Stochastic Scheduling with Release Dates and Due Dates

Article Abstract:

Stochastic scheduling problems in which the processing times of jobs are independent exponentially distributed random variables are considered. Also the release dates are random variables with an arbitrary joint distribution and the due dates are random variables with a joint distribution that satisfies certain conditions. Simple policies that minimize such criteria as the expected weighted sum of completion times and the expected weighted number of late jobs are developed. These results contrast markedly with the deterministic counterparts of these models for which no polynomial time algorithms are known.

Statistics (Data), Statistics, Probability, Exponential Time

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On Scheduling Unit-Length Jobs with Multiple Release Time- Deadline Intervals

Article Abstract:

The problem of scheduling a number of unit-time jobs with multiple time-deadline intervals is considered. The general problem is shown to be NP-complete. A case is presented where it can be determined in polynomial time that a feasible schedule is or is not available. If available, a schedule that minimizes the maximum completion time and one that minimizes the sum of the completion times of all jobs is presented.

Algorithm Analysis, NP-Complete Problems, Execution Time

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(s,S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

Article Abstract:

A periodic review, single-item inventory system where unfilled demand is backlogged is analyzed. Lead time between placement and delivery of an order varies randomly. Results that have been derived for fixed lead times generalize easily. The infinite- horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s,S) policies.

Inventory control, Dynamic programming, Modeling, Data modeling software, Backlog, Lead Times

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