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Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product

Received: 4 July 2018     Accepted: 17 July 2018     Published: 17 August 2018
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Abstract

We consider the EOQ model with an opportunity cost of capital, i.e. an amount x invested now will yield (1+i)x at the beginning of the next period. Here i is the interest rate. Given a cost stream i.e. a stream of costs incurred over time, the Net Present Value (NPV) is used to decide the total cost of the cost stream. This total cost takes into account the opportunity cost of capital. The Discounted Average Cost changes the NPV, which is a total, into a cost rate per unit time. The discounted average cost is a cost rate. If we incur this cost rate for the entire period of time under consideration, it will lead to the same NPV as the actual NPV of the cost stream. The discounted average cost under continuous compounding is thus an alternative objective to the standard objective of average cost, which is also a cost rate. We minimize the discounted average cost under continuous compounding for two EOQ models, one with a regular product and the other with a perishable product. Perishable products include food, medicines, certain chemicals and blood in blood banks. In the EOQ model with a perishable product, inventory decays at a constant rate over time. We find the optimal order quantity for the two models while minimizing discounted average cost under continuous compounding.

Published in American Journal of Operations Management and Information Systems (Volume 3, Issue 2)
DOI 10.11648/j.ajomis.20180302.13
Page(s) 52-60
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Inventory, EOQ Model, Discounted Average Cost, Continuous Compounding, Perishable Product

References
[1] Porteus, E. L. Foundations of Stochastic Inventory Theory, 2002, Stanford University Press: Stanford, California.
[2] Nahmias, S. Production and Operations Analysis, 1989, Irwin: Boston, MA.
[3] Zipkin, P. Foundations of Inventory Management. 2000. McGraw Hill Higher Education.
[4] Ouyang, L. Y., C. T. Chang and J. T. Teng (2005). An EOQ model for deteriorating items under trade credit. Journal of the Operational Research Society. Vol. 56, No. 6, 719-726.
[5] Tripathy, P. K., W. M. Wee and P. R. Majhi (2003). An EOQ model with process reliability considerations. Journal of the Operational Research Society. Vol. 54, No. 5, 549.
[6] Eroglu, A. and G. Ozdemir (2007). An economic order quantity model with defective items and shortages. International Journal of Production Economics. Vol. 106, No. 2, 544-549.
[7] Giri, B. C., A. K. Jalan and K. S. Chaudhuri (2003). Economic Order Quantity model with Weibull deterioration distribution, shortage and ramp-type demand. International Journal of Systems Science. Vol. 34, No. 4, 237-243.
[8] Salameh, M. K. and M. Y. Jaber (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics. Vol. 64, No. 1, 59-64.
[9] Ouyang, L. Y., J. T. Teng, S. K. Goyal and C. T. Yang (2009). An Economic Order Quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. European Journal of Operational Research. Vol. 194, No. 2, 418-431.
[10] Chua, P., K. J. Chung and S. P. Lan (1998). Economic Order Quantity of deteriorating items under permissible delay in payments. Computers and Operations Research. Vol. 25, No. 10, 817-824.
Cite This Article
  • APA Style

    Siddharth Mahajan, Krishna Sundar Diatha. (2018). Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product. American Journal of Operations Management and Information Systems, 3(2), 52-60. https://doi.org/10.11648/j.ajomis.20180302.13

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    ACS Style

    Siddharth Mahajan; Krishna Sundar Diatha. Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product. Am. J. Oper. Manag. Inf. Syst. 2018, 3(2), 52-60. doi: 10.11648/j.ajomis.20180302.13

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    AMA Style

    Siddharth Mahajan, Krishna Sundar Diatha. Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product. Am J Oper Manag Inf Syst. 2018;3(2):52-60. doi: 10.11648/j.ajomis.20180302.13

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  • @article{10.11648/j.ajomis.20180302.13,
      author = {Siddharth Mahajan and Krishna Sundar Diatha},
      title = {Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product},
      journal = {American Journal of Operations Management and Information Systems},
      volume = {3},
      number = {2},
      pages = {52-60},
      doi = {10.11648/j.ajomis.20180302.13},
      url = {https://doi.org/10.11648/j.ajomis.20180302.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajomis.20180302.13},
      abstract = {We consider the EOQ model with an opportunity cost of capital, i.e. an amount x invested now will yield (1+i)x at the beginning of the next period. Here i is the interest rate. Given a cost stream i.e. a stream of costs incurred over time, the Net Present Value (NPV) is used to decide the total cost of the cost stream. This total cost takes into account the opportunity cost of capital. The Discounted Average Cost changes the NPV, which is a total, into a cost rate per unit time. The discounted average cost is a cost rate. If we incur this cost rate for the entire period of time under consideration, it will lead to the same NPV as the actual NPV of the cost stream. The discounted average cost under continuous compounding is thus an alternative objective to the standard objective of average cost, which is also a cost rate. We minimize the discounted average cost under continuous compounding for two EOQ models, one with a regular product and the other with a perishable product. Perishable products include food, medicines, certain chemicals and blood in blood banks. In the EOQ model with a perishable product, inventory decays at a constant rate over time. We find the optimal order quantity for the two models while minimizing discounted average cost under continuous compounding.},
     year = {2018}
    }
    

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    AU  - Siddharth Mahajan
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    AB  - We consider the EOQ model with an opportunity cost of capital, i.e. an amount x invested now will yield (1+i)x at the beginning of the next period. Here i is the interest rate. Given a cost stream i.e. a stream of costs incurred over time, the Net Present Value (NPV) is used to decide the total cost of the cost stream. This total cost takes into account the opportunity cost of capital. The Discounted Average Cost changes the NPV, which is a total, into a cost rate per unit time. The discounted average cost is a cost rate. If we incur this cost rate for the entire period of time under consideration, it will lead to the same NPV as the actual NPV of the cost stream. The discounted average cost under continuous compounding is thus an alternative objective to the standard objective of average cost, which is also a cost rate. We minimize the discounted average cost under continuous compounding for two EOQ models, one with a regular product and the other with a perishable product. Perishable products include food, medicines, certain chemicals and blood in blood banks. In the EOQ model with a perishable product, inventory decays at a constant rate over time. We find the optimal order quantity for the two models while minimizing discounted average cost under continuous compounding.
    VL  - 3
    IS  - 2
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Author Information
  • Production and Operations Management Area, Indian Institute of Management, Bangalore, India

  • Production and Operations Management Area, Indian Institute of Management, Bangalore, India

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