Scheduling to Maximize the Number of Just-in-Time Jobs: A Survey

  • Dvir ShabtayEmail author
  • George Steiner
Part of the Springer Optimization and Its Applications book series (SOIA, volume 60)


In just-in-time (JIT) scheduling, the usual objective is to minimize a cost function which includes a penalty for both the early and tardy completion of jobs. In this paper, we survey results for a cost function that is related to the number of early and tardy jobs rather than the actual earliness and tardiness values. More specifically, we study the problem of maximizing the weighted number of jobs which are completed exactly on their due date (i.e., in JIT mode). Our survey covers the literature for various scheduling environments both with fixed and controllable processing times. We also describe several new algorithms for certain flow-shop problems.


Flow Shop Feasible Schedule Open Shop Identical Parallel Machine Unrelated Parallel Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Alidaee, B., Ahmadian, A.: Two Parallel Machine Sequencing Problems Involving Controllable Job Processing Times. European Journal of Operational Research 70, 335-341 (1993)zbMATHCrossRefGoogle Scholar
  2. 2.
    Arkin, E.M., Silverberg, E.L.: Scheduling Jobs with Fixed Start and Finish Times. Discrete Applied Mathematics 18, 1-8 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baker, K.R., Scudder, G.D.: Sequencing with Earliness and Tardiness Penalties: A Review. Operations Research 38, 22-36 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bouzina, K.I., Emmons, H.: Interval Scheduling on Identical Machines. Journal of Global Optimization 9, 379-393 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Carlisle, M.C., Lloyd, E.L.: On the k-coloring of Intervals. Discrete Applied Mathematics 59, 225-235 (1995)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Cheng, T.C.E., Janiak, A., Kovalyov, M.Y.: Bicriterion Single Machine Scheduling with Resource Dependent Processing Times. SIAM Journal on Optimization 8(2), 617-630 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Choi, B.C., Yoon, S.H.: Maximizing the Weighted Number of Just-in-Time Jobs in Flow Shop Scheduling. Journal of Scheduling 10, 237-243 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Čepek, O., Sung, S. C.: A Quadratic Time Algorithm to Maximize the Number of Just-in-Time Jobs on Identical Parallel Machines. Computers and Operations Research 32, 3265-3271 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chudzik, K., Janiak, A., Lichtenstein, M.: Scheduling Problems with Resource Allocation. In A. Janiak, ed., Scheduling in Computer and Manufacturing Systems, WK L, Warszawa (2006)Google Scholar
  10. 10.
    Frank, A.: On Chains and Antichains Families of a Partially Ordered Set. Journal of Combinatorial Theory Series B 29, 176-184 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and Approximation in Deterministic Sequencing and Scheduling: A Survey. Annals Discrete Mathematics 5, 287-326 (1979)Google Scholar
  12. 12.
    Hsiao, J.Y., Tang, C.Y., Chang, R.S.: An Efficient Algorithm for Finding a Maximum Weight  2-independent Set of Interval Graphs. Information Processing Letters 43, 229-235 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hiraishi, K., Levner, E., Vlach, M.: Scheduling of Parallel Identical Machines to Maximize the Weighted Number of Just-in-Time Jobs. Computers and Operations Research 29(7), 841-848 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Janiak, A.: One-Machine Scheduling with Allocation of Continuously-Divisible Resource and with No Precedence Constraints. Kybernetika 23(4), 289-293 (1987)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Janiak, A., Kovalyov, M.Y.: Single Machine Scheduling Subject to Deadlines and Resource Dependent Processing Times. European Journal of Operational Research 94, 284-291 (1996)zbMATHCrossRefGoogle Scholar
  16. 16.
    Janiak, A., Janiak, W., Lichtenstein, M.: Resource Management in Machine Scheduling Problems: A Survey. Decision Making in Manufacturing and Services 1, 59-89 (2007)zbMATHMathSciNetGoogle Scholar
  17. 17.
    Józefowska, J.: Just-in-time Scheduling: Models and Algorithms for Computer and Manufacturing Systems, Springer-Verlag New York Inc (2007)Google Scholar
  18. 18.
    Kaspi, M., Shabtay, D.: Optimization of Machining Economics Problem for a Multi-Stage Transfer Machine Under Failure, Opportunistic and Integrated Replacement Strategies. International Journal of Production Research 41(10), 2229-2248 (2003)zbMATHCrossRefGoogle Scholar
  19. 19.
    Kayan, R.K., Akturk, M.S.: A New Bounding Mechanism for the CNC Machine Scheduling Problem with Controllable Processing Times. European Journal of Operational Research 167, 624-643 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Kovalyov, M.Y., Ng, C.T., Cheng, T.C.E.: Fixed Interval Scheduling: Models, Applications, Computational Complexity and Algorithms. European Journal of Operational Research 178, 331-342 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Lann, A., Mosheiov, G.: Single Machine Scheduling to Minimize the Number of Early and Tardy Jobs. Computers and Operations Research 23, 765-781 (1996)CrossRefGoogle Scholar
  22. 22.
    Leyvand Y., Shabtay, D., Steiner, G., Yedidsion, L.: Just-in-Time Scheduling with Controllable Processing Times on Parallel Machines. Journal of Combinatorial Optimization 19(3), 347-368 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Ng, C.T.D., Cheng, T.C.E., Janiak, A., Kovalyov, M.Y.: Group Scheduling with Controllable Setup and Processing Times: Minimizing Total Weighted Completion Time. Annals of Operations Research 133, 163-174 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Nowicki, E., Zdrzalka, S.: A Survey of Results for Sequencing Problems with Controllable Processing Times. Discrete Applied Mathematics 26, 271-287 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Pal, M., Bhattacharjee, G.P.: A Sequential Algorithm for Finding a Maximum Weight K-independent Set on Interval Graphs. International Journal of Computer Mathematics 60, 205-214 (1996)zbMATHCrossRefGoogle Scholar
  26. 26.
    Saha, A., Pal, M.: Maximum Weight k-independent Set Problem on Permutation Graphs. International Journal of Computer Mathematics 80, 1477-1487 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Sarrafzadeh, M., Lou, R.D.: Maximum k-Covering of Weighted Transitive Graph with Applications. Algorithmica 9, 84-100 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Shabtay, D.: Single and a Two-Resource Allocation Algorithms for Minimizing the Maximal Lateness in a Single Machine-Scheduling Problem. Computers and Operations Research, 31(8), 1303-1315 (2004)zbMATHCrossRefGoogle Scholar
  29. 29.
    Shabtay, D., Kaspi, M.: Minimizing the Total Weighted Flow Time in a Single Machine with Controllable Processing Times. Computers and Operations Research 31(13), 2279-2289 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Shabtay, D., Kaspi, M., Steiner, G.: The No-Wait Two-Machine Flow-Shop Scheduling Problem with Convex Resource-Dependent Processing Times. IIE Transactions 39(5), 539–557 (2007)CrossRefGoogle Scholar
  31. 31.
    Shabtay, D., Steiner, G.: A Survey of Scheduling with Controllable Processing Times. Discrete Applied Mathematics 155(13), 1643-1666 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Shabtay, D., Bensoussan, Y.: Maximizing the Weighted Number of Just-in-Time Jobs in a Two Machine Flow and Open Shop Scheduling Systems. Journal of Scheduling, DOI: 10.1007/s10951-010-0204-yGoogle Scholar
  33. 33.
    Shabtay, D., Bensusan, Y., Kaspi, M.: A Bicriteria Approach to Maximize the Weighted Number of Just-In-Time Jobs and to Minimize the Total Resource Consumption Cost in a Two-Machine Flow-Shop Scheduling System, International Journal of Production Economics, to appearGoogle Scholar
  34. 34.
    Shakhlevich, N.V., Strusevich, V.A.: Pre-emptive Scheduling Problems with Controllable Processing Times. Journal of Scheduling 8, 233-253 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  35. 35.
    Steiner, G.: Finding the Largest Suborder of Fixed Width. Order 9, 357-360 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Sung, S.C., Vlach, M.:Maximizing Weighted Number of Just-in-Time Jobs on Unrelated Parallel Machines, Journal of Scheduling 8, 453-460 (2005)Google Scholar
  37. 37.
    Trick, M.: Scheduling Multiple Variable-Speed Machines. Operations Research 42, 234-248 (1994)zbMATHGoogle Scholar
  38. 38.
    Vickson, R.G.: Two Single Machine Sequencing Problems Involving Controllable Job Processing Times. AIIE Transactions 12(3), 258-262 (1980)CrossRefMathSciNetGoogle Scholar
  39. 39.
    Yannakakis, M., Gavril, F.: The Maximum k-Colorable Subgraph Problem for Chordal Graphs. Information Processing Letters 24, 133-137 (1987)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Industrial Engineering and ManagementBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Operations Management Area, DeGroote School of BusinessMcMaster UniversityHamiltonCanada

Personalised recommendations