Existence theorems, lower bounds and algorithms for scheduling to meet two objectives

We give general results about the existence of schedules which simultaneously minimize two criteria. Our results are general in that (i) they apply to any scheduling environment and (ii) they apply to all pairs of metrics in which the first metric is one of maximum flow time, makespan, or maximum lateness and the second metric is one of average flow time, average completion time, average lateness, or number of on-time jobs. For most of the pairs of metrics we consider, we show the existence of near-optimal schedules for both metrics as well as some lower bound results. For some pairs of metrics such as (maximum flow time, average weighted flow time) and (maximum flow time, number of on-time jobs), we prove negative results on the ability to approximate both criteria within a constant factor of optimal. For many other criteria we present lower bounds that match or approach our bicriterion existence results.

[1]  Rakesh K. Sarin,et al.  Scheduling with multiple performance measures: the one-machine case , 1986 .

[2]  Clifford Stein,et al.  Improved bicriteria existence theorems for scheduling , 2002, SODA '99.

[3]  Ludo Gelders,et al.  Solving a bicriterion scheduling problem , 1980 .

[4]  Seiki Kyan,et al.  Worst Case Bound of an LRF Schedule for the Mean Weighted Flow-Time Problem , 1986, SIAM J. Comput..

[5]  Rajeev Motwani,et al.  Approximation techniques for average completion time scheduling , 1997, SODA '97.

[6]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[7]  Clifford Stein,et al.  On the existence of schedules that are near-optimal for both makespan and total weighted completion time , 1997, Oper. Res. Lett..

[8]  Han Hoogeveen,et al.  Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time , 1994, Oper. Res. Lett..

[9]  Michael Pinedo,et al.  Scheduling n Independent Jobs on m Uniform Machines with both Flowtime and Makespan Objectives: A Parametric Analysis , 1995, INFORMS J. Comput..

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

[11]  David B. Shmoys,et al.  Scheduling to Minimize Average Completion Time: Off-Line and On-Line Approximation Algorithms , 1997, Math. Oper. Res..

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

[13]  Han Hoogeveen.  Minimizing Maximum Promptness and Maximum Lateness on a Single Machine , 1996, Math. Oper. Res..

[14]  Cynthia A. Phillips,et al.  Minimizing average completion time in the presence of release dates , 1998, Math. Program..

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

[16]  Cynthia A. Phillips,et al.  Improved Scheduling Algorithms for Minsum Criteria , 1996, ICALP.

[17]  Éva Tardos,et al.  An approximation algorithm for the generalized assignment problem , 1993, Math. Program..

[18]  Wayne E. Smith.  Various optimizers for single‐stage production , 1956 .

[19]  Han Hoogeveen,et al.  Single-Machine Scheduling to Minimize a Function of Two or Three Maximum Cost Criteria , 1996, J. Algorithms.

[20]  April Rasala,et al.  Existence Theorems for Scheduling to Meet Two Objectives , 1999 .

[21]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .