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'Sequential assignment match processes' is a term that refers to models where M random 'offers' arriving sequentially are paired with N waiting 'candidates.' Matching between a candidate and an offer is done one at a time, and an offer that has been accepted or declined is no longer available for future assignments. A sequential matching problem is considered in which each of the waiting candidates, as well as each of the arriving offers, is distinguished by a fixed-length vector of random attribute obtained from a known, discrete-value, joint probability distribution function. The greater the compatibility between the assignment and the offer, the bigger the reward realized by the matching. Several cases are analyzed, including the general case where M is greater than or equal to N, special cases where M is equal to N and where M is greater than N, and the case where not all candidates must be assigned.

Markov decision processes (MDPs) are used to describe and control large and complicated stochastic systems. MDPs require efficient computational procedures such as the value iteration algorithm. Two innovations to this procedure for solving discounted MDPs, based on one-step lookahead analysis, are proposed. The approach involves tha application of two criteria that yield good adaptive relaxation factors: minimum difference and minimum variance. These considerably speed up algorithmic convergence. The proposed procedure is tested using several sample problems, including Howard's automobile replacement problem. The results indicate that the procedure yields savings in computation times compared to those associated with existing value iteration procedures. The proposed method has been demonstrated using real-life problems in cellular telephony.

Optimal scheduling policies for minimizing the anticipated completion time and the variance of completion time are presented for the sequential processing of a number of jobs on a single machine. Jobs can deteriorate while they are waiting to be processed, which causes processing time to increase. The completion time, as well as the processing time, is a function of the scheduling policy.

A time-dependent mathematical stopping problem is stated such that it applies to decisions of whether to accept kidneys offered for transplantation. The value of kidney offerings are modeled as a sequence of variables that are independent, randomly distributed and positive. The problem ends (or stops) each time a decision is made to accept a kidney offered. In addition, a first-order differential equation is devised to calculate control-limit functions associated with non-homogeneous Poisson arrivals of kidney offers to the system. The models and equations developed by the research are applied to cases of actual kidney offerings, acceptance, and transplantation.