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The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball is eligible to be put into box i, i = 1... n. The vector is revealed when a ball arrives and the ball is put in an alive box for which it is eligible. Here alive means a box needs more balls. Assuming that vectors are independent and identically distributed among the successive balls, following a specified joint distribution; this problem continues until there are at least si balls in box i, i = 1...n. By the nature of being an assignment problem, the SEP could be applied to an organizational employment decision problem, with the interpretation being that boxes are the types of jobs and 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 studied. Such as, balls arrive according to a renewal process; each alive box incurs a cost per unit time; each box has a lifetime following a specified distribution, etc. Thus, SEP could be considered as a Stochastic Scheduling Problem in a single server queuing system. It has native applications in channel/processor scheduling problems in communications/computer industry. The SEP could also be applied to organ transplant decision problems, with the box lifetime being a patient's lifetime and the ball vector indicating which patients the incoming organ fits. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]