Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.

/pdf/stochastic-programming-approaches-to-stochastic-scheduling-32us4zr4g0.pdf

Single Machine Scheduling Subject to Random Breakdowns.

Stochastic Programming Approaches to Stochastic Scheduling

Optimal match-up strategies in stochastic scheduling

We present a scheduling heuristic for the stochastic job shop. In a stochastic job shop, operation processing times may vary randomly, or machines may fail at random intervals, or both. Dispatching rules based on substituting expected values for random quantities are often used for scheduling in this uncertain environment. The scheduling heuristic we propose performs restricted dynamic updating of an initial schedule for the shop, using limited distribution information about the random quantities. In particular, we allow general dependence among the stochastic quantities and require at most two moments of each distribution function. Our objective is to minimize expected tardiness. We investigate the benefits of the scheduling heuristic versus a dispatching rule using a simulation study.

/pdf/using-second-moment-information-in-stochastic-scheduling-4blwnkcpqq.pdf

Single Machine Scheduling Subject to Random Breakdowns.

Citations

Stochastic Programming Approaches to Stochastic Scheduling

Optimal match-up strategies in stochastic scheduling

Using second moment information in stochastic scheduling

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