A stochastic employment problem

This dissertation studied a Stochastic Assignment Problem, called “A Stochastic Employment Problem(SEP)”. There are n boxes having quota S =(S₁...Sn), that is box i needs Si balls, i = 1. . . n. Balls arrive sequentially,with each one having a binary vector X = (X₁, X₂...Xn) attached, with the interpretation being that if Xᵢ = 1 this ball is eligible to be put in box i, i = 1. . . n. When a ball arrives, its vector is revealed and the ball is put in one box for which it is eligible. Assuming the vectors are independent and identically distributed among the successive balls, this problem continues until there are at least Si balls in box i, for all i. The SEP could be applied to an organizational employment decision problem, with the interpretation being that the boxes are the types of jobs and the balls are the job seekers, with Si implying the number of type i jobs and X indicating which jobs a seeker is qualified to take. ❧ Variations of the Stochastic Employment Problem were considered. Such as, balls arrive according to a renewal process and each box has a lifetime under a specified distribution. Thus the SEP could be considered as a stochastic control problem associated with a single server queuing system. Therefore it could be applied to channel/processor scheduling in telecommunication/computer industry. For example, in a time slotted network, n users share one channel with user i having Si packets to transmit i = 1. . . n, and X indicating which users are connected hence able to transmit. The SEP could also be applied to an organ transplant decision problem, with the box lifetime being a patient’s lifetime and the ball vector indicating which patients an arriving organ fits.