you can add them using this form.