Response time variability

Response time variability is a new optimization problem with a broad range of applications and a distinctive number of theoretic flavour. The problem occurs whenever events, jobs, clients or products need to be sequenced so as to minimize the variability of time for which they wait for the next turn in obtaining the resources necessary for their advance. The problem has numerous real-life applications. We study its computational complexity, present efficiency, polynomial time algorithms for some cases, and the NP-hardness proof for a general problem. We propose a position exchange heuristic and apply it to improve the total response time variability of an initial sequence. The latter is the optimum bottleneck sequence, Webster or Jefferson sequence of the apportionment, or a random sequence. We report on computational experiments with the heuristic.

[1]  A. Grigoriev,et al.  High multiplicity scheduling problems , 2003 .

[2]  Wieslaw Kubiak,et al.  On small deviations conjecture , 2003 .

[3]  W. Kubiak.  Minimizing variation of production rates in just-in-time systems: A survey☆ , 1993 .

[4]  Natalia Moreno Palli.  Solving the product rate variation problem (prvp= of large dimensions as an assignment problem) , 2002 .

[5]  Joaquín Bautista,et al.  A Note on the Relation between the Product Rate Variation (PRV) Problem and the Apportionment Problem , 1996 .

[6]  Eitan Altman,et al.  Multimodularity, Convexity, and Optimization Properties , 2000, Math. Oper. Res..

[7]  Carl A. Waldspurger,et al.  Stride Scheduling: Deterministic Proportional- Share Resource Management , 1995 .

[8]  S. Sethi,et al.  A Note on "Level Schedules for Mixed-Model Assembly Lines in Just-in-Time Production Systems" , 1991 .

[9]  Randeep Bhatia,et al.  Minimizing service and operation costs of periodic scheduling , 2002, SODA '98.

[10]  John B. Kidd,et al.  Toyota Production System , 1993 .

[11]  Jennifer C. Hou,et al.  Distance-Constrained Scheduling and Its Applications to Real-Time Systems , 1996, IEEE Trans. Computers.

[12]  M. Resende,et al.  A probabilistic heuristic for a computationally difficult set covering problem , 1989 .

[13]  G. Steiner,et al.  Level Schedules for Mixed-Model, Just-in-Time Processes , 1993 .

[14]  J. Miltenberg,et al.  Level schedules for mixed-model assembly lines in just-in-time production systems , 1989 .

[15]  Alexander Grigoriev,et al.  On the complexity of high multiplicity scheduling problems , 2001 .

[16]  Alexander Grigoriev,et al.  A Framework for the Complexity of High-Multiplicity Scheduling Problems , 2005, J. Comb. Optim..

[17]  Celia A. Glass,et al.  The Scheduling of Maintenance Service , 1998, Discret. Appl. Math..

[18]  Joaquín Bautista,et al.  Modelling and solving the production rate variation problem (PRVP) , 1997 .

[19]  Rami G. Melhem,et al.  Time slot allocation for real-time messages with negotiable distance constraints , 1998, Proceedings. Fourth IEEE Real-Time Technology and Applications Symposium (Cat. No.98TB100245).