Triply stochastic sequential assignment problem with the uncertainty in worker survival

2021 ◽  
Author(s):  
Siddhartha Nambiar ◽  
Alexander Nikolaev ◽  
Eduardo Pasiliao
Keyword(s):  
Assignment Problem ◽  
Sequential Assignment

scholarly journals Limiting Behavior of the Target-Dependent Stochastic Sequential Assignment Problem

2014 ◽  
Vol 51 (4) ◽  
pp. 943-953 ◽  
Author(s):  
Golshid Baharian ◽  
Sheldon H. Jacobson
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Assignment Problem ◽  
Sequential Assignment ◽  
Threshold Probability ◽  
Limiting Behavior ◽  
Target Value ◽  
Long Run ◽  
Stochastic Parameters ◽  
Optimal Policies

The stochastic sequential assignment problem assigns distinct workers to sequentially arriving tasks with stochastic parameters. In this paper the assignments are performed so as to minimize the threshold probability, which is the probability of the long-run reward per task failing to achieve a target value (threshold). As the number of tasks approaches infinity, the problem is studied for independent and identically distributed (i.i.d.) tasks with a known distribution function and also for tasks that are derived from r distinct unobservable distributions (governed by a Markov chain). Stationary optimal policies are presented, which simultaneously minimize the threshold probability and achieve the optimal long-run expected reward per task.

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.

Doubly Stochastic Sequential Assignment Problem

2016 ◽  
Vol 63 (2) ◽  
pp. 124-137 ◽  
Author(s):  
Arash Khatibi ◽  
Sheldon H. Jacobson
Keyword(s):  
Assignment Problem ◽  
Sequential Assignment ◽  
Doubly Stochastic

Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem

1972 ◽  
Vol 19 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Chris Albright ◽  
Cyrus Derman
Keyword(s):  
Assignment Problem ◽  
Sequential Assignment ◽  
Optimal Policies

The Stochastic Sequential Assignment Problem With Random Deadlines

1987 ◽  
Vol 1 (2) ◽  
pp. 189-202 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Simple Form ◽  
Optimal Policy ◽  
Assignment Problem ◽  
Independent Random Variables ◽  
Sequential Assignment ◽  
Activity System ◽  
Combined System ◽  
Expected Return ◽  
Batch Arrivals ◽  
Activity Models

Resources are to be allocated sequentially to activities to maximize the total expected return, where the return from an allocation is the product of the value of the resource and the value of the activity. The set of activities and their values are given ahead of time, but the resources arrive according to a Poisson process and their values are independent random variables that are observed upon arrival. It is assumed that either there is a single random deadline for all activities, which is the same as discounting the returns, or the activities have independent random deadlines. The model has applications machine scheduling, packet switching, and kidney allocation for transplant. It is known that the optimal policy in the discounted case has a very simple form that does not depend on the activity values. We show that this is also true when the deadlines are independent and in this case the solution can expressed in terms of solutions to single activity models. These results also hold when there are batch arrivals of resources. The effects of pooling separate identical systems with a single activity into a combined system is investigated for both models. When activities have independent deadlines it is optimal to reject a resource in the combined system if and only if it is optimal to reject it in the single activity system. However, when returns are discounted, it is sometimes optimal to accept a resource in the combined system that would be rejected in the single activity system.

Stochastically maximizing the number of successes in a sequential assignment problem

1990 ◽  
Vol 27 (2) ◽  
pp. 351-364 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Finite Number ◽  
Poisson Process ◽  
Optimal Policy ◽  
Assignment Problem ◽  
Sequential Assignment ◽  
Expected Number ◽  
Expected Return ◽  
Threshold Policy ◽  
The Given

In the classical sequential assignment problem as introduced by Derman et al. (1972) there are n workers who are to be assigned a finite number of sequentially arriving jobs. If a worker of value p is assigned a job of value x the return is px, where we interpret the return as the probability that the given worker correctly completes the given job. The job value is a random value that is observed upon arrival, and jobs must be assigned or rejected when they arrive. Each worker can only do one job. Derman et al. showed that when the objective is to maximize the expected return, i.e., the expected number of correctly completed jobs, the optimal policy is a simple threshold policy, which does not depend on the worker values. Their result was extended by Albright (1974) to allow job arrivals according to a Poisson process and a single random deadline for job completion (which is equivalent to discounting). Righter (1987) further extended the result to permit workers to have independent random deadlines for job completions. Here we show that when there are independent deadlines a simple threshold policy that is independent of the worker values stochastically maximizes the number of correctly completed jobs, and therefore maximizes the expected number of correctly completed jobs. We also show that there is no policy that stochastically maximizes the number of correctly completed jobs when there is a single deadline. However, when there is single deadline and the objective is to maximize the probability that n jobs are done correctly by n workers, then the optimal policy is determined by a single threshold that is independent of n and of the worker values.

Stochastically maximizing the number of successes in a sequential assignment problem

1990 ◽  
Vol 27 (02) ◽  
pp. 351-364 ◽  
Author(s):  
Rhonda Righter
Keyword(s):  
Finite Number ◽  
Poisson Process ◽  
Optimal Policy ◽  
Assignment Problem ◽  
Sequential Assignment ◽  
Expected Number ◽  
Expected Return ◽  
Threshold Policy ◽  
The Given

In the classical sequential assignment problem as introduced by Derman et al. (1972) there are n workers who are to be assigned a finite number of sequentially arriving jobs. If a worker of value p is assigned a job of value x the return is px, where we interpret the return as the probability that the given worker correctly completes the given job. The job value is a random value that is observed upon arrival, and jobs must be assigned or rejected when they arrive. Each worker can only do one job. Derman et al. showed that when the objective is to maximize the expected return, i.e., the expected number of correctly completed jobs, the optimal policy is a simple threshold policy, which does not depend on the worker values. Their result was extended by Albright (1974) to allow job arrivals according to a Poisson process and a single random deadline for job completion (which is equivalent to discounting). Righter (1987) further extended the result to permit workers to have independent random deadlines for job completions. Here we show that when there are independent deadlines a simple threshold policy that is independent of the worker values stochastically maximizes the number of correctly completed jobs, and therefore maximizes the expected number of correctly completed jobs. We also show that there is no policy that stochastically maximizes the number of correctly completed jobs when there is a single deadline. However, when there is single deadline and the objective is to maximize the probability that n jobs are done correctly by n workers, then the optimal policy is determined by a single threshold that is independent of n and of the worker values.

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