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
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: Suggested Citation