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Multicriteria scheduling problems: a survey

Published online by Cambridge University Press:  15 August 2002

V. T'kindt  and
J.-C. Billaut
V. T'kindt
Affiliation:
Laboratoire d'Informatique, École d'Ingénieurs en Informatique pour l'Industrie, 64 avenue Jean Portalis, 37200 Tours, France; tkindt@e3i.univ-tours.fr.
J.-C. Billaut
Affiliation:
Laboratoire d'Informatique, École d'Ingénieurs en Informatique pour l'Industrie, 64 avenue Jean Portalis, 37200 Tours, France; billaut@e3i.univ-tours.fr.
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Abstract

This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing notation for scheduling problems is proposed for multicriteria scheduling problems. Then, basic results from the literature on multicriteria optimization are presented. These results are used to build the final scheduling problem to solve. Finally a survey is presented for one-machine, parallel machines and flowshop multicriteria scheduling problems.

Keywords

Schedulingmulticriteria optimizationstate-of-the-art.
Type
Research Article
Information
RAIRO - Operations Research , Volume 35 , Issue 2: ROADEF'99 , April 2001 , pp. 143 - 163
Copyright
© EDP Sciences, 2001

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References

Adamopoulos, G. and Pappis, C., Scheduling jobs with different job-dependent earliness and tardiness penalties using the SLK method. Eur. J. Oper. Res. 88 (1996) 336-344. CrossRef
Ahmed, M. and Sundararaghavan, P., Minimizing the weighted sum of late and early completion penalties in a single machine. IEEE Trans. 22 (1990) 288-290. CrossRef
D. Alcaide, J. Riera and J. Sicilia, An approach to solve bicriterion flow-shop scheduling problems, in Proc. of the 6th International Workshop on Project Management and Scheduling (PMS'98). Istanbul, Turkey (1998) 151-154.
Alidaee, B. and Ahmadian, A., Two parallel machine sequencing problems involving controllable job processing times. Eur. J. Oper. Res. 70 (1993) 335-341. CrossRef
M. Azizoglu, S.K. Kondakci and M. Koksalan, Bicriteria scheduling: Minimizing flowtime and maximum earliness on a single machine, edited by J. Climaco, Multicriteria Analysis. Springer-Verlag (1997) 279-288.
Azizoglu, M. and Webster, S., Scheduling job families about an unrestricted common due date on a single machine. Internat. J. Production Res. 35 (1997) 1321-1330. CrossRef
Bagchi, U., Chang, Y.-L. and Sullivan, R., Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date. Naval Res. Logist. 34 (1987) 739-751. 3.0.CO;2-3>CrossRef
Bagchi, U., Sullivan, R. and Chang, Y.-L., Minimizing mean absolute deviation of completion times about a common due date. Naval Res. Logist. Quarterly 33 (1986) 227-240. CrossRef
Bagchi, U., Sullivan, R. and Chang, Y.-L., Minimizing mean squared deviation of completion times about a common due date. Management Sci. 33 (1987) 894-906. CrossRef
Bansal, S., Single machine scheduling to minimize weighted sum of completion times with secondary criterion - a branch and bound approach. Eur. J. Oper. Res. 5 (1980) 177-181. CrossRef
Barnes, J. and Vanston, L., Scheduling jobs with linear delay penalties and sequence dependent setup costs. Oper. Res. 29 (1981) 146-160. CrossRef
Bector, C., Gupta, Y. and Gupta, M., Determination of an optimal common due date and optimal sequence in a single machine job shop. Internat. J. Production Res. 26 (1988) 613-628. CrossRef
J.-C. Billaut, V. T'kindt, P. Richard and C. Proust, Three exact methods and an efficient heuristic for solving a bicriteria flowshop scheduling problem, in Multiconference on Computational Engineering in Systems Applications (CESA 98), Symposium on Industrial and Manufacturing Systems, IEEE-SMC/IMACS. Nabeul-Hammamet, Tunisia (1998) 371-377.
J. Blazewicz, K. Ecker, E. Pesch, G. Schmidt and J. Weglarz, Scheduling computer and manufacturing processes. Springer-Verlag (1996).
Bourgade, V., Aguilera, L., Penz, B. and Binder, Z., Problème industriel d'ordonnancement bicritère sur machine unique : modélisation et aide à la décision. APII 29 (1995) 331-341.
V. Bowman, On the relationship of the tchebycheff norm and the efficient frontier of multiple-criteria objectives, edited by H. Thiriez and S. Zionts, Multiple Criteria Decision Making. Springer-Verlag (1976) 76-85.
Burns, R., Scheduling to minimize the weighted sum of completion times with secondary criteria. Naval Res. Logist. Quarterly 23 (1976) 125-129. CrossRef
S. Chand and H. Schneeberger, Single machine scheduling to minimize weighted completion time with maximum allowable tardiness, Research report. University of Purdue (1984).
Chand, S. and Schneeberger, H., A note on the single machine scheduling problem with minimum weighted completion time and maximum allowable tardiness. Naval Res. Logist. Quarterly 33 (1986) 551-557. CrossRef
Chand, S. and Schneeberger, H., Single machine scheduling to minimize weighted earliness subject to no tardy jobs. Eur. J. Oper. Res. 34 (1988) 221-230. CrossRef
Chen, C.-L. and Bulfin, R., Scheduling unit processing time jobs on a single machine with multiple criteria. Comput. Oper. Res. 17 (1990) 1-7. CrossRef
Chen, C.-L. and Bulfin, R., Complexity of single machine, multi-criteria scheduling problems. Eur. J. Oper. Res. 70 (1993) 115-125. CrossRef
C.-L. Chen and R. Bulfin, Complexity of multiple machines, multi-criteria scheduling problems, in 3rd Industrial Engineering Research Conference (IERC'94). Atlanta, USA (1994) 662-665.
Chen, Z.-L., Scheduling and common due date assignment with earliness and tardiness penalties and batch delivery costs. Eur. J. Oper. Res. 93 (1996) 49-60. CrossRef
Cheng, T. and Chen, Z.-L., Parallel-machine scheduling problems with earliness and tardiness penalties. J. Oper. Res. Soc. 45 (1994) 685-695. CrossRef
Daniels, R. and Chambers, R., Multiobjective flow-shop scheduling. Naval Res. Logist. 37 (1990) 981-995. 3.0.CO;2-H>CrossRef
Dileepan, P. and Sen, T., Bicriterion static scheduling research for a single machine. Omega 16 (1998) 53-59. CrossRef
Dileepan, P. and Sen, T., Bicriterion jobshop scheduling with total flowtime and sum of squared lateness. Engrg. Costs and Production Economics 21 (1991) 295-299. CrossRef
M. Ehrgott, Multiple Criteria Optimization: Classification and Methodology, Ph.D. Thesis. University of Kaiserslautern, Germany, in English (1997).
Emmons, H., A note on a scheduling problem with dual criteria. Naval Res. Logist. Quarterly 22 (1975) 615-616. CrossRef
Emmons, H., One machine sequencing to minimize mean flow time with minimum number tardy. Naval Res. Logist. Quarterly 22 (1975) 585-592. CrossRef
Emmons, H., Scheduling to a common due date on parallel uniform processors. Naval Res. Logist. 34 (1987) 803-810. 3.0.CO;2-2>CrossRef
Evans, G., An overview of techniques for solving multiobjective mathematical programs. Management Sci. 30 (1984) 1268-1282. CrossRef
Fry, T., Armstrong, R. and Blackstone, R., Minimizing weighted absolute deviation in single machine scheduling. IEEE Trans. 19 (1987) 445-450. CrossRef
Fry, T., Armstrong, R. and Lewis, H., A framework for single machine multiple objective sequencing research. Omega 17 (1989) 595-607. CrossRef
Fry, T. and Blackstone, R., Planning for idle time: A rationale for underutilization of capacity. Int. J. Prod. Res. 26 (1988) 1853-1859. CrossRef
Fry, T. and Leong, G., Bi-criterion single-machine scheduling with forbidden early shipments. Engrg. Costs and Production Sci. 10 (1986) 133-137. CrossRef
Fry, T. and Leong, G., A bi-criterion approach to minimizing inventory costs on a single machine when early shipments are forbidden. Comput. Operat. Res. 14 (1987) 363-368. CrossRef
Fry, T., Leong, G. and Rakes, T., Single machine scheduling: A comparison of two solution procedures. Omega 15 (1987) 277-282. CrossRef
Gangadharan, R. and Rajendran, C., A simulated annealing heuristic for scheduling in a flowshop with bicriteria. Comput. Industrial Engrg. 27 (1994) 473-476. CrossRef
Garey, M., Tarjan, R. and Wilfong, G., One-processor scheduling with symmetric earliness and tardiness penalties. Math. Oper. Res. 13 (1988) 330-348. CrossRef
F. Gembicki, Vector Optimization for Control with Performance and Parameter Sensitivity Indices, Ph.D. Thesis. Case Western Reserve University, Cleveland, USA (1973).
Geoffrion, A., Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22 (1968) 618-630. CrossRef
Gupta, J., Ho, J. and VanderVeen, A., Single machine hierarchical scheduling with customer orders and multiple job classes. Ann. Oper. Res. 70 (1997) 127-143. CrossRef
J. Gupta, V. Neppalli and F. Werner, Minimizing total flow time in a two-machine flowshop problem with minimum makespan. Internat. J. Production Economics (to appear).
Gupta, S. and Sen, T., Minimizing a quadratic function of job lateness on a single machine. Engrg. Costs and Production Economic 7 (1983) 187-194. CrossRef
Y. Haimes, L. Ladson and D. Wismer, On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Systems, Man and Cybernetics 1 (1971) 296-297.
Heck, H. and Roberts, S., A note on the extension of a result on scheduling with secondary criteria. Naval Res. Logist. Quarterly 19 (1972) 4. CrossRef
J. Hoogeveen, Single-Machine Bicriteria Scheduling, Ph.D. Thesis. CWI Amsterdam (1992).
Hoogeveen, J. and VandeVelde, S., Minimizing total completion time and maximum cost simultaneously is solvable in polynomial time. Oper. Res. Lett. 17 (1995) 205-208. CrossRef
John, T., Tradeoff solutions in single machine production scheduling for minimizing flow time and maximum penalty. Comput. Oper. Res. 16 (1984) 471-479. CrossRef
Kanet, J., Minimizing the average deviation of job completion times about a common due date. Naval Res. Logist. Quarterly 28 (1981) 643-651. CrossRef
S. Kondakci, E. Emre and M. Koksalan, Scheduling of unit processing time jobs on a single machine, edited by G. Fandel and T. Gal, Multiple Criteria Decision Making. Springer-Verlag, Lecture Notes in Econom. and Math. Systems (1997) 654-660.
Koulamas, C., Single-machine scheduling with time windows and earliness/tardiness penalties. Eur. J. Oper. Res. 91 (1996) 190-202. CrossRef
Lakshminarayan, S., Lakshmanan, R., Papineau, R. and Rochette, R., Optimal single-machine scheduling with earliness and tardiness penalties. Oper. Res. 26 (1978) 1079-1082. CrossRef
C.-Y. Lee and G. Vairaktarakis, Complexity of single machine hierarchical scheduling: A survey, edited by P.M. Pardalos, Complexity in Numerical Optimization. World Scientific Publishing Co. (1993) 269-298.
Leung, J.-T. and Young, G., Minimizing schedule length subject to minimum flow time. SIAM J. Comput. 18 (1989) 314-326. CrossRef
Li, C.-L. and Cheng, T., The parallel machine min-max weighted absolute lateness scheduling problem. Naval Res. Logist. 41 (1994) 33-46. 3.0.CO;2-S>CrossRef
Liao, C.-J., Yu, W.-C. and Joe, C.-B., Bicriterion scheduling in the two-machine flowshop. J. Oper. Res. Soc. 48 (1997) 929-935. CrossRef
Lin, K., Hybrid algorithm for sequencing with bicriteria. J. Opt. Theor. Appl. 39 (1983) 105-124. CrossRef
McCormick, S. and Pinedo, M., Scheduling n independant jobs on m uniform machines with both flowtime and makespan objectives: A parametric analysis. ORSA J. Comput. 7 (1995) 63-77. CrossRef
K. Miettinen. On the Methodology of Multiobjective Optimization with Applications, Ph.D. Thesis. University of Jyvaskyla, Department of Mathematics (1994).
Miyazaki, S., One machine scheduling problem with dual criteria. J. Oper. Res. Soc. Jpn. 24 (1981) 37-50. CrossRef
A. Nagar, J. Haddock and S. Heragu, Multiple and bicriteria scheduling: A literature survey. Eur. J. Oper. Res. (1995) 88-104.
Nagar, A., Heragu, S. and Haddock, J., A branch-and-bound approach for a two-machine flowshop scheduling problem. J. Oper. Res. Soc. 46 (1995) 721-734. CrossRef
Nelson, R., Sarin, R. and Daniels, R., Scheduling with multiple performance measures: The one-machine case. Management Sci. 32 (1986) 464-479. CrossRef
Neppalli, V., Chen, C.-L. and Gupta, J., Genetic algorithms for the two-stage bicriteria flowshop problem. Eur. J. Oper. Res. 95 (1996) 356-373. CrossRef
Ow, P. and Morton, T., Filtered beam search in scheduling. Internat. J. Production Res. 26 (1988) 35-62. CrossRef
Ow, P. and Morton, T., The single machine early/tardy problem. Management Sci. 35 (1989) 177-190. CrossRef
Panwalker, S., Smith, M. and Seidmann, A., Common due date assignment to minimize total penalty for the one machine scheduling problem. Oper. Res. 30 (1982) 391-399. CrossRef
Rajendran, C., Two-stage flowshop scheduling problem with bicriteria. J. Oper. Res. Soc. 43 (1992) 871-884. CrossRef
Rajendran, C., A heuristic for scheduling in flowshop and flowline-based manufacturing cell with multi-criteria. Internat. J. Production Res. 32 (1994) 2541-2558. CrossRef
Rajendran, C., Heuristics for scheduling in flowshop with multiple objectives. Eur. J. Oper. Res. 82 (1995) 540-555. CrossRef
F. Riane, N. Meskens and A. Artiba, Bicriteria scheduling hybrid flowshop problems, in International Conference on Industrial Engineering and Production Managment (IEPM'97). Lyon, France (1997) 34-43.
B. Roy, Méthodologie multicritère d'aide à la décision. Economica (1985).
Sayin, S. and Karabati, S., A bicriteria approach to the two-machine flow shop scheduling problem. Eur. J. Oper. Res. 113 (1999) 435-449. CrossRef
Seidmann, A., Panwalker, S. and Smith, M., Optimal assignment of due-dates for a single processor scheduling problem. Internat. J. Production Res. 19 (1981) 393-399. CrossRef
Selen, W. and Hott, D., A mixed integer goal-programming formulation of a flowshop scheduling problem. J. Oper. Res. Soc. 37 (1986) 1121-1128. CrossRef
Sen, T. and Gupta, S., A branch-and-bound procedure to solve a bicriterion scheduling problem. IEEE Trans. 15 (1983) 84-88. CrossRef
Sen, T., Raiszadeh, F. and Dileepan, P., A branch-and-bound approach to the bicriterion scheduling problem involving total flowtime and range of lateness. Management Sci. 34 (1988) 255-260. CrossRef
Serifoglu, F. and Ulusoy, G., A bicriteria two-machine permutation flowshop problem. Eur. J. Oper. Res. 107 (1998) 414-430. CrossRef
Shantikumar, J., Scheduling n jobs on one machine to minimize the maxium tardiness with minimum number tardy. Comput. Oper. Res. 10 (1983) 255-266. CrossRef
Sidney, J., Optimal single-machine scheduling with earliness and tardiness penalties. Oper. Res. 25 (1977) 62-69. CrossRef
Smith, W., Various optimizers for single-stage production. Naval Res. Logist. Quarterly 3 (1956) 59-66. CrossRef
Soland, R., Multicriteria optimization: A general characterization of efficient solutions. Decision Sci. 10 (1979) 27-38. CrossRef
R. Steuer, Multiple criteria optimization: Theory, computation and application. Wiley (1986).
Sundararaghavan, P. and Ahmed, M., Minimizing the sum of absolute lateness in single-machine and multimachine scheduling. Naval Res. Logist. Quarterly 31 (1984) 325-333. CrossRef
Szwarc, W., Single-machine scheduling to minimize absolute deviation of completion times from a common due date. Naval Res. Logist. 36 (1989) 663-673. 3.0.CO;2-X>CrossRef
V. T'kindt and J.-C. Billaut, L'ordonnancement multicritère. Presses de l'Université de Tours (2000).
T'kindt, V., Billaut, J.-C. and Houngbossa, H., A multi-criteria heuristic to solve a 2-stage hybrid flowshop scheduling problem. Eur. J. Automation (JESA) 34 (2000) 1187-1200.
V. T'kindt, J.-C. Billaut, S. Laurin and O. Meslet, Un algorithme optimal polynomial pour résoudre un problème d'ordonnancement bicritère à machines parallèles, in Conference on Automation-Computers Engineering-Image-Signal (AGIS'97). Angers, France (1997) 179-184.
T'kindt, V., Billaut, J.-C. and Proust, C., Solving a bicriteria scheduling problem on unrelated parallel machines occuring in the glass bottle industry. Eur. J. Oper. Res. 135 (2001) 42-49. CrossRef
V. T'kindt, P. Richard, C. Proust and J.-C. Billaut, Resolution of a 2-machine bicriteria flowshop scheduling problem, in Int. Conference on Methods and Applications of Multicriteria Decision Making (MAMDM'97). Mons, Belgium (1997) 139-143.
M. VandenAkker, H. Hoogeveen and S. VandeVelde, in 6th International Workshop on Project Management and Scheduling (PMS'98). Istanbul, Turkey (1998).
VanWassenhove, L. and Baker, K., A bicriterion approach to time/cost trade-offs in sequencing. Eur. J. Oper. Res. 11 (1982) 48-54. CrossRef
VanWassenhove, L. and Gelders, L., Four solution techniques for a general one machine scheduling problem: A comparative study. Eur. J. Oper. Res. 2 (1978) 281-290. CrossRef
VanWassenhove, L. and Gelders, L., Solving a bicriterion scheduling problem. Eur. J. Oper. Res. 4 (1980) 42-48. CrossRef
Vickson, R., Choosing the job sequence and processing times to minimize total processing plus flow cost on a single machine. Oper. Res. 28 (1980) 115-167.
Vickson, R., Two single machine sequencing problems involving controllable job processing times. IEEE Trans. 12 (1980) 158-162.
A. Vignier, J.-C. Billaut and C. Proust, Solving k-stage hybrid flowshop scheduling problems, in Multiconference on Computational Engineering in Systems Applications (CESA'96), Symposium on Discrete Events and Manufacturing Systems (IEEE-SMC/IMACS). Lille, France (1996) 250-258.
Vignier, A., Billaut, J.-C. and Proust, C., Les flowshop hybrides : état de l'art. RAIRO: Oper. Res. 33 (1999) 117-183. CrossRef
Webster, S., Job, P. and Gupta, A., A genetic algorithm for scheduling job families on a single machine with arbitrary earliness/tardiness penalties and an unrestricted common due date. Internat. J. Production Res. 36 (1998) 2543-2551. CrossRef
A. Wierzbicki, The use of reference objectives in multiobjective optimization, edited by G. Fandel and T. Gal, Multiple criteria decision making, theory and application. Springer-Verlag (1990) 468-486.
Wilson, J., Alternative formulations of a flow-shop scheduling problem. J. Oper. Res. Soc. 40 (1989) 395-399. CrossRef
Zegordi, S., Itoh, K. and Enkawa, T., A knowledgeable simulated annealing scheme for the early/tardy flow shop scheduling problem. Internat. J. Production Res. 33 (1995) 1449-1466. CrossRef