Beyond Smith's Rule: An Optimal Dynamic Index, Rule for Single Machine Stochastic Scheduling with Convex Holding Costs

Universitat Pompeu Fabra Economics and Business Working Paper No. 514

21 Pages Posted: 29 Jun 2001

See all articles by José Niño Mora

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Date Written: November 12, 2000

Abstract

We study a model for scheduling 'n' classes of stochastic jobs on a single machine, with the objective of minimizing the total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable, nondecreasing and convex on the number of jobs in each class. We formulate the problem as a linear program over a certain greedoid polytope, and establish that it is solved optimally by a dynamic (priority) index rule, which extends the classical Smith's rule (1956) for the linear case.

Keywords: Stochastic scheduling, dynamic index rule, decomposition, convex holding costs, conservation laws, achievable region, linear programming relaxation, polyhedral methods.

JEL Classification: C60, C61

Suggested Citation

Niño Mora, José, Beyond Smith's Rule: An Optimal Dynamic Index, Rule for Single Machine Stochastic Scheduling with Convex Holding Costs (November 12, 2000). Universitat Pompeu Fabra Economics and Business Working Paper No. 514, Available at SSRN: https://ssrn.com/abstract=273398 or http://dx.doi.org/10.2139/ssrn.273398

José Niño Mora (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 26 73 (Phone)
(34-3) 542 17 46 (Fax)

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