Order scheduling with controllable processing times, common due date and the processing deadline

  • Qing Yue
  • Guohua Wan


Due date quotation and scheduling are important tools to match demand with production capacity in the MTO (make-to-order) environment. We consider an order scheduling problem faced by a manufacturing firm operating in an MTO environment, where the firm needs to quote a common due date for the customers, and simultaneously control the processing times of customer orders (by allocating extra resources to process the orders) so as to complete the orders before a given deadline. The objective is to minimize the total costs of earliness, tardiness, due date assignment and extra resource consumption. We show the problem is NP-hard, even if the cost weights for controlling the order processing times are identical. We identify several polynomially solvable cases of the problem, and develop a branch and bound algorithm and three Tabu search algorithms to solve the general problem. We then conduct computational experiments to evaluate the performance of the three Tabu-search algorithms and show that they are generally effective in terms of solution quality.


Order scheduling due date assignment controllable processing times deadline 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors thank the editor and the two anonymous reviewers for their helpful comments and suggestions on earlier versions of the paper. This work is supported in part by NSF of China (Grants No. 71125003, 71421002), and Specialized Research Fund for the Doctoral Program of High Education (20130073110066).


  1. [1]
    Baker, K. & Scudder, G. (1990). Sequencing with earliness and tardiness penalties: a review. Operations Research, 38(1): 22–36.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Beicourt, M. (2006). Outsourcing - the benefits and risks. Human Resource Management Review, 16(2): 269–279.CrossRefGoogle Scholar
  3. [3]
    Biskup, D. & Jahnke, H. (2001). Common due date assignment for scheduling on a single machine with jointly reducible processing times. International Journal of Production Economics, 69(3): 317–322.CrossRefGoogle Scholar
  4. [4]
    Cheng, T.C.E. & Shakhlevich, N.V. (2007). Two machine open shop problem with controllable processing times. Discrete Optimization, 4(1): 175–184.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Cheng, T.C.E., Ding, Q. & Lin, B.M.T. (2004). A concise survey on the scheduling problems with deteriorating processing times. European Journal Operational Research, 152 (1):1–13.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Cheng, T.C.E., Oğaz, C. & Qi, X.D. (1996). Due-date assignment and single machine scheduling with compressible processing times. International Journal of Production Economics, 43(1-2): 29–35.CrossRefGoogle Scholar
  7. [7]
    Choi, B-C, Leung JY-T & Pinedo, M.L. (2010). Complexity of a scheduling problem with controllable processing times. Operations Research Letters, 38 (2):123–126.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Della, C.F., Narayan, V. & Tadei, R. (1996). The two-machine total completion time flow shop problem. European Journal of Operational Research, 90(2): 227–237.CrossRefzbMATHGoogle Scholar
  9. [9]
    Garey, M.R. & Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco.zbMATHGoogle Scholar
  10. [10]
    Gordon, V., Proth J.M. & Chu, C.B. (2002b). Due date assignment and scheduling: SLK, TWK and other due date assignment models. Production Planning & Control, 13(2): 117–132.CrossRefGoogle Scholar
  11. [11]
    Gordon, V., Proth, J. M. & Chu, C.B. (2002a). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139(1): 1–25.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Gordon, V.S. & Strusevich, V. A. (1999). Earliness penalties on a single machine subject to precedence constraints: SLK due date assignment. Computers & Operations Research, 26 (2):157–177.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Gunasekaran, A. & Ngai, E.W.T. (2005). Build-to-order supply chain management: a literature review and framework for development. Journal of Operations Management, 23(5): 423–451.CrossRefGoogle Scholar
  14. [14]
    Hall, N.G. & Posner, M.E. (1991). Earliness-tardiness scheduling problems, I: weighted deviation of completion times about a common due date. Operations Research, 39(5): 836–846.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Hall, N.G., Kubiak, W. & Sethi, S.P. (1991). Earliness-tardiness scheduling problems, II: deviation of completion times about a restrictive common due date. Operations Research, 39(5): 847–856.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Hardy, G.H., Littlewood, J.E. & Polya, G. (1934). Inequalities. Cambridge University Press, NY.zbMATHGoogle Scholar
  17. [17]
    He, Y., Qi, W. & Cheng, T.C. (2007). Single-machine scheduling with trade-off between number of tardy jobs and compression cost. Journal of Scheduling, 10(5): 303–310.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Huynh, T.N. & Ameur, S. (2010). Due dates assignment and JIT scheduling with equal size jobs. European Journal of Operational Research, 205(2): 280–289.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    Janiak, A. (1989). Minimization of resource consumption under a given deadline in the two-processor flow-shop scheduling problem. Information Processing Letters, 32(3): 101–112.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Jansen, K., Mastrolilli, M. & Solis-Oba, R. (2005). Approximation schemes for job shop scheduling problems with controllable processing times. European Journal of Operational Research, 167(2): 297–319.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    Kaminsky, P. & Lee, Z.H. (2002). On-line algorithms for flow shop due date quotation. University of California, Berkeley (California, USA). sky/papers/ddq_flowshop.pdf.Google Scholar
  22. [22]
    Kaminsky, P. & Lee, Z.H. (2008). Effective on-line algorithms for reliable due date quotation and-large-scale scheduling. Journal of Scheduling, 11(3): 187–204.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Kaspi, M. & Shabtay, D. (2004). Convex resource allocation for minimizing the makespan in a single machine with job release dates. Computers & Operations Research, 31(9): 1481–1489.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Lawler, E.L. & Wood, D.E. (1966). Branch-and-bound methods: a survey. Operations Research, 14(4): 699–719.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Leyvand, Y., Shabtay, D. & Steiner, G. (2010). Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times. IIE Transactions, 42(3): 221–231.CrossRefGoogle Scholar
  26. [26]
    Mitten, L. G. (1970). Branch-and-bound methods: general formulation and properties. Operations Research, 18(1): 24–34.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Monma, C.L., Schrijver, A., Todd, M. J. & Wei, V. K. (1990). Convex resource allocation problems on directed acyclic graphs: duality, complexity, special cases and extensions. Mathematics of Operations Research, 15(4): 736–748.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    Ng, C.T.D., Cheng, T.C.E., Kovalyov, M.Y. & Lam, S. S. (2003). Single machine scheduling with a variable common due date and resource-dependent processing times. Computers & Operations Research, 30(8): 1173–1185.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    Nowicki, E. & Zdrzalka, S. (1995). A bicriterion approach to preemptive scheduling of parallel machines with controllable job processing times. Discrete Applied Mathematics, 63(3): 237–256.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    Panwalkar, S.S., Smith, M.L. & Seidmann, A. (1982). Common due date assignment to minimize total penalty for the one machine scheduling problem. Operations Research, 30(2): 391–399.CrossRefzbMATHGoogle Scholar
  31. [31]
    Pinedo, M. (2012). Scheduling: Theory, Algorithms and Systems (4th ed.). Springer, Berlin.CrossRefzbMATHGoogle Scholar
  32. [32]
    Qi, X. & Tu, F-S. (1998). Scheduling a single machine to minimize earliness penalties subject to the SLK due-date determination method. European Journal of Operations Research, 105(3): 502–508.CrossRefzbMATHGoogle Scholar
  33. [33]
    Shabtay, D. & Steiner, G. (2006). Two due date assignment problems in scheduling a single machine. Operations Research Letters, 34(6): 683–691.MathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    Shabtay, D. & Steiner, G. (2007a). A survey of scheduling with controllable processing times. Discrete Applied Mathematics, 155(13): 1643–1666.MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Shabtay, D. & Steiner, G. (2007b). Optimal due date assignment and resource allocation to minimize the weighted number of tardy jobs on a single machine. Manufacturing & Service Operations Management, 9(3): 332–350.CrossRefGoogle Scholar
  36. [36]
    Shabtay, D. & Steiner, G. (2008). The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times. Annals of Operation Research, 159(1): 25–40.MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    Shabtay, D. & Kaspi, M. (2006). Parallel machine scheduling with a convex resource consumption function. European Journal of Operational Research, 173(1): 92–107.MathSciNetCrossRefzbMATHGoogle Scholar
  38. [38]
    Slotnick, S.A. & Sobel, M.J. (2005). Manufacturing lead-time rules: customer retention versus tardiness costs. European Journal of Operational Research, 163(3): 825–856.CrossRefzbMATHGoogle Scholar
  39. [39]
    Spearman, M.L. & Zhang, R.Q. (1999). Optimal lead time policies. Management Science, 45 (2): 290–295.CrossRefzbMATHGoogle Scholar
  40. [40]
    Tseng, C.T., Liao, C.J. & Huang, K.L. (2009). Minimizing total tardiness on a single machine with controllable processing times. Computers & Operations Research, 36(6): 1852–1858.MathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    Wan, G.H., Yen, B.P.C. & Li, C.-L. (2001). Single machine scheduling to minimize total processing plus weighted flow cost is NP-hard. Information Processing Letters, 79(6): 273–280.MathSciNetCrossRefzbMATHGoogle Scholar
  42. [42]
    Xu, K.L., Feng, Z.R. & Ke, L.J. (2011). Single machine scheduling with total tardiness criterion and convex controllable processing times. Annals of Operations Research, 186(1): 383–391.MathSciNetCrossRefzbMATHGoogle Scholar
  43. [43]
    Yedidsion, Y., Shabtay, D. & Kaspi, M. (2011). Complexity analysis of an assignment problem with controllable assignment costs and its applications in scheduling. Discrete Applied Mathematics, 159(12): 1264–1278.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Systems Engineering Society of China and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Antai College of Economics and ManagementShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations