Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review

1. Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review by John J. Kanet and V. Sridharan IE 575 Presentation by Ipek Keles

2. Introduction Inserted idle time (IIT) occurs whenever a resource is deliberately kept idle in the face of waiting jobs. Particularly relevant in multimachine industrial situations where earliness costs and/or dynamically arriving jobs with due dates come into play. Taxonomy of environments in which IIT scheduling is relevant Review the extant literature on IIT scheduling Identify areas of opportunity for future research

3. Introduction IIT schedule as a feasible schedule in which a machine is kept idle at a time when it could begin processing an operation (complement of nondelay schedules) Unnecessary to consider idle time: single machine problem, with all jobs simultaneously available for a regular performance measure (nondecreasing function of job completion times) when a preempt-resume scheduling regime is enforced (simultaneous job arrivals assumption relaxed )

4. Literature of IIT Scheduling Problems w/ a Regular Objective Function Problems w/ a Non-regular Objective Function

5. Problems w/ a Regular Objective Function Earliest known work: Giffler and Thompson (1960) limited the scope of consideration to the set of active schedule (no task’s completion time can be reduced without increasing some other task’s completion time) comprise a dominant set for scheduling situations in which the performance measure is regular focus on the static job shop scheduling problem (J| |reg) extended easily to the more general case of J | rj |reg

6. Minimizing Maximum Lateness

7. Minimizing Flow Time Related Measures

8. Minimizing Tardiness

9. improve the procedures to determine a soon-to-arrive jobs by directly applying the Giffer and Thompson specification for an active schedule PROPOSITION: Assume a machine is idle with at least one waiting job at time t. For any regular performance measure,it is unnecessary to consider inserted idle time for any job with arrival time greater than min {rj’+ pj} – t where rj’ = max{t; rj}. PROOF: Assume to the contrary, namely that some schedule S was constructed with a delay longer than min {rj’+ pj } – t. Then one could schedule the job with min {rj’+ pj } in the idle period without delaying the completion of any other job, yieldng a schedule no worse than S. redefine soon to arriving jobs obtain a smaller set faster/never permit worse solution/guarantee an active schedule

10. Minimizing Tardiness

11. Problems w/ a Nonregular Objective Function Scheduling problems in which the performance measure is not regular most obvious case is when there are penalties incurred for earliness IIT may be beneficial

12. Earliness/Tardiness Problems

13. Optimizing Procedures

14. E/T Heuristics

15. Heuristic Search

16. Heuristic Search

17. Timetabling Algorithms

18. Timetabling Algorithms

19. 3 major situations in which it may be sensible to deliberately introduce idle time into a schedule; SITUATION 1: When there is more than one processor SITUATION 2: When there are jobs with nonidentical ready times SITUATION 3: When the scheduling performance measure is nonregular Problem Taxonomy

20. Problem Taxonomy relevant problem sets are: Group 1 (1| rj |reg): Single machine, nonidentical ready times, regular performance measure. Group 2 (m| |reg): Multimachine, identical ready times, regular performance measure. Group 3 (1| |nonreg): Single machine, identical ready times, nonregular performance measure. Group 4 (m| rj |reg): Multimachine, nonidentical ready times, regular performance measure. Group 5 (m| |nonreg): Multimachine, identical ready times, nonregular performance measure. Group 6 (1| rj |nonreg): Single machine, nonidentical ready times, nonregular performance measure. Group 7 (m| rj |nonreg): Multimachine, nonidentical ready times, nonregular performance measure.

21. Problem Taxonomy

22. Problem Taxonomy

23. Research Opportunities Further research in inserted idle time scheduling: Further development of algorithms and dominance properties Integration of timetabling into search procedures Development of heuristic methods for constructing inserted idle time schedules

24. Research Opportunities Further development of algorithms and dominance properties For developing timetable procedures: When the objective function is well behaved then the algorithm of Szwarc and Mukhopadhyay (1995) could be adapted to efficiently re-timetable jobs. For more general cost functions, the available algorithm is that of Davis and Kanet (1993) with complexity O(nH). Opportunity for further development along two avenues: by exploiting the properties of a specific type of function by deployment of general line search methods In the area of complexity analysis: The unrestricted problem 1|| max {g({ Ej}), h (max {Tj})} and its variants remain open for analysis. polynomial (in n) time algorithms NP-hard problems For developing dominance properties: exploit the results of Bianco and Ricciardelli (1992) extend the work of Chu and Portmann (1992) on establishing dominance properties

25. Research Opportunities Integration of Timetabling into Search Procedures Growing knowledge in the area of advanced computer search methods for scheduling: heuristic branch and bound, simulated annealing, beamsearch, tabu search, etc. Other promising approaches: application of genetic algorithms (Kanet and Sridharan 1991 and Lee and Choi 1995) Embedding a timetabling algorithm in to genetic-based search procedure: significantly better results application of basic decision theory (Chryssolouris et al. 1988, Kanet and Zhou 1993, Sridharan and Zhou 1996a and 1996b) application of neural networks (Johnston and Adorf 1992)

26. Research Opportunities Development of Heuristics for Construction of IIT Important: IIT scheduling problems are extremely complex exact solution methods not practical Problem definition is under constant revision because of the dynamic nature of real-life scheduling environments need for quick solutions single machine tardiness problems: examine the effects of redefining soon-to-arrive jobs as suggested here and report the computational experience investigate the behavior of procedures to problems with sequence dependent set up times how idle time insertion procedures might be designed/adapted for situations when the penalty function is nonregular effects of environmental variables on the improvement on performance: utilization due date tightness/range

27. Research Opportunities Development of Heuristics for Construction of IIT On-line algorithms seem to hold the maximum potential for use all published research has focused on offline algorithms extending and improving heuristics incorporating queuing theory based busy period analysis determine the look-ahead window for nearly on-line algorithms In addition to combining hold-off and sneak-in heuristics to priority dispatching methods [Carroll (1965) and Morton and Ramnath (1992)] a decision theory approach as described by Chryssolouris et al. (1988) and Kanet and Zhou (1993) adapt to include inserted idle time as one of the alternatives