Parallel machine batching and scheduling with deadlines

Journal of Scheduling

Volumn 3, Issue 2, 2000, Pages 109-123

  Cheng, T C Edwin ^a   Kovalyov, Mikhail Y ^b  

^a HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^b UNITED INSTITUTE OF INFORMATICS PROBLEMS   (Belarus)

Author keywords

Approximation scheme; Batching; Parallel machine scheduling

Indexed keywords

EID: 0347699598     PISSN: 10946136     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1099-1425(200003/04)3:2<109::aid-jos38>3.0.co;2-0     Document Type: Article

References (36)

1. Graham R L, Lawler EL, Lenstra JK, Rinnooy AHG. Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 1979; 5:287-326.
2. Dobson G, Karmarkar US, Rummel JL. Batching to minimize flow times on one machine. Management Science 1987; 33:784-799.
3. Naddef D, Santos C. One-pass batching algorithms for the one machine problem. Discrete Applied Mathematics 1988; 21:133-145.
4. Coffman EG, Nozari A, Yannakakis M. Optimal scheduling of products with two subassemblies on a single machine. Operations Research 1989; 37:426-436.
5. Coffman EG, Yannakakis M, Magazine MJ, Santos C. Batch sizing and sequencing on a single machine. Annals of Operations Research 1990; 26:135-147.
6. Albers S, Brucker P. The complexity of one-machine batching problems. Discrete Applied Mathematics 1993; 47:87-107.
7. Shallcross DF. A polynomial algorithm for a one machine batching problem. Operations Research Letters 1992; 11:213-218.
8. Hochbaum DS, Landy D. Scheduling with batching: minimizing the weighted number of tardy jobs. Operations Research Letters 1994; 16:79-86.
9. Brucker P, Kovalyov MY. Single machine batch scheduling to minimize the weighted number of late jobs. Mathematical Methods of Operations Research 1996; 43:1-8.
10. Webster S, Baker KR. Scheduling groups of jobs on a single machine. Operations Research 1995; 4:692-703.
11. Cheng TCE, Gordon VS. Batch delivery scheduling on a single machine. Journal of the Operational Research Society 1994; 45:1211-1215.
12. Cheng TCE, Kahlbacher HG. Scheduling with delivery and earliness penalties. Asia-Pacific Journal of Operational Research 1993; 10:145-152.
13. Cheng TCE, Gordon VS, Kovalyov MY. Single machine scheduling with batch deliveries. European Journal of Operational Research 1996; 94:277-283.
14. Cheng TCE, Kovalyov MY, Lin BMT. Single machine scheduling to minimize batch delivery and job earliness penalties. SI AM Journal on Optimization 1997; 7:547-559.
15. Potts CN, Van Wassenhove LN. Integrating scheduling with batching and lot-sizing: a review of algorithms and complexity. Journal of the Operational Research Society 1992; 43:395-406.
16. Potts CN, Kovalyov MY. Scheduling with batching: a review. European Journal of Operational Research 1999; 120:228-249.
17. Monma CL, Potts CN. On the complexity of scheduling with batch set-up times. Operations Research 1989; 37:798-804.
18. Ghosh JB. Batch scheduling to minimize total completion time. Operations Research Letters 1994; 16:271-275.
19. Brucker P, Kovalyov MY, Shafransky YM, Werner F. Parallel machine batch scheduling with deadlines and sequence independent set-uptimes. Annals of Operations Research 1998; 83:393-404.
20. Cheng TCE, Chen ZL, Kovalyov MY, Lin BMT. Parallel-machine batching and scheduling to minimize total completion time. IIE Transactions 1997; 28:953-956.
21. Garey MR, Johnson DS. Computers and Intractability. A Guide to the Theory of NP-Completeness. W.H. Freeman and Co: San Francisco, 1979.
22. Barat LG. Linear functions on N-dimensional unit cube. Doklady Akademii Nauk SSSR 1975; 222(4):761-762.
23. Ibarra OH, Kim CE. Fast approximation algorithms for the knapsack and sum of subset problems. Journal of the Association for Computing Machinery 1975; 22:463-468.
24. Sahni S. Algorithms for scheduling independent tasks. Journal of the Association for Computing Machinery 1976; 23:116-127.
25. Sahni S. General techniques for combinatorial approximation. Operations Research 1977; 25:920-936.
26. Horowitz E, Sahni S. Exact and approximate algorithms for scheduling nonidentical processors, Journal of the Association for Computing Machinery 1976; 23:317-327.
27. Gens GV, Levner EV. Fast approximation algorithms for job sequencing with deadlines. Discrete Applied Mathematics 1981; 3:313-318.
28. Lawler EL. A fully polynomial approximation scheme for the total tardiness problem. Operations Research Letters 1982; 1:207-208.
29. Kovalyov MY, Shafransky YM, Strusevich VA, Tanaev VS, Tuzikov AV. Approximation scheduling algorithms: a survey. Optimization 1990; 20:859-878.
30. Hochbaum DS, Shmoys DB. Using dual approximation algorithms for scheduling problems: theoretical and practical results. Journal of the Association for Computing Machinery 1987; 34:144-162.
31. Hochbaum DS, Shmoys DB. A polynomial approximation scheme for machine scheduling on uniform processors: using the dual approximating approach. SI AM Journal on Computing 1988; 17:539-551.
32. Hall LA, Shmoys DB. Approximation schemes for constrained scheduling problems. Proceedings of IEEE 30th Annual Symposium on the Foundations of Computer Science, 1989.
33. Chen B, Potts CN, Woeginger GJ. A review of machine scheduling: complexity, algorithms and approximability. In Handbooks of Combinatorial Optimization, Du DZ, Pardalos PM (eds). Kluwer Academic Publishers: Dordrecht, 1998; 21-169.
34. Kovalyov MY, Potts CN, Van Wassenhove LN. A fully polynomial approximation scheme for scheduling a single machine to minimize total weighted late work. Mathematics of Operations Research 1994; 19:86-93.
35. Kovalyov MY. A rounding technique to construct approximation algorithms for knapsack and partition type problems. Applied Mathematics and Computer Science 1996; 6:101-113.
36. Dessouky MI, Lageweg BJ, Lenstra JK, Van De Velde SL. Scheduling identical jobs on uniform parallel machines. Statistica Neerlandica 1990; 44:115-123.