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Production Planning with Convex Costs: A Parametric Study

Author

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  • Arthur F. Veinott, Jr.

    (Stanford University, Stanford, California)

Abstract

We consider the problem of choosing the amounts of a single product to produce in each of a finite number of time periods so as to minimize the (convex) production and (convex) inventory carrying costs over the periods while satisfying known requirements. The effect of changes in the various parameters, viz., the requirements and the production and inventory capacity limits, upon the optimal production levels is studied. The results obtained are exploited to provide simple and intuitive computational procedures for finding optimal production schedules for a range of parameter values.

Suggested Citation

  • Arthur F. Veinott, Jr., 1964. "Production Planning with Convex Costs: A Parametric Study," Management Science, INFORMS, vol. 10(3), pages 441-460, April.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:3:p:441-460
    DOI: 10.1287/mnsc.10.3.441
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    Cited by:

    1. Jian Yang & Xiangtong Qi & Gang Yu, 2005. "Disruption management in production planning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 420-442, August.
    2. Hoesel C.P.M. van & Wagelmans A.P.M., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Archis Ghate & Robert L. Smith, 2009. "Optimal Backlogging Over an Infinite Horizon Under Time-Varying Convex Production and Inventory Costs," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 362-368, June.
    4. Iara Ciurria-Infosino & Daniel Granot & Frieda Granot & Arthur F. Veinott, 2015. "Multicommodity Production Planning: Qualitative Analysis and Applications," Manufacturing & Service Operations Management, INFORMS, vol. 17(4), pages 589-607, October.
    5. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    6. van Hoesel, C.P.M. & Wagelmans, A., 1997. "Fully polynomial approximation schemes for single-item capacitated economic lot-sizing problems," Research Memorandum 029, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Gutierrez, J. & Puerto, J. & Sicilia, J., 2004. "The multiscenario lot size problem with concave costs," European Journal of Operational Research, Elsevier, vol. 156(1), pages 162-182, July.
    8. C. P. M. van Hoesel & A. P. M. Wagelmans, 2001. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 339-357, May.
    9. van Hoesel, C.P.M. & Wagelmans, A.P.M., 1997. "Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems," Econometric Institute Research Papers EI 9735/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Shaw, D.X. & Wagelmans, A.P.M., 1995. "An Algorithm for Single-item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Econometric Institute Research Papers EI 9526-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Robert L. Smith & Rachel Q. Zhang, 1998. "Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs," Management Science, INFORMS, vol. 44(9), pages 1313-1320, September.
    12. Li, Xiang & Li, Yongjian & Cai, Xiaoqiang, 2013. "Double marginalization and coordination in the supply chain with uncertain supply," European Journal of Operational Research, Elsevier, vol. 226(2), pages 228-236.
    13. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.
    14. Xie, Weijun & Ouyang, Yanfeng, 2015. "Optimal layout of transshipment facility locations on an infinite homogeneous plane," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 74-88.
    15. Sreekumar Bhaskaran & Karthik Ramachandran & John Semple, 2010. "A Dynamic Inventory Model with the Right of Refusal," Management Science, INFORMS, vol. 56(12), pages 2265-2281, December.

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