TEK VE PARALEL MAKİNALI PROBLEMLERDE ÇOK ÖLÇÜTLÜ ÇİZELGELEME PROBLEMLERİ İÇİN BİR LİTERATÜR TARAMASI

Yıl 2002, Cilt: 17 Sayı: 4, 0 - , 12.04.2013

Tamer Eren Ertan Güner

Öz

Çizelgeleme problemleri ile ilgili gerçek uygulamada karar vericiler genellikle birden fazla ölçütün en iyilenmesine çalışırlar. Ancak tek bir ölçütle ilişkili olarak en iyi değeri veren bir çözüm, birden fazla ölçüt söz konusu olduğunda aynı sonucu vermeyebilir. Bu nedenle karar verme sürecinde birden fazla ölçüt dikkate alındığında ölçütler arasında ödünleşimler söz konusu olur. Çizelgeleme literatüründe çok ölçütlü çalışmalar, tek ölçütlü çalışmalar ile kıyaslandığında çok daha azdır. Bu çalışmada, tek makinalı ve paralel makinalı problemler, çok ölçütlü, deterministik ve stokastik çizelgeleme problemleri ele alınarak bir literatür taraması yapılmıştır.

Anahtar Kelimeler

Sıralama, çizelgeleme, çok ölçüt, eniyileme, literatür taraması.

Kaynakça

• Baker, K. R., Introduction to Sequencing and Scheduling, John Wiley and Sons, New York, 1974.
• Baker, K. R., and Schrage, L. E., “Finding an Optimal Sequencing by Dynamic Programming: An Extension to Precedence-Related Tasks”, Operations Research, Volume 26, No: 1, 1978.
• Gupta, S., and Kyparisis, J., “Single Machine Scheduling Research”, OMEGA International Journal of Management Science, Volume 15, No: 3, pp. 207-227, 1987.
• Dileepan, P., and Sen, T., “Bicriterion Static Scheduling Research For A Single Machine”, OMEGA International Journal of Management Science, Volume 16, No: 1, pp. 53-59, 1988.
• Van Wassenhove, L. N., and Gelders, F., “Solving A Bicriterion Scheduling Problem”, European Journal of Operational Research, Volume 4, No: 1, pp. 42-48, 1980.
• Cheun, C., and Bulfin, R.L., “Scheduling Unit Processing Time Jobs on a Single Machine with Multiple Criteria”, Computers and Operations Research, Volume 17, No: 1, pp. 1-7, 1990.
• Dileepan, P., and Sen, T., “Bicriteria Scheduling with Total Flowtime and Sum of Squared Lateness”, Engineering Cost and Production Economics, Volume 21, No: 8, pp. 295-299, 1991.
• Sen, T., and Gupta, S. K., “A Branch and Bound to Solve a Bicriterion Scheduling Problem”, IEE Transactions, Volume 15, pp. 84-88, 1983.
• Sen, T., Raiszadeh, F. M. E., and Dileepan, P., “A Branch-and-Bound Approach to The Bicriterion Scheduling Problem Involving Total Flowtime and Range of Lateness”, Management Science, Volume 34, No: 2, pp. 255-260, 1988.
• Fry, T. D., Armstrong, R. D., and Lewis, H., “A Framework for Single Machine Multiple Objective Sequencing Research”, OMEGA, Volume 17, No: 6, pp. 595-607, 1989.
• Nagar, A., Hadddock, J., and Heragu, S., “Multiple and Bicriteria Scheduling: A Literature Survey”, European Journal of Operational Research, Volume 81, pp. 88-104, 1995.
• T’kint, V., and Billaut J.-C., “Multicriteria Scheduling Problems: A Survey”, RAIRO Operations Research, Volume 35, pp. 143-163, 2001.
• Van Wassenhove, L. N., and Gelders, F., “Four Solution Techniques for a General One Machine Scheduling Problem: A Comparative Study”, European Journal of Operational Research, Volume 2, No: 4, pp. 281-290, 1978.
• John, T. C., “Trade off Solution in Single Machine Production Scheduling for Minimizing Flowtime and Maximum Penalty”, Computers and Operations Research, Volume 16, No: 5, pp. 471-479, 1989.
• Morton, T. E., Pentico, D. W., Heuristic Scheduling Systems, Wiley, New York, 1993.
• Pinedo, M. L., Scheduling: Theory, Algorithms, and Systems, Prentice-Hall, Englewood, 1995.
• Pinedo, M. L., and Chao, X., Operations Scheduling with Applications in Manufacturing and Services, Irwin McGraw-Hill, Singapore, 1999.
• Baker, K. R., Elementes of Sequencing and Scheduling, Dartmouth College, Hanover, 1997.
• Kirkpatrick, S., Gelatt, C. D., and. Vecchi, M. P., “Optimization by Simulated Annealing”, Science, Volume 220, pp. 671–680, 1983.
• Glover, F., and Laguna, M., Tabu Search, Kluwer Academic Publishers, United Stated of America, 1997.
• Glover, F., "Future Paths For Integer Programming and Links to Artificial Intelligence", Computers and Operations Research, Volume 13, No: 5, pp. 533-549, 1986.
• Glover, F., "Tabu Search - Part I", ORSA Journal on Computing, Volume 1, No: 3, pp. 190-206, 1989.
• Glover, F., "Tabu Search - Part II", ORSA Journal on Computing, Volume 2, No: 1, pp .4-32, 1990.
• Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, M. A, 1989.
• Jones, D. F., Mirrazavi, S. K., and Tamiz, M., “Multi-Objective Meta-Heuristics: An Overview of The Current State-of-The-Art”, European Journal of Operational Research, Volume 137, No: 1, pp. 1-9, 2002.
• Kan, A. H. G., Machine Scheduling Problems, Martinus Nijhoff, The Hague, 1976.
• Lenstra, J. K., Sequencing by Enumerative Method, Second Printing, Mathemtisch Centrum, 1985.
• Cheun, C.-L., and Bulfin, R. L., “Complexity of Single Machine Multi-criteria Scheduling Problems”, European Journal of Operational Research, Volume 70, pp. 115-125, 1993.
• Blazewicz, J., Ecker, K., Schmidt, G., and Weglarz, J., Scheduling in Computer and Manufacturing Systems, Springer, Berlin, 1993.
• Tanaev, V. S., Gordon, V. S., and Shafransky, Y. M., Scheduling Theory: Single-Stage Systems, Kluwer, Dordrecht, 1994.
• Tanaev, V. S., Sotskov, Y. N., and Strusevich, V. A., Scheduling Theory: Multi-Stage Systems, Kluwer, Dordrecht, 1994.
• Chretienne, P., Co Man, Jr., E. G., Lenstra, J. K., Liu, Z., Scheduling Theory and Its Applications, Wiley, Chichester, 1995.
• Blazewicz, J., Ecker, K., Pesch, E., Schmidt, G., Weglarz, J., Scheduling Computer and Manufacturing Processes, Springer, Berlin, 1996.
• Sen, T., Gupta, S. K., “A State-of-Art Survey of Static Scheduling Research Involving Due Dates”, OMEGA, Volume 12, pp. 63–76, 1984.
• Raghavachari, M., “Scheduling Problem with Non-Regular Penalty Functions-A Review”, Opsearch, Volume 25, No: 3, pp. 144-164, 1988.
• Kawaguchi, T., and Kyan, S., “Deterministic Scheduling in Computer Systems: A Survey”, Journal of The Operational Research Society of Japan, Volume 31, pp. 190–217, 1988.
• Baker, K. R., and Scudder, G. D., “Sequencing with Earliness and Tardiness Penalties: A Review”, Operations Research, Volume 38, No: 1, pp. 22-36, 1990.
• Cheng, T. C. E., Gupta, M. C., “Survey of Scheduling Research Involving Due Date Determination Decisions”, European Journal of Operational Research, Volume 38, pp. 156–166, 1989.
• Cheng, T. C. E., Sin, C. C. S., “A State-of-The-Art Review of Parallel-Machine Scheduling Research”, European Journal of Operational Research, Volume 47, pp. 271–292, 1990.
• Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., Shmoys, D. B., Sequencing and Scheduling: Algorithms and Complexity, In: Graves S.C., Zipkin P.H., Rinnooy, 1993.
• Koulamas, C., “The Total Tardiness Problem: Review and Extensions”, Operations Research, Volume 42, pp. 1025–1041, 1994.
• Hoogeveen, J. A., Van de Velde, S. L., “Earliness–Tardiness Scheduling Around Almost Equal Due Date”, INFORMS Journal on Computing, Volume 9, pp. 92–99, 1997.
• Gordon, V., Proth, J.-M., and Chu, C., “A Survey of The State-of-The-Art of Common Due Date Assignment and Scheduling Research”, European Journal of Operational Research, Volume 139, pp. 1-25, 2002.
• Lung, C. C., Multicriteria Scheduling For A Single Machine: Analysis and Algorithms, Ph.D., Auborn University, 1989.
• Graham, R. L., Lawler, E. L., and Rinnooy Kan, A. H. G., “Optimization and Approximation in Deterministic Sequencing and Scheduling”, Annals of Discrete Mathematics, Volume 5, pp. 287-326, 1979.
• Evans, G. W., “An Owerview of Techniques For Solving Multi-Objective Mathematical Programs”, Management Science, Volume 30, No: 11, pp. 1268-1283, 1984.
• De, P., Grosh, J. B., and Wells C. E., “Some Clarifications on the Bicriteria Scheduling of Unit Execution Time Jobs on a Single Machine”, Computers and Operations Research, Volume 18, No: 8, pp. 717-720, 1991.
• Smith, W. E., “Varios Optimizers for Single-Stage Production”, Naval Research Logistics Quarterly, Volume 3, pp. 59-66, 1956.
• Jackson, J. R., Scheduling a Production Line To Minimize Maksimum Tardiness, Research Report, University of California at Los Angeles, 1965.
• Heck, H., and Roberts, S., “A Note on The Extension of a Result on Scheduling with Secondary Criteria”, Naval Research Logistics Quarterly, Volume 19, pp. 403-405, 1972.
• Van Wassenhove, L. N., and Baker, K. R., “A Bicriterion Approach to Time Cost Trade-Offs in Sequencing”, European Journal of Operational Research, Volume 11, pp. 48-54, 1982.
• Townsend, W., “Single Machine Problem with Quadratic Penalty Function of Completion Times: A Branch and Bound solution”, Management Science, Volume 24, No: 5, pp. 530-534, 1978.
• Nelson, R. T., Sarin, R. K. and Daniels, R. L., “Scheduling with Multiple Performance Measures: The One-Machine Case”, Management Science, Volume 32, No: 4, pp. 464-479, 1986.
• Liao, C-J., Huang, R-H., and Tseng, S-T., “Use of Variable Range in Solving Multiple Criteria Scheduling Problems”, Computers and Operations Research, Volume 19, No: 5, pp. 453-460, 1992.
• Hoogeveen, J. A., and Van de Velde S. L., “Minimizing Total Completion Time and Maximum Cost Simultaneously is Solvable in Polynomial Time”, Operations Research Letters, Volume 17, pp. 205-208, 1995.
• Köksalan, M., “A Heuristic Approach to Bicriteria Scheduling”, Naval Research Logistic, Volume 46, pp. 777-789, 1999.
• Burns, R. N., “Scheduling to Minimize The Weighted Sum of Completion Times with Secondary Criteria”, Naval Research Logistic Quarterly, Volume 23, No: 1, pp. 125-129, 1976.
• Bansal, S. P., “Single Machine Scheduling to Minimize Weighted Sum of Completion Times With Secondary Criterion: A Branch and Bound Approach”, European Journal of Operational Research, Volume 5, pp. 177–181, 1980.
• Miyazaki, S., “One Machine Scheduling Problem with Dual Criteria”, Journal of Operations Research Society of Japan, Volume24, No: 1, pp. 37-50, 1981.
• Shanthikumar, J., and Buzacott, J. A., “On The Use of Decomposition Approaches in A Single Machine Scheduling Problem”, Journal of The Operations Research Society of Japan, Volume 25, No: 1, pp. 29-47, 1983.
• Potts, C. N., and Van Wassenhove, L. N., “An Algorithm for Single Machine Sequencing with Deadlines to Minimize Total Weighted Completion Time”, European Journal of Operational Research, Volume 12, pp. 379-387, 1983.
• Posner, M. E., “Minimizing Weighted Completion Times with Deadlines”, Operations Research, Volume 33, No: 3, pp. 562-574, 1985.
• Chand, S. and Schneeberger, H., “A Note on The Single-Machine Scheduling Problem with Minimum weighted Completion Time and Maximum Allowable Tardiness”, Naval Research Logistic, Volume 33, pp. 551-557, 1986.
• Bagchi, U., and Ahmadi, R. H., “An Improved Lower Bound for Minimizing Weighted Completion Times with Deadlines”, Operations Research, Volume 35, pp. 311-313, 1987.
• Emmons, H., “One Machine Sequencing To Minimize Mean Flow Time with Minimum Number Tardy”, Naval Research Logistics Quarterly, Volume 22, pp. 585-592, 1975.
• Moore, J. M., “An n Jobs, One Machine Sequencing Algorithm for Minimizing The Number of Late Jobs”, Management Science, Volume 15, No: 1, pp. 102-109, 1968.
• Hodgson, T. J., “A Note on Single-Machine Sequencing with Random Processing Times”, Management Science, Volume 23, pp. 1144-1146, 1977.
• Kiran, A. S., and Unal, A. T., “A Single Machine Problem with Multiple Criteria”, Naval Research Logistics Quarterly, Volume 38, pp. 721-727, 1991.
• Kondakci, S. K. and Bekiroğlu, T., “Scheduling with Bicriteria Scheduling: Total Flowtime and Number of Tardy Jobs”, International Journal of Production Economics, Volume 53, pp. 91-99, 1997.
• Karasakal, E. K. and Köksalan, M., “A Simulated Annealing Approach to Bicriteria Scheduling Problems on a Single Machine”, Journal of Heuristics, Volume 6, pp. 311-327, 2000.
• Lawler, E. L., “Optimal Sequencing of A Single Machine Subject To Precedence Constraints”, Managemet Science, Volume 19, pp. 544-546, 1973.
• John, T. C., and Sadowski, R. P., On A Bicriteria Scheduling Problem, Presented at ORSA / Tims Meeting, Dallas, Texas, November, 1984.
• Cheng, T. C. E., “An Improved Solution Procedure for The Scheduling Problem”, Journal of Operations Research Society of Japan, Volume 42, No: 5, pp. 413-417, 1991.
• Hoogeveen, J. A., and Van de Velde, S. L., “Polinomial-Time Algorithms for Single Machine Multicriteria Scheduling”, Centre for Mathematics and Computer Science, P.O.Box. 4079, 1009 AB Amsterdam, The Netherland, 1-13, 1990.
• Köksalan, M., Azizoğlu, M. and Kondakçı, S. K., “Minimizing Flowtime and Maximum Earliness on a Single Machine”, IEE Transactions, Volume 30, pp. 192-200, 1998.
• Gelders, L. F., and Kleindorfer, P. R., “Coordinating Aggregate and Detailed Scheduling in The One Machine Job Shop, Part I. Theory”, Operations Research, Volume 22, pp. 46-60, 1974.
• Gelders, L. F., and Kleindorfer, P. R., “Coordinating Aggregate and Detailed Scheduling in The One Machine Job Shop, Part II. Computation and Structure”, Operations Research, Volume 23, No: 2, pp. 312-324, 1975.
• Fry, T. D., Leong, G. K. ve Rakes T. R., “Single Machine Scheduling: A Comparison of Two Solution Procedures”, OMEGA International Journal of Management Science, Volume 15, No: 4, pp. 277-282, 1987.
• Taboun, S. M., Abib, A. H. and Atmani, A., “Generating Efficient Points of Bicriteria Scheduling Problem by Using Compromise Programming”, Computers and Industrial Engineering, Volume 29, No: 1-4, pp. 227-231, 1995.
• Vickson, R. G., “Choosing The Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine”, Operations Research, Volume 28, No: 5, pp. 1155-1167, 1980.
• Cheng, T. C. E., Kovalyov, M. Y., and Tuzikov, A. V., “Single Machine Group Scheduling with Two Ordered Criteria”, Journal of Operational Research Society, Volume 47, pp. 315-320, 1996.
• Fry, T. D. and Leong, G. K., “A Bi-criterion Approach to Minimizing Inventory Costs on a Single Machine When Early Shipments Are Forbidden”, Computers and Operations Research, Volume 14, No: 5, pp. 363-368, 1987.
• Elmaghraby, S. E., and Pulat, P. S., “Optimal Project Compresion with Due Dated Events”, Naval Research Logistics Quarterly, Volume 26, pp. 331-348, 1979.
• Lin K. S., “Hybrid Algorithm for Sequencing with Bicriteria”, Journal of Optimization Theory and Applications, Volume 39, No: 1, pp. 105-124, 1983.
• Hoogeveen, J. A., and Van De Velde, S. L., “Scheduling with Target Start Times”, European Journal of Operational Research, Volume 129, pp. 87-94, 2001.
• Gupta, J. N. D., Ho, J. C., and Van Der Veen, J. A. A., “Single Machine Hierarchical Scheduling with Customer Orders and Multiple Job Classes”, Annals of Operations Research, Volume 70, pp. 127-143, 1997.
• Ishii, H., Tada, M., and Nishida, T., “Bi-criteria Scheduling Problem on Uniform Processors”, Mathematical Japonica, Volume 35, No: 3, pp. 515-519, 1990.
• Daniels, R. L., “Incorporating Preference Information Into Multi-objective Scheduling”, European Journal of Operational Research, Volume 77, pp. 272-286, 1994.
• Shanthikumar, J. G., “Scheduling n Jobs on One Machine to Minimize the Maximum Tardiness with Minimum Number Tardy”, Computers and Operations Research, Volume 10, No: 3, pp. 255-266, 1983.
• Gupta, J. N. D., and Ramnarayanan, R., “Single Facility Scheduling with Dual Criteria: Minimizing Maximum Tardiness Subject to Minimum Number of Tardy Jobs”, Production Planning and Control, Volume 70, pp. 127-143, 1996.
• Gupta, J. N. D., Hariri, A. M. A. and Potts, C. N., “Single-Machine Scheduling to Minimize Maximum Tardiness with Minimum Number of Tardy Jobs”, Annals of Operations Research, Volume 92, pp. 107-123, 1999.
• Gupta, S., and Sen, T., “Minimizing The Range of Lateness on a Single Machine”, Journal of The Operations Research Society, Volume35, No: 9, pp. 853-857, 1984.
• Tegze, M., and Vlach, M., “Improved Bounds for The Range of Lateness on a Single Machine”, Journal of The Operations Research Society, Volume 39, No: 1, pp. 675-680, 1988.
• Liao, C-J., and Huang R-H., “An Algorithm for Minimizing The Range of Lateness on a Single Machine”, Journal of Operations Research Society, Volume 42, No: 2, pp. 183-186, 1991.
• Güner, E., Tek Makinalı Sistemler İçin Çok Ölçütlü Çizelgeleme Algoritmaları, Ph. D., Gazi Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 1994.
• Güner, E., Erol, S., and Tani, K., “One Machine Scheduling to Minimize The Maximum Earliness with Minimum Number of Tardy Jobs”, International Journal of Production Economics, Volume 55, pp. 213-219, 1998.
• Hoogeveen, J. A., “Minimizing Maximum Promptness and Maximum Lateness on A Single Machine”, Mathematics of Operations Research, Volume 21, No: 1, 100-114, 1996.
• Carraway, R. L., Chambers, R. J., Morin, T. L., and Moskowitz, H., “Single machine Sequencing with Nonlinear Multicriteria Cost Functions: An Application of Generalized Dynamic Programming”, Computers and Operations Research, Volume 19, No: 1, pp. 69-77, 1992.
• Chang, P. C., and Su, L. H., “Scheduling n Jobs on One Machine to Minimize The Maximum Lateness with a Minimum Number of Tardy Jobs”, Computers and Industrial Engineering, Volume 40, pp. 349-360, 2001.
• Duffuaa, S. O., Raouf, A., Ben-Daya, M., and Makkı, M., “One-Machine Scheduling to Minimize Mean Tardiness with Minimum Number Tardy”, Production Planning ve Control, Volume 8, No: 3, pp. 226-230, 1997.
• Chang, P. C. and Lee, H. C., “A Greedy Heuristic for Bicriterion Single Machine Scheduling Problems”, Computers and Industrial Engineering, Volume 22, No: 2, pp. 121-131, 1992.
• De, P., Grosh, J. B., and Wells C. E., “Heuristic Estimation of The Efficent Frontier for a Bi-Criteria Scheduling Problem”, Decision Sciences, Volume 23, No: 3, pp. 596-609, 1992.
• Cheng, T. C. E., and Chen, Z.-L., Li, C.-L., and Lin, B. M. T., “Scheduling to Minimize The Total Compression and Late Costs”, Naval Research Logistics Quarterly, Volume 45, pp. 67-82, 1998a.
• Cheng, T. C. E., Janiak, A., and Kovalyov, M. Y., “Bicriterion Single Machine Scheduling with Resource Dependent Processing Time”, SIAM Journal on Optimization, Volume 8, No: 2, pp. 617-630, 1998b.
• Diskup, D., and Cheng, T. C. E., “Single-Machine Scheduling with Controllable Processing Times and Earliness, Tardiness and Completion Time Penalties”, Engineering Optimization, Volume 31, pp. 329-336, 1999.
• Klamroth, K., and Wiecek, M. M., “A Time-Dependent Multiple Criteria Single Machine Scheduling Problem”, European Journal of Operational Research, Volume 135, pp. 17-26, 2001.
• Lin, C-H., and Lee, C-Y., “Single-Machine Stochastic Scheduling with Dual Criteria”, IIE Transactions, Volume 27, pp. 244-249, 1995.
• Crabill T. B., and Maxwell, W. L., “Single-Machine Sequencing with Random Processing Time and Random Due-Dates”, Naval Research Logistics Quarterly, Volume 16, pp. 549-554, 1969.
• Frost, F. G., “Bicriterion Stochastic Scheduling on One or more Machines”, European Journal of Operational Research, Volume 80, pp. 404-409, 1995.
• Lawler, E. L., and Labetoulle, J., “On Preemptive Scheduling of Unrelated Parallel Processor”, Journal of The Association for Computing Machinery, Volume 25, pp. 612-619, 1978.
• Sundararaghavan, P., and Ahmed M., “Minimizing The Sum of Absolute Lateness in Single Machine and Multimachine Scheduling”, Naval Research Logistic Quarterly, Volume 31, pp. 325-333, 1984.
• Emmons, H., “Scheduling to A Common Due Date on Parallel Uniform Processors”, Naval Research Logistic, Volume 34, pp. 803-810, 1987.
• Leung, J.-T., and Young, G., “Minimizing Schedule Length Subject to Minimum flow Time”, SIAM Journal on Computing, Volume 18, pp. 314-326, 1989.
• Alidaee, B., and Ahmadian, A., “Two Parallel Machine Sequencing Problems Involving Controllable Job Processing Times”, European Journal of Operational Research, Volume 70, pp. 335-341, 1993.
• Cheng, T., and Chen, Z.–L., “Parallel-machine Scheduling Problems with Earliness and Tardiness Penalties”, Journal of Operational Research Society, Volume 45, pp. 685-695, 1994.
• Li, C.-J., and Cheng, T., “The Parallel Machine Min-max Weighted Absolute Lateness Scheduling Problem”, Naval Research Logistic, Volume 41, pp. 33-46, 1994.
• McCormick, S., and Pinedo, M., “Scheduling n Independent Jobs on m Uniform Machines with Both Flowtime and Makespan Objectives: A Parametric Analysis”, ORSA Journal on Computing, Volume 7, pp. 63-77, 1995.
• Suresh, V., and Chaudhuri, D., “Bicriteria Scheduling Problem for Unrelated Parallel Machines”, Computers and Industrial Engineering, Volume 30, No: 1, pp. 77-82, 1996.
• Mohri, S., Masuda, T., and Ishii, H., “Bi-criteria Scheduling Problem on Three Identical Parallel Machines”, International Journal of Production Economics, Volume 60-61, pp. 529-536, 1999.
• Sahni, S., “Preemptive Scheduling with Due Dates”, Operations Research, Volume 17, pp. 515-519, 1979.
• Gupta, J. N. D. and Ruiz-Torres, A. J., “Minimizing Makespan Subject to Minimum Total Flow-Time on Identical Parallel Machines”, European Journal of Operational Research, Volume 125, pp. 370-380, 2000.
• Gupta, J. N. D., Ho, J. C., and Webster, S., “Bicriteria Optimisation of The Makespan and Mean Flowtime on Two Identical Parallel Machines”, Journal of Operational Research Society, Volume 51, pp. 1330-1339, 2000.
• T’kindt, V., Billaut, J.-C., and Proust C., “Solving a Bicriteria Scheduling Problem on Unrelated Parallel Machines Occurring in The Glass Bottle Industry”, European Journal of Operational Research, Volume 135, pp. 42-49, 2001.