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Derivation of a Linear Decision Rule for Production and Employment


  • Charles C. Holt

    (Graduate School of Industrial Administration, Carnegie Institute of Technology)

  • Franco Modigliani

    (Graduate School of Industrial Administration, Carnegie Institute of Technology)

  • John F. Muth

    (Graduate School of Industrial Administration, Carnegie Institute of Technology)


An application of linear decision rules to production and employment scheduling was described in the last issue of this journal [Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October).]. The hypothetical performance of these rules represented a significant improvement over the actual company performance as measured by independent cost estimates and other managerial measures of efficiency. The quadratic cost function which was used should be applicable to production and employment scheduling decisions in many other situations. Also the general approach of approximating decision criteria with quadratic functions and obtaining linear decision rules can usefully be extended to many decision problems. In the present paper we will demonstrate (a) how optimal (i.e., minimum expected cost) decision rules may be derived for a quadratic cost function involving inventory, overtime, and employment costs, and (b) how the numerical coefficients of the rules may be computed for any set of cost parameters.

Suggested Citation

  • Charles C. Holt & Franco Modigliani & John F. Muth, 1956. "Derivation of a Linear Decision Rule for Production and Employment," Management Science, INFORMS, vol. 2(2), pages 159-177, January.
  • Handle: RePEc:inm:ormnsc:v:2:y:1956:i:2:p:159-177
    DOI: 10.1287/mnsc.2.2.159

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    2. Marvin D. Troutt & Wan-Kai Pang & Shui-Hung Hou, 2006. "Behavioral Estimation of Mathematical Programming Objective Function Coefficients," Management Science, INFORMS, vol. 52(3), pages 422-434, March.
    3. 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 33rd Brazilian Economics Meeting] 016, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    4. Saravanan Kesavan & Bradley R. Staats & Wendell Gilland, 2014. "Volume Flexibility in Services: The Costs and Benefits of Flexible Labor Resources," Management Science, INFORMS, vol. 60(8), pages 1884-1906, August.
    5. Elizabeth Chase MacRae, 1972. "Linear Decision with Experimentation," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 4, pages 437-447, National Bureau of Economic Research, Inc.
    6. Krishna Kumar, C. & Sinha, Bani K., 1999. "Efficiency based production planning and control models," European Journal of Operational Research, Elsevier, vol. 117(3), pages 450-469, September.
    7. 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.
    8. Körpeoglu, Ersin & Yaman, Hande & Selim Aktürk, M., 2011. "A multi-stage stochastic programming approach in master production scheduling," European Journal of Operational Research, Elsevier, vol. 213(1), pages 166-179, August.
    9. Chen, Yao & Djamasbi, Soussan & Du, Juan & Lim, Sungmook, 2013. "Integer-valued DEA super-efficiency based on directional distance function with an application of evaluating mood and its impact on performance," International Journal of Production Economics, Elsevier, vol. 146(2), pages 550-556.
    10. Andrea Borenich & Peter Greistorfer & Marc Reimann, 2020. "Model-based production cost estimation to support bid processes: an automotive case study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(3), pages 841-868, September.
    11. Harvey M. Wagner, 2002. "And Then There Were None," Operations Research, INFORMS, vol. 50(1), pages 217-226, February.
    12. 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.

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