Scheduling with stochastic gert precedence constraints
Single-machine and parallel-machine scheduling problems with stochastic task duration times are considered where the precedence constraints are given by a stochastic project network (GERT network). We present some complexity results as well as exact and heuristic algorithms. First we discuss single-machine problems with generally distributed task durations and so-called OR networks (GERT networks having some tree structure) as precedence constraints. If the expected weighted flow time is to be minimized, an optimal scheduling policy can be computed in polynomial time. If we restrict ourselves to so-called precedence schedules instead of general scheduling policies, there is a polynomial algorithm for minimizing the maximum expected lateness. Single-machine min-sum scheduling problems with general GERT precedence constraints can be reduced to problems of stochastic dynamic programming. All GERT scheduling problems for several identical parallel machines seem to be NP-hard. Even the computation of the objective function value for a given schedule is in general NP-hard. To obtain heuristic schedule construction procedures for min-sum and min-max problems, some algorithms can be generalized that solve corresponding deterministic scheduling problems.
- OSTI ID:
- 36340
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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