Sequential stochastic assignment problem with time-dependent random success rates

The sequential stochastic assignment problem (SSAP) allocates distinct workers with deterministic values to sequentially arriving tasks with stochastic parameters to maximize the expected total reward. In this paper we study an extension of the SSAP, in which the worker values are considered to be random variables, taking on new values upon each task arrival. Several SSAP models with different assumptions on the distribution of the worker values and closed-form expressions for optimal assignment policies are presented.

THE SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM WITH POSTPONEMENT OPTIONS

The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.

STOCHASTIC SEQUENTIAL ASSIGNMENT PROBLEM WITH ARRIVALS

We extend the classic sequential stochastic assignment problem to include arrivals of workers. When workers are all of the same type, we show that the socially optimal policy is the same as the individually optimal policy for which workers are given priority according to last come–first served. This result also holds under several variants in the model assumptions. When workers have different types, we show that the socially optimal policy is determined by thresholds such that more valuable jobs are given to more valuable workers, but now the individually optimal policy is no longer socially optimal. We also show that the overall value increases when worker or job values become more variable.