Using second moment information 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.

[1]  R. A. Blau.  N-Job, One Machine Sequencing Problems Under Uncertainty , 1973 .

[2]  James C. Bean,et al.  Matchup Scheduling with Multiple Resources, Release Dates and Disruptions , 1991, Oper. Res..

[3]  Kevin D. Glazebrook,et al.  On stochastic scheduling problems with due dates , 1983 .

[4]  A.H.G. Rinnooy Kan,et al.  Single‐machine scheduling subject to stochastic breakdowns , 1990 .

[5]  Michael Pinedo,et al.  Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions , 1980, Journal of Applied Probability.

[6]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[7]  Gideon Weiss,et al.  Stochastic scheduling problems I — General strategies , 1984, Z. Oper. Research.

[8]  Kevin D. Glazebrook,et al.  Sensitivity Analysis for Stochastic Scheduling Problems , 1987, Math. Oper. Res..

[9]  Kevin D. Glazebrook,et al.  Evaluating the effects of machine breakdowns in stochastic scheduling problems , 1987 .

[10]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[11]  James C. Bean,et al.  Match-up real-time scheduling , 1985 .

[12]  John R. Birge,et al.  Bounds on Expected Project Tardiness , 1995, Oper. Res..

[13]  William T. Ziemba,et al.  Short Term Financial Planning under Uncertainty , 1982 .

[14]  Ari P. J. Vepsalainen.  Priority rules for job shops with weighted tardiness costs , 1987 .

[15]  Kevin D. Glazebrook,et al.  Scheduling stochastic jobs on a single machine subject to breakdowns , 1984 .

[16]  Franz Josef Radermacher,et al.  Preselective strategies for the optimization of stochastic project networks under resource constraints , 1983, Networks.

[17]  John R. Birge.  Real-Time Adaptive Scheduling in Flexible Manufacturing Systems , 1989 .

[18]  Roger J.-B. Wets,et al.  Stochastic Programming: Solution Techniques and Approximation Schemes , 1982, ISMP.

[19]  Gideon Weiss,et al.  Stochastic scheduling problems II-set strategies- , 1985, Z. Oper. Research.

[20]  R. Wets,et al.  Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse , 1986 .

[21]  Stephen C. Graves,et al.  A Review of Production Scheduling , 1981, Oper. Res..

[22]  A. G. Lockett,et al.  Job shop scheduling heuristics and frequency of scheduling , 1982 .

[23]  Franz Josef Radermacher,et al.  Algorithmic approaches to preselective strategies for stochastic scheduling problems , 1983, Networks.