Sequential stochastic assignment problem with time-dependent random success rates

2016 ◽  
Vol 53 (4) ◽  
pp. 1052-1063
Author(s):  
Golshid Baharian ◽  
Arash Khatibi ◽  
Sheldon H. Jacobson
Keyword(s):  
Closed Form ◽  
Assignment Problem ◽  
Random Variables ◽  
Time Dependent ◽  
Success Rates ◽  
Optimal Assignment ◽  
Total Reward ◽  
Stochastic Parameters ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

Abstract 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

2012 ◽  
Vol 27 (1) ◽  
pp. 25-51 ◽  
Author(s):  
Tianke Feng ◽  
Joseph C. Hartman
Keyword(s):  
Stochastic Process ◽  
Decision Maker ◽  
Assignment Problem ◽  
Lower Risk ◽  
Care Management ◽  
Optimal Assignment ◽  
Threshold Policies ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment ◽  
Heterogeneous Resources

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.

The sequential stochastic assignment problem with random success rates

2014 ◽  
Vol 46 (11) ◽  
pp. 1169-1180 ◽  
Author(s):  
Arash Khatibi ◽  
Golshid Baharian ◽  
Estelle R. Kone ◽  
Sheldon H. Jacobson
Keyword(s):  
Assignment Problem ◽  
Success Rates ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

A SEQUENTIAL STOCHASTIC ASSIGNMENT PROBLEM

1970 ◽  
Author(s):  
Gerald J. Lieberman ◽  
Sheldon M. Ross ◽  
Cyrus Derman
Keyword(s):  
Assignment Problem ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

STOCHASTIC SEQUENTIAL ASSIGNMENT PROBLEM WITH ARRIVALS

2011 ◽  
Vol 25 (4) ◽  
pp. 477-485 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Assignment Problem ◽  
Sequential Assignment ◽  
Different Types ◽  
Job Values ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

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.

Extensions of the sequential stochastic assignment problem

2015 ◽  
Vol 82 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Arash Khatibi ◽  
Golshid Baharian ◽  
Banafsheh Behzad ◽  
Sheldon H. Jacobson
Keyword(s):  
Assignment Problem ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

scholarly journals Generalized Sequential Stochastic Assignment Problem

2018 ◽  
Vol 8 (4) ◽  
pp. 293-306
Author(s):  
Arash Khatibi ◽  
Sheldon H. Jacobson
Keyword(s):  
Assignment Problem ◽  
Stochastic Assignment ◽  
Sequential Stochastic Assignment

A Stochastic Assignment Problem with Unknown Eligibility Probabilities

2020 ◽  
Author(s):  
Sheldon M. Ross ◽  
Gideon Weiss ◽  
Zhengyu Zhang
Keyword(s):  
Optimal Policy ◽  
Assignment Problem ◽  
Binary Vector ◽  
Random Variables ◽  
Bernoulli Random Variables ◽  
Stochastic Assignment ◽  
Vector Formula

Consider [Formula: see text] initially empty boxes, numbered 1 through [Formula: see text]. Balls arrive sequentially. Each ball has a binary vector [Formula: see text] attached to it, with the interpretation that the ball is eligible to be put in box [Formula: see text] if [Formula: see text]. An arriving ball can be put in any empty box for which it is eligible. Assume that components of the vector are independent Bernoulli random variables with initially unknown probabilities [Formula: see text]. In “A Stochastic Assignment Problem with Unknown Eligible Probabilities,” Ross, Weiss, and Zhang discuss policies that aim at minimizing the number of balls needed until all boxes are filled. When full memory is allowed, the optimal policy is identified in the sense that it stochastically minimizes the number of balls taken. Two random policies are considered and compared when no memory is allowed. A reordering rule is proposed when one can only keep partial memory.

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