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A simple method to compute economic order quantities

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  • Teng, Jinn-Tsair

Abstract

In this note, a simple method by using the arithmetic-geometric-mean-inequality theorem is proposed to computer the global minimum economic order quantities without taking complex differential calculus or using tedious algebraic manipulations. In contrast to (Minner, S., 2007. A note on how to compute economic order quantity without derivatives by cost comparisons. International Journal of Production Economics 105, 293-296; Wee, H.M., Wang, W.T., Chung, C.J., 2009. A modified method to computer economic order quantities without derivatives by cost-difference comparisons. European Journal of Operational Research) based on a local cost minimum initially to derive the solution and then proven it's the global minimum, the proposed method yields the global minimum cost immediately and explicitly without using the cost comparisons and letting the time horizon to infinity.

Suggested Citation

  • Teng, Jinn-Tsair, 2009. "A simple method to compute economic order quantities," European Journal of Operational Research, Elsevier, vol. 198(1), pages 351-353, October.
  • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:351-353
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    References listed on IDEAS

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    1. Grubbstrom, Robert W. & Erdem, Asli, 1999. "The EOQ with backlogging derived without derivatives," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 529-530, March.
    2. Wee, Hui-Ming & Wang, Wan-Tsu & Chung, Chun-Jen, 2009. "A modified method to compute economic order quantities without derivatives by cost-difference comparisons," European Journal of Operational Research, Elsevier, vol. 194(1), pages 336-338, April.
    3. Jason Chang, S.K. & Chuang, Jones P.C. & Chen, Hsiao-Jung, 2005. "Short comments on technical note--The EOQ and EPQ models with shortages derived without derivatives," International Journal of Production Economics, Elsevier, vol. 97(2), pages 241-243, August.
    4. Sphicas, Georghios P., 2006. "EOQ and EPQ with linear and fixed backorder costs: Two cases identified and models analyzed without calculus," International Journal of Production Economics, Elsevier, vol. 100(1), pages 59-64, March.
    5. Wee, Hui Ming & Chung, Chun Jen, 2007. "A note on the economic lot size of the integrated vendor-buyer inventory system derived without derivatives," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1289-1293, March.
    6. Ronald, Robert & Yang, Gino K. & Chu, Peter, 2004. "Technical note: The EOQ and EPQ models with shortages derived without derivatives," International Journal of Production Economics, Elsevier, vol. 92(2), pages 197-200, November.
    7. Cardenas-Barron, Leopoldo Eduardo, 2001. "The economic production quantity (EPQ) with shortage derived algebraically," International Journal of Production Economics, Elsevier, vol. 70(3), pages 289-292, April.
    8. Minner, Stefan, 2007. "A note on how to compute economic order quantities without derivatives by cost comparisons," International Journal of Production Economics, Elsevier, vol. 105(1), pages 293-296, January.
    9. Cárdenas-Barrón, Leopoldo Eduardo, 2007. "Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 647-654, September.
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    Cited by:

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    2. Chen, Sheng-Chih & Cárdenas-Barrón, Leopoldo Eduardo & Teng, Jinn-Tsair, 2014. "Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity," International Journal of Production Economics, Elsevier, vol. 155(C), pages 284-291.
    3. Dellino, Gabriella & Kleijnen, Jack P.C. & Meloni, Carlo, 2010. "Robust optimization in simulation: Taguchi and Response Surface Methodology," International Journal of Production Economics, Elsevier, vol. 125(1), pages 52-59, May.
    4. Chang, Hung-Chi & Ho, Chia-Huei, 2010. "Exact closed-form solutions for "optimal inventory model for items with imperfect quality and shortage backordering"," Omega, Elsevier, vol. 38(3-4), pages 233-237, June.
    5. Vedran Kojić & Zrinka Lukač, 2014. "Solving the production cost minimization problem with the Cobb – Douglas production function without the use of derivatives," EFZG Working Papers Series 1403, Faculty of Economics and Business, University of Zagreb.
    6. R. Sundara rajan & R. Uthayakumar, 2017. "Comprehensive solution procedure for optimizing replenishment policies of instantaneous deteriorating items with stock-dependent demand under partial trade credit linked to order quantity," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1343-1373, November.
    7. Vedran Kojić, 2015. "Solving the utility maximization problem with CES and Cobb-Douglas utility function via mathematical inequalities," EFZG Working Papers Series 1504, Faculty of Economics and Business, University of Zagreb.
    8. Teng, Jinn-Tsair & Lou, Kuo-Ren & Wang, Lu, 2014. "Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs," International Journal of Production Economics, Elsevier, vol. 155(C), pages 318-323.
    9. Vedran Kojić & Zrinka Lukač, 2018. "An alternative approach to solving cost minimization problem with Cobb–Douglas technology," 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. 26(3), pages 629-643, September.

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