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Budget Allocation for Permanent and Contingent Capacity under Stochastic Demand

  • Mincsovics, Gergely
  • Jeunet, Jully
  • Dellaert, Nico
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    We develop a model of budget allocation for permanent and contingent workforce under stochastic demand. The level of permanent capacity is determined at the beginning of the horizon and is kept constant throughout, whereas the number of temporary workers to be hired must be decided in each period. Compared to existing budgeting models, this paper explicitly considers a budget constraint. Under the assumption of a restricted budget, the objective is to minimize capacity shortages. When over-expenditures are allowed, both budget deviations and shortage costs are to be minimized. The capacity shortage cost function is assumed to be either linear or quadratic with the amount of shortage, which corresponds to different market structures or different types of services. We thus examine four variants of the problem that we model and solve either approximately or to optimality when possible. A comprehensive experimental design is designed to analyze the behavior of our models when several levels of demand variability and parameter values are considered. The parameters consist of the initial budget level, the unit cost of temporary workers and the budget deviation penalty/reward rates. Varying these parameters produce several trade-offs between permanent and temporary workforce levels, and between capacity shortages and budget deviations. Numerical results also show that the quadratic cost function leads to smooth and moderate capacity shortages over the time periods, whereas all shortages are either avoided or accepted when the cost function is linear.

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    Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/4010.

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    Date of creation: 2011
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    Publication status: Published in International Journal of Production Economics, 2011, Vol. 131, no. 1. pp. 128-138.Length: 10 pages
    Handle: RePEc:dau:papers:123456789/4010
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    1. Edward P. C. Kao & Maurice Queyranne, 1985. "Budgeting Costs of Nursing in a Hospital," Management Science, INFORMS, vol. 31(5), pages 608-621, May.
    2. Berman, Oded & Larson, Richard C., 1994. "Determining optimal pool size of a temporary call-in work force," European Journal of Operational Research, Elsevier, vol. 73(1), pages 55-64, February.
    3. Wild, Bernhard & Schneewei, Christoph, 1993. "Manpower capacity planning -- A hierarchical approach," International Journal of Production Economics, Elsevier, vol. 30(1), pages 95-106, July.
    4. D. Michael Warner & Juan Prawda, 1972. "A Mathematical Programming Model for Scheduling Nursing Personnel in a Hospital," Management Science, INFORMS, vol. 19(4-Part-1), pages 411-422, December.
    5. Herman, Oded & Larson, Richard C., 1993. "Optimal workforce configuration incorporating absenteeism and daily workload variability," Socio-Economic Planning Sciences, Elsevier, vol. 27(2), pages 91-96, June.
    6. Pinker, Edieal J. & Larson, Richard C., 2003. "Optimizing the use of contingent labor when demand is uncertain," European Journal of Operational Research, Elsevier, vol. 144(1), pages 39-55, January.
    7. Techawiboonwong, Atthawit & Yenradee, Pisal & Das, Sanchoy K., 2006. "A master scheduling model with skilled and unskilled temporary workers," International Journal of Production Economics, Elsevier, vol. 103(2), pages 798-809, October.
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