A unified approach for scheduling with convex resource consumption functions using positional penalties

European Journal of Operational Research

Volumn 206, Issue 2, 2010, Pages 301-312

  Leyvand, Yaron ^a   Shabtay, Dvir ^a   Steiner, George ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b MCMASTER UNIVERSITY   (Canada)

Author keywords

Controllable processing times; Due date assignment; Polynomial time algorithm; Positional penalties; Resource allocation; Single machine scheduling

Indexed keywords

CONTROLLABLE PROCESSING TIME; DUE-DATE ASSIGNMENT; POLYNOMIAL-TIME ALGORITHM; POLYNOMIAL-TIME ALGORITHMS; SINGLE-MACHINE SCHEDULING;

COMPUTER RESOURCE MANAGEMENT; GROUP TECHNOLOGY; MACHINERY; POLYNOMIAL APPROXIMATION; RESOURCE ALLOCATION; SCHEDULING ALGORITHMS; TRAVELING SALESMAN PROBLEM;

PROBLEM SOLVING;

EID: 77950371029     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2010.02.026     Document Type: Article

References (46)

1. Adamopoulos G.I., and Pappis C.P. Single machine scheduling with flow allowances. J. Oper. Res. Soc. 47 (1996) 1280-1285
2. Alidaee B., and Ahmadian A. Two parallel machine sequencing problems involving controllable job processing times. Eur. J. Oper. Res. 70 (1993) 335-341
3. Armstrong R., Gu S., and Lei L. An algorithm for the two-resource allocation problem with a non-differentiable convex objective function. J. Oper. Res. Soc. 46 (1995) 116-122
4. Armstrong R., Gu S., and Lei L. Solving a class of two-resource allocation problems by equivalent load method. J. Oper. Res. Soc. 48 (1997) 818-825
5. Bagchi U.B. Simultaneous minimization of mean and variation of flow time and waiting time in single machine systems. Oper. Res. 37 (1989) 118-125
6. Biskup D., and Cheng T.C.E. Single machine scheduling with controllable processing times and earliness, tardiness and completion time penalties. Eng. Optim. 31 (1999) 329-336
7. Biskup D., and Jahnke H. Common due date assignment for scheduling on a single machine with jointly reducible processing times. Int. J. Prod. Econ. 69 (2001) 317-322
8. Cheng T.C.E., Oǧaz C., and Qi X.D. Due date assignment and single machine scheduling with compressible processing times. Int. J. Prod. Econ. 43 (1996) 29-35
9. Cheng T.C.E., and Janiak A. A permutation flow-shop scheduling problem with convex models of operation processing times. Ann. Oper. Res. 96 (2000) 39-60
10. Cheng T.C.E., Kovalyov M.Y., and Shakhlevich N. Scheduling with controllable release dates and processing times: Total completion time minimization. Eur. J. Oper. Res. 175 (2006) 769-781
11. De P., Ghosh J.B., and Wells C.E. Optimal delivery time quotation and order sequencing. Decis. Sci. 22 (1991) 379-390
12. Gordon V., Proth J.M., and Chu C.B. A survey of the state-of-the-art of common due date assignment and scheduling research. Eur. J. Oper. Res. 139 (2002) 1-25
13. Gordon V., Proth J.M., and Chu C.B. Due date assignment and scheduling: SLK, TWK and other due date assignment models. Prod. Planning Control 13 2 (2002) 117-132
14. Gordon V., Proth J.M., and Strusevich V.A. Scheduling with due date assignment. In: Leung J.Y.-T. (Ed). Handbook of Scheduling (2004), CRC Press, Boca Raton, FL 21-1-21-22
15. Graham R.L., Lawler E.L., Lenstra J.K., and Rinnooy Kan A.H.G. Optimization and approximation in deterministic sequencing and scheduling: A survey. Ann. Discrete Math. 3 (1979) 287-326
16. Hoogeveen H., and Woeginger G.J. Some comments on sequencing with controllable processing times. Computing 68 (2002) 181-192
17. Kahlbacher H.G., and Cheng T.C.E. Parallel machine scheduling to minimize costs for earliness and number of tardy jobs. Discrete Appl. Math. 47 (1993) 139-164
18. Kaminsky P., and Hochbaum D. Due date quotation models and algorithms. In: Leung J.Y.-T. (Ed). Handbook of Scheduling (2004), CRC Press, Boca Raton, FL 20-1-20-22
19. Kanet J.J. Minimizing variation of flow time in single machine systems. Manage. Sci. 27 12 (1981) 1453-1459
20. Janiak A. One-machine scheduling with allocation of continuously-divisible resource and with no precedence constraints. Kybernetika 23 4 (1987) 289-293
21. A. Janiak, Selected problems and algorithms for task scheduling and resource allocation, in Problemy Wspolczesnej Nauki, Teoria i Zastosowania-Informatyka, Akad, Oficyna Wydawnicza PLJ, Warszawa, 1999, (in Polish).
22. Janiak A., and Kovalyov M.Y. Single machine scheduling subject to deadlines and resource-dependent processing times. Eur. J. Oper. Res. 94 (1996) 284-291
23. Liman S.D., Panwalkar S.S., and Thongmee S. A single machine scheduling problem with common due window and controllable processing times. Ann. Oper. Res. 70 (1997) 145-154
24. Liman S.D., Panwalkar S.S., and Thongmee S. Common due window size and location determination in a single machine scheduling problem. J. Oper. Res. Soc. 49 (1998) 1007-1010
25. Monma C.L., Schrijver A., Todd M.J., and Wei V.K. Convex resource allocation problems on directed acyclic graphs: Duality, complexity special cases and extensions. Math. Oper. Res. 15 (1990) 736-748
26. Ng C.T.D., Cheng T.C.E., Kovalyov M.Y., and Lam S.S. Single machine scheduling with a variable common due date and resource-dependent processing times. Comput. Oper. Res. 30 (2003) 1173-1185
27. Ng C.T.D., Cheng T.C.E., Janiak A., and Kovalyov M.Y. Group scheduling with controllable setup and processing times: Minimizing total weighted completion time. Ann. Oper. Res. 133 (2005) 163-174
28. Nowicki E., and Zdrzalka S. A survey of results for sequencing problems with controllable processing times. Discrete Appl. Math. 26 (1990) 271-287
29. Papadimitriou C.H., and Steiglitz K. Combinatorial Optimization: Algorithms and Complexity (1982), Prentice-Hall, Englewood Cliffs, NJ
30. Panwalkar S.S., Smith M.L., and Seidmann A. Common due date assignment to minimize total penalty for the one machine scheduling problem. Oper. Res. 30 (1982) 391-399
31. Panwalkar S.S., and Rajagopalan R. Single machine sequencing with controllable processing times. Eur. J. Oper. Res. 59 (1992) 298-302
32. Scott S.C., and Jefferson T.R. Allocation of resources in project management. Int. J. Syst. Sci. 26 2 (1995) 413-420
33. Seidmann A., Panwalkar S.S., and Smith M.L. Optimal assignment of due dates for a single processor scheduling problem. Int. J. Prod. Res. 19 (1981) 393-399
34. Shabtay D. Single and a two-resource allocation algorithms for minimizing the maximal lateness in a single machine scheduling problem. Comput. Oper. Res. 31 8 (2004) 1303-1315
35. Shabtay D., and Kaspi M. Minimizing the total weighted flow time in a single machine with controllable processing times. Comput. Oper. Res. 31 13 (2004) 2279-2289
36. D. Shabtay, G. Steiner, The earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times, in: Proc. of the MISTA 2005 Conference, New York, NY, 2005, pp. 149-161.
37. Shabtay D., and Steiner G. Two due date assignment problems in scheduling a single machine. Oper. Res. Lett. 34 (2006) 683-691
38. Shabtay D., and Steiner G. Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine. Manuf. Serv. Oper. Manage. 9 3 (2007) 332-350
39. Shabtay D., and Steiner G. A survey of scheduling with controllable processing times. Discrete Appl. Math. 155 13 (2007) 1643-1666
40. Shakhlevich N.V., and Strusevich V.A. Pre-emptive scheduling problems with controllable processing times. J. Scheduling 8 (2005) 233-253
41. Shakhlevich N.V., and Strusevich V.A. Single machine scheduling with controllable release and processing parameters. Discrete Appl. Math. 154 (2006) 2178-2199
42. Trick M. Scheduling multiple variable-speed machines. Oper. Res. 42 (1994) 234-248
43. Vickson R.G. Two single machine sequencing problems involving controllable job processing times. AIIE Trans. 12 3 (1980) 258-262
44. Wang J.B., and Xia Z.Q. Single machine scheduling problems with controllable processing times and total absolute differences penalties. Eur. J. Oper. Res. 177 (2007) 638-645
45. In: Williams T.J. (Ed). Analysis and Design of Hierarchical Control Systems: With Special Reference to Steel Plant Operations (1986), North Holland, Amsterdam
46. Yedidsion L., Shabtay D., and Kaspi M. A bicriterion approach to maximal lateness and resource consumption in scheduling with convex resource-dependent processing times. J. Scheduling 10 6 (2007) 341-352