A Stochastic Assignment Problem with Unknown Eligibility Probabilities

Operations Research ◽

10.1287/opre.2020.1988 ◽

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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STOCHASTIC SEQUENTIAL ASSIGNMENT PROBLEM WITH ARRIVALS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964811000143 ◽

2011 ◽

Vol 25 (4) ◽

pp. 477-485 ◽

Cited By ~ 1

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.

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Sequential stochastic assignment problem with time-dependent random success rates

Journal of Applied Probability ◽

10.1017/jpr.2016.64 ◽

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.

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On improvements of the order of approximation in the Poisson limit theorem

Journal of Applied Probability ◽

10.1017/s0021900200103808 ◽

1996 ◽

Vol 33 (01) ◽

pp. 146-155 ◽

Cited By ~ 1

Author(s):

K. Borovkov ◽

D. Pfeifer

Keyword(s):

Limit Theorem ◽

Random Variables ◽

Poisson Approximation ◽

Order Of Approximation ◽

Operator Semigroups ◽

Bernoulli Random Variables ◽

Usual Rate ◽

Poisson Limit ◽

Poisson Measures ◽

Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

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