Heuristic procedures for parallel-machine schedulingproblems with stochastic precedence constraints

This paper is concerned with stochastic scheduling problems with several identical parallel machines, where the task durations and precedence constraints are stochastic. The stochastic precedence constraints are given by special GERT networks. At first, basic concepts and results are surveyed for GERT networks and for single-machine and parallel-machine scheduling with GERT network precedence constraints. An example shows where GERT scheduling problems occur in practice. After that, two types of heuristics for identical parallel-machine GERT scheduling problems with objective functions E(Cmax), maxE(C),and E(∑ C) are proposed: generalizations of algorithms for corresponding deterministic scheduling problems and so-called priority-rule methods. An empirical analysis shows the best heuristics for each of the objective functions considered.

[1]  W. A. Horn.  Single-Machine Job Sequencing with Treelike Precedence Ordering and Linear Delay Penalties , 1972 .

[2]  Bruce L. Golden,et al.  A decision-theoretic framework for comparing heuristics , 1984 .

[3]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[4]  Esther Frostig,et al.  A Stochastic Scheduling Problem with Intree Precedence Constraints , 1988, Oper. Res..

[5]  Panos M. Pardalos,et al.  A branch and bound algorithm for the maximum clique problem , 1992, Comput. Oper. Res..

[6]  Rolf H. Möhring,et al.  Introduction to Stochastic Scheduling Problems , 1985 .

[7]  K. Neumann,et al.  GERT networks and the time-oriented evaluation of projects , 1979 .

[8]  M. Fujii,et al.  Optimal Sequencing of Two Equivalent Processors , 1969 .

[9]  T. C. Hu.  Parallel Sequencing and Assembly Line Problems , 1961 .

[10]  Klaus Neumann,et al.  Algorithms for single-machine scheduling with stochastic outtree precedence relations to minimize expected weighted flow time or maximum expected lateness , 1994, Math. Methods Oper. Res..

[11]  Kevin Mahon,et al.  Deterministic and Stochastic Scheduling , 1983 .

[12]  Michael Pinedo,et al.  Scheduling Jobs with Exponentially Distributed Processing Times and Intree Precedence Constraints on Two Parallel Machines , 1985, Oper. Res..

[13]  Klaus Neumann,et al.  Stochastic Project Networks , 1990 .

[14]  J.M. Schopf,et al.  Stochastic Scheduling , 1999, ACM/IEEE SC 1999 Conference (SC'99).

[15]  Eugene L. Lawler,et al.  Optimal Sequencing of a Single Machine Subject to Precedence Constraints , 1973 .

[16]  Matthias Bücker.  Time complexity of single machine scheduling with stochastic precedence constraints , 1992, ZOR Methods Model. Oper. Res..