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A Linear Programming Approach to Production and Employment Scheduling

Author

Listed:
  • Fred Hanssmann

    (Case Institute of Technology)

  • Sidney W. Hess

    (Case Institute of Technology)

Abstract

The problem of production and employment scheduling may be stated as follows. Given the monthly demands for the product turned out by a factory, what should be the monthly production rates and work force levels in order to minimize the total cost of regular payroll and overtime, hiring and layoffs, inventory and shortages incurred during a given planning interval of several months? This problem has received a classical solution in two papers by Holt, Modigliani, Muth, and Simon (Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October); Holt, C. C., F. Modigliani, J. F. Muth. 1956. Derivation of a linear decision rule for production and employment. Management Sci. (January).). These authors assumed quadratic cost functions. Their treatment of the problem will be referred to as "quadratic programming." It appears, however, that in the majority of practical applications and theoretical models the cost functions are assumed to be linear. It, therefore, seems desirable to have a method of solution for the linear case as well. In this paper it is shown that a solution can be obtained by linear programming methods. From the linear programming viewpoint, this paper is of an expository nature. "Management Technology", ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.

Suggested Citation

  • Fred Hanssmann & Sidney W. Hess, 1960. "A Linear Programming Approach to Production and Employment Scheduling," Management Science, INFORMS, vol. 0(1), pages 46-51, January.
    • Handle: RePEc:inm:ormnsc:v:mt-1:y:1960:i:1:p:46-51
    DOI: 10.1287/mantech.1.1.46
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    Cited by:

    1. Michael J. Fry & Michael J. Magazine & Uday S. Rao, 2006. "Firefighter Staffing Including Temporary Absences and Wastage," Operations Research, INFORMS, vol. 54(2), pages 353-365, April.
    2. 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.
    3. Black, Ben & Ainslie, Russell & Dokka, Trivikram & Kirkbride, Christopher, 2023. "Distributionally robust resource planning under binomial demand intakes," European Journal of Operational Research, Elsevier, vol. 306(1), pages 227-242.
    4. Rujira Visuthirattanamanee & Krung Sinapiromsaran & Aua-aree Boonperm, 2020. "Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    5. 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.
    6. 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.
    7. 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.
    8. Wang, Reay-Chen & Fang, Hsiao-Hua, 2001. "Aggregate production planning with multiple objectives in a fuzzy environment," European Journal of Operational Research, Elsevier, vol. 133(3), pages 521-536, September.
    9. Karmarkar, Uday S. & Rajaram, Kumar, 2012. "Aggregate production planning for process industries under oligopolistic competition," European Journal of Operational Research, Elsevier, vol. 223(3), pages 680-689.
    10. 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.
    11. Hax, Arnoldo C. & Meal, Harlan C., 1973. "Hierarchical integration of production planning and scheduling," Working papers 656-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. Gordon H. Lewis & Ashok Srinivasan & Eswaran Subrahmanian, 1998. "Staffing and Allocation of Workers in an Administrative Office," Management Science, INFORMS, vol. 44(4), pages 548-570, April.
    13. 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.

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