Production Planning Under Uncertainty with Workload-Dependent Lead Times: Lagrangean Bounds and Heuristics

  • Gregory Dobson
  • Uday S. Karmarkar
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 152)


Advances in modeling production system behavior over the past three decades have made it apparent that work-in-process (WIP) inventories, created by the dynamics of manufacturing systems, are an important characteristic of these systems. Furthermore, the recognition of the importance of lead times and the variability of lead times for system performance has lent additional emphasis to this behavior. Consequently, consideration of WIP and lead times has been a key aspect addressed in the analysis and development of various types of scheduling and job release systems, of which Kanban and workload-based methods are examples.


Lead Time Planning Model Capacity Planning Safety Stock Clearing Function 
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.



The authors appreciate the assistance provided by Mike Pangburn in conducting numerical experiments with the algorithms.


  1. Asmundsson J, Rardin RL, Uzsoy R (2006) “Tractable nonlinear production planning models for semiconductor wafer fabrication facilities,” IEEE Trans Semicond Manuf 19(1):1–17CrossRefGoogle Scholar
  2. Bechte W (1982) “Controlling manufacturing lead time and work-in-process inventory by means of load-oriented order release”. 25th Annual International Conference. Proceedings, APICS, APICS Fall Church VA, pp 67–72Google Scholar
  3. Bertrand J (1981) “The effect of workload control on order flow-times”. Proc. IXth IFORS Conference on Operations Research. North Holland, AmsterdamGoogle Scholar
  4. Bertrand JWM (1983) “The use of workload information to control job lateness in controlled and uncontrolled release production systems”. J Oper Manag 3:67–78CrossRefGoogle Scholar
  5. Bertrand JWM (1985) “Multiproduct optimal batch sizes with in-process inventories and multiwork centres”. IIE Trans 17:157–163CrossRefGoogle Scholar
  6. Bitran GR, Haas EA, Matsuo H (1986) “Production planning of style goods with high setup costs and forecast revisions.” Oper Res 34(2):226–236CrossRefGoogle Scholar
  7. Bitran GR, Yanasse HH (1984) “Deterministic approximations to stochastic production problems.” Oper Res 32(5):999–1018CrossRefGoogle Scholar
  8. Bowman EH (1956) “Production scheduling by the transportation method of linear programming.” Oper Res 4(1):100–103CrossRefGoogle Scholar
  9. Charnes A, Cooper WW (1959) “Chance constrained programming.” Manag Sci 5:73–79CrossRefGoogle Scholar
  10. Deleersnyder JL, Hodgson TJ, Muller H, O’Grady PJ (1989) “Kanban controlled pull systems: an analytic approach”. Manag Sci 35:1079–1091CrossRefGoogle Scholar
  11. Denardo EV, Tang CS (1992) “Linear control of a markov production system”. Oper Res 40: 259–278CrossRefGoogle Scholar
  12. Gferer H, Zäpfel G (1995) “Hierarchical model for production planning in case of uncertain demand.” Eur J Oper Res 86(1):142–161CrossRefGoogle Scholar
  13. Graves SC (1986) “A tactical planning model of a job shop”. Oper Res 34:522–533CrossRefGoogle Scholar
  14. Hausman WH, Sides RGS (1974) “Mail-order demands for style goods: Theory and data analysis,” Manag Sci 20:191–202CrossRefGoogle Scholar
  15. Hanssmann F, Hess SW (1960) “A linear programming approach to production and employment scheduling,” Manag Tech 1Google Scholar
  16. Hax AC (1978). “Aggregate production planning”. In: Moder J, Elmaghraby SE (eds.) Handbook of operation research, Chap. 5, vol. 2. Van Nostrand, ReinholdGoogle Scholar
  17. Homem-de-Mello T, Shapiro A, Spearman ML (1999) “Finding optimal material release times using simulation-based optimization.” Manag Sci 45(1):86–102CrossRefGoogle Scholar
  18. Holt CC, Modigliani F, Muth JF, Simon HA (1960) Planning production, inventories and work force. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  19. Karmarkar US (1987a) “The multilocation multi-period inventory problem: bounds and approximations,” Manag Sci 33:86–94CrossRefGoogle Scholar
  20. Karmarkar US (1987b) “Lot sizes, lead times and in-process inventories”. Manag Sci 33:409–418CrossRefGoogle Scholar
  21. Karmarkar US (1989) “Capacity loading and release planning with work-in-progress (WIP) and leadtimes”. J Manuf Oper Manag 2:105–123Google Scholar
  22. Karmarkar US (1993) “Manufacturing lead times, order release and capacity loading”. In: Graves S, Rinnooy Kan AHG, Zipkin P (eds.) Handbook in operations research and management science, Vol. 4. Logistics of Production and Inventory. North HollandGoogle Scholar
  23. Karmarkar US, Kekre S (1989) “Batching policy in Kanban systems”. J Manuf Syst 8:317–328CrossRefGoogle Scholar
  24. Karmarkar US, Kekre S, Kekre S, Freeman S (1985) “Lotsizing and lead time performance in a manufacturing cell”. Interfaces 15:1–9CrossRefGoogle Scholar
  25. Karmarkar US, Lin S (1988) “Production planning with uncertain yields and demands”. Simon School of Management Working Paper, University of RochesterGoogle Scholar
  26. Karmarkar US, Rajaram K (2002) “Product cycling with uncertain yields: analysis and application to the process industry” Oper Res 50:680–691CrossRefGoogle Scholar
  27. Karmarkar US, Yoo J (1994) “Stochastic dynamic product cycling problem”. Eur J Oper Res 73:360–373CrossRefGoogle Scholar
  28. Kimball GE (1988) “General principles of inventory control”. J. Manuf Oper Manag 1:119–130Google Scholar
  29. Land M, Gaalman G (1996) “Workload control concepts in job shops – a critical assessment”. Int J Prod Econ 46–47:535–548CrossRefGoogle Scholar
  30. Lasdon LS, Terjung RC (1971) “An efficient algorithm for multi-item scheduling”. Oper Res 19(4):946–969CrossRefGoogle Scholar
  31. Lasserre JB, Mercé C (1990) Robust hierarchical production planning under uncertainty. Ann Oper Res 26:73–87CrossRefGoogle Scholar
  32. Lin SC (1986) “Production with uncertainty”. Ph.D. Dissertation, William E. Simon Graduate School of Business Administration, University of Rochester, unpublishedGoogle Scholar
  33. Manne AS (1958) “Programming of economic lot sizes.” Manag Sci 4:115–135CrossRefGoogle Scholar
  34. Missbauer H (2002) “Aggregate order release planning for time-varying demand”. Int J Prod Res 40(3):699–718CrossRefGoogle Scholar
  35. Nam S, Logendran R (1992) “Aggregate production planning – a survey of models and methodologies”. Eur J Oper Res 61:255–272CrossRefGoogle Scholar
  36. Pahl J, Voß S, Woodruff DL (2005) “Production planning with load dependent lead times”. 4OR Q J Oper Res 3(4):257–302Google Scholar
  37. Perona M, Portioli A (1998) “The impact of parameters setting in load oriented manufacturing control”. Int J Prod Econ 55:133–142CrossRefGoogle Scholar
  38. Riaño G (2002) “Transient behavior of stochastic networks: application to production planning with load-dependent lead times.” Ph.D. Dissertation, Georgia Institute of TechnologyGoogle Scholar
  39. Sahinidis NV (2004) “Optimization under uncertainty: state-of-the-art and opportunities”. Comput Chem Eng 28:971–983CrossRefGoogle Scholar
  40. Spearman ML, Zazanis MA (1992) “Push and pull production systems: issues and comparisons”. Oper Res 40:521–532CrossRefGoogle Scholar
  41. Zijm WHM, Buitenhoek R (1996) “Capacity planning and leadtime management”. Int J Prod Econ 46–47:165–179CrossRefGoogle Scholar
  42. Zipkin PH (1986) “Models for design and control of stochastic, multi-item batch production systems”. Oper Res 34:91–104CrossRefGoogle Scholar

Copyright information

© Springer New York 2011

Authors and Affiliations

  1. 1.Simon SchoolUniversity of RochesterRochesterUSA

Personalised recommendations