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A Linear Decision Rule for Production and Employment Scheduling


Author Info

  • Charles C. Holt

    (Carnegie Institute of Technology)

  • Franco Modigliani

    (Carnegie Institute of Technology)

  • Herbert A. Simon

    (Carnegie Institute of Technology)


The decision problems involved in setting the aggregate production rate of a factory and setting the size of its work force are frequently both complex and difficult. The quality of these decisions can be of great importance to the profitability of an individual company, and when viewed on a national scale these decisions have a significant influence on the efficiency of the economy as a whole. This paper reports some of the findings of a research team that has been developing new methods to enable production executives to make better decisions and to make them more easily than they can with prevailing procedures. With the cooperation of a manufacturing concern, the new methods have been developed in the context of a set of concrete production scheduling problems that were found in a factory operated by the company. The new method which is presented in this paper, involves: (1) formalizing and quantifying the decision problem (using a quadratic approximation to the criterion function) and (2), calculating a generalized optimal solution of the problem in the form of a (linear) decision rule. Like a rule of thumb, an optimal decision rule prescribes a course of action when it is applied to a particular set of circumstances; but, unlike most rules of thumb, an optimal decision rule prescribes courses of action for which the claim can be made that the decisions are "the best possible," the meaning of "best" being clearly specified. The ultimate test, of course, must be whether the new decision methods do or do not outperform prevailing decision methods when full allowance is made for the cost of obtaining the optimal decisions.

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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 2 (1955)
Issue (Month): 1 (October)
Pages: 1-30

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Handle: RePEc:inm:ormnsc:v:2:y:1955:i:1:p:1-30

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Cited by:
  1. Gomes da Silva, Carlos & Figueira, José & Lisboa, João & Barman, Samir, 2006. "An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming," Omega, Elsevier, vol. 34(2), pages 167-177, April.
  2. Wang, Reay-Chen & Liang, Tien-Fu, 2005. "Applying possibilistic linear programming to aggregate production planning," International Journal of Production Economics, Elsevier, vol. 98(3), pages 328-341, December.
  3. Joglekar, Nitin R. & Ford, David N., 2005. "Product development resource allocation with foresight," European Journal of Operational Research, Elsevier, vol. 160(1), pages 72-87, January.
  4. Aghezzaf, El-Houssaine, 2000. "Lot-sizing problem with setup times in labor-based capacity production systems," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 1-9, March.
  5. Sanders, Nada R. & Graman, Gregory A., 2009. "Quantifying costs of forecast errors: A case study of the warehouse environment," Omega, Elsevier, vol. 37(1), pages 116-125, February.
  6. Yi Wen, 2011. "Input and output inventory dynamics," Working Papers 2011-008, Federal Reserve Bank of St. Louis.
  7. Graves, Stephen C. & Meal, Harlan C. & Dasu, Sririam. & Qui, Yuping., 1985. "Two-stage production planning in a dynamic environment," Working papers 1698-85., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  8. Danese, Pamela & Kalchschmidt, Matteo, 2011. "The role of the forecasting process in improving forecast accuracy and operational performance," International Journal of Production Economics, Elsevier, vol. 131(1), pages 204-214, May.
  9. Pedro Garcia Duarte, 2005. "A FEASIBLE AND OBJECTIVE CONCEPT OF OPTIMALITY: THE QUADRATIC LOSS FUNCTION AND U. S. MONETARY POLICY IN THE 1960's," Anais do XXXIII Encontro Nacional de Economia [Proceedings of the 33th Brazilian Economics Meeting] 016, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  10. Lurie, Nicholas H. & Swaminathan, Jayashankar M., 2009. "Is timely information always better? The effect of feedback frequency on decision making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 108(2), pages 315-329, March.
  11. Corominas, Albert & Lusa, Amaia & Olivella, Jordi, 2012. "A detailed workforce planning model including non-linear dependence of capacity on the size of the staff and cash management," European Journal of Operational Research, Elsevier, vol. 216(2), pages 445-458.
  12. Singhal, Jaya & Singhal, Kalyan, 1996. "Alternate approaches to solving the Holt et al. model and to performing sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 91(1), pages 89-98, May.
  13. Wu, Chia-Chin & Chang, Ni-Bin, 2004. "Corporate optimal production planning with varying environmental costs: A grey compromise programming approach," European Journal of Operational Research, Elsevier, vol. 155(1), pages 68-95, May.
  14. Mirzapour Al-e-hashem, S.M.J. & Baboli, A. & Sazvar, Z., 2013. "A stochastic aggregate production planning model in a green supply chain: Considering flexible lead times, nonlinear purchase and shortage cost functions," European Journal of Operational Research, Elsevier, vol. 230(1), pages 26-41.
  15. Mirzapour Al-e-hashem, S.M.J. & Malekly, H. & Aryanezhad, M.B., 2011. "A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty," International Journal of Production Economics, Elsevier, vol. 134(1), pages 28-42, November.
  16. White, Sheneeta W. & Badinelli, Ralph D., 2012. "A model for efficiency-based resource integration in services," European Journal of Operational Research, Elsevier, vol. 217(2), pages 439-447.
  17. Singer, Marcos & Obach, Juan José, 2013. "Listening to workers: The overtime versus hiring dilemma," Journal of Business Research, Elsevier, vol. 66(10), pages 1771-1779.
  18. Buxey, Geoff, 2003. "Strategy not tactics drives aggregate planning," International Journal of Production Economics, Elsevier, vol. 85(3), pages 331-346, September.


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