Stochastic Shop Scheduling: A Survey

In this paper a survey is made of some of the recent results in stochastic shop scheduling. The models dealt with include: (i) Open shops. (ii) Flow shops with infinite intermediate storage (permutation flow shops). (iii) Flow shops with zero intermediate storage and blocking. (iv) Job shops. Two objective functions are considered: Minimization of the expected completion time of the last job, the so-called makespan, and minimization of the sum of the expected completion times of all jobs, the so-called flow time. The decision-maker is not allowed to preempt. The shop models with two machines and exponentially distributed processing times usually turn out to have a very nice structure. Shop models with more than two machines are considerably harder.

[1]  C. V. Ramamoorthy,et al.  On the Flow-Shop Sequencing Problem with No Wait in Process † , 1972 .

[2]  P C Bagga.  N-JOB, 2-MACHINE SEQUENCING PROBLEM WITH STOCHASTIC SERVICE TIMES , 1970 .

[3]  James R. Jackson,et al.  An extension of Johnson's results on job IDT scheduling , 1956 .

[4]  Michael Pinedo.  On the Optimal Order of Stations in Tandem Queues , 1982 .

[5]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[6]  Michael Pinedo,et al.  Minimizing the Expected Makespan in Stochastic Flow Shops , 1982, Oper. Res..

[7]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..

[8]  Sheldon M. Ross,et al.  Minimizing expected makespan in stochastic open shops , 1982, Advances in Applied Probability.

[9]  Michael Pinedo.  A note on the two machine job shop with exponential processing times , 1981 .

[10]  R. Weber.  THE INTERCHANGEABILITY OF -/M/1 QUEUES IN SERIES , 1979 .

[11]  Teofilo F. Gonzalez,et al.  Open Shop Scheduling to Minimize Finish Time , 1976, JACM.

[12]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[13]  D. A. Wismer,et al.  Solution of the Flowshop-Scheduling Problem with No Intermediate Queues , 1972, Oper. Res..

[14]  B. Avi-Itzhak,et al.  A SEQUENCE OF SERVICE STATIONS WITH ARBITRARY INPUT AND REGULAR SERVICE TIMES , 1965 .

[15]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .