- Email: [email protected]
A note on: Optimal ordering policies in response to a discount offer
ARTICLE IN PRESS
Int. J. Production Economics 112 (2008) 1000–1001 www.elsevier.com/locate/ijpe
Short communication
A note on: Optimal ordering policies in response to a discount offer S.K. Goyala, M.Y. Jaberb, a
Decision Sciences & MIS, John Molson School of Business, Concordia University, Montreal, Quebec, Canada H3G1M8 b Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3 Received 9 September 2007; accepted 12 October 2007 Available online 20 February 2008
Abstract In this short note, we are suggesting a marginal analysis approach over the approach used by Sarker and Al Kindi [2006, Optimal ordering policies in response to a discount offer. International Journal of Production Economics 100(2), 195–211] for developing models for determining the optimal ordering policy for an item for which the supplies offer a price discount during a sale period. r 2007 Elsevier B.V. All rights reserved. Keywords: EOQ; Discount
In their paper, Sarker and Al Kindi (2006) develop a number of models to determine the optimal ordering policy during the sale period of a product for various situations. They obtained the optimal ordering policy by maximizing the difference between the two costs: Regular EOQ cost and special quantity cost during the sale period. The readers of the International Journal of Production Economics may be interested in knowing that marginal analysis offers a far easier approach for developing the optimal order quantity models than the approach adopted by Sarker and Al Kindi (2006) of maximizing the difference between the two types of costs: Regular EOQ cost and special quantity cost during the sale period. To illustrate the simplicity of DOI of original article: 10.1016/j.ijpe.2005.12.011
Corresponding author. Tel.: +1 416 979 5000x7623;
fax: +1 416 979 5265. E-mail address: [email protected] (M.Y. Jaber).
the marginal analysis approach, we develop the model for Case 1 of Sarker and Al Kindi (2006) where the sale period coincides with the replenishment time. Using the following notations: D Qs Q A i C d
annual demand special order quantity during the sale period regular economic order quantity ordering cost per order annual interest rate purchasing cost per item discount per item
the marginal cost of the Qsth item (when a special order is placed) is given by ðC dÞ þ iðC dÞQs =D. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Substituting Q by 2AD=iC in Eq. (1), of Sarker and Al Kindi (2006), which is the EOQ cost
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2007.10.004
ARTICLE IN PRESS S.K. Goyal, M.Y. Jaber / Int. J. Production Economics 112 (2008) 1000–1001
function, and dividing the result by D, the marginal cost of the Qsth item (when no special order is placed) is given by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DC þ 2iDAC . D On equating the two types of marginal costs at Qs ¼ Qs , we get Qs ¼
Dð2A þ dQÞ . iQðC dÞ
1001
We leave it to the readers of the International Journal of Production Economics to decide for themselves between the two approaches they will prefer.
Reference Sarker, B.R., Al Kindi, M., 2006. Optimal ordering policies in response to a discount offer. International Journal of Production Economics 100 (2), 195–211.
Int. J. Production Economics 112 (2008) 1000–1001 www.elsevier.com/locate/ijpe
Short communication
A note on: Optimal ordering policies in response to a discount offer S.K. Goyala, M.Y. Jaberb, a
Decision Sciences & MIS, John Molson School of Business, Concordia University, Montreal, Quebec, Canada H3G1M8 b Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario, Canada M5B 2K3 Received 9 September 2007; accepted 12 October 2007 Available online 20 February 2008
Abstract In this short note, we are suggesting a marginal analysis approach over the approach used by Sarker and Al Kindi [2006, Optimal ordering policies in response to a discount offer. International Journal of Production Economics 100(2), 195–211] for developing models for determining the optimal ordering policy for an item for which the supplies offer a price discount during a sale period. r 2007 Elsevier B.V. All rights reserved. Keywords: EOQ; Discount
In their paper, Sarker and Al Kindi (2006) develop a number of models to determine the optimal ordering policy during the sale period of a product for various situations. They obtained the optimal ordering policy by maximizing the difference between the two costs: Regular EOQ cost and special quantity cost during the sale period. The readers of the International Journal of Production Economics may be interested in knowing that marginal analysis offers a far easier approach for developing the optimal order quantity models than the approach adopted by Sarker and Al Kindi (2006) of maximizing the difference between the two types of costs: Regular EOQ cost and special quantity cost during the sale period. To illustrate the simplicity of DOI of original article: 10.1016/j.ijpe.2005.12.011
Corresponding author. Tel.: +1 416 979 5000x7623;
fax: +1 416 979 5265. E-mail address: [email protected] (M.Y. Jaber).
the marginal analysis approach, we develop the model for Case 1 of Sarker and Al Kindi (2006) where the sale period coincides with the replenishment time. Using the following notations: D Qs Q A i C d
annual demand special order quantity during the sale period regular economic order quantity ordering cost per order annual interest rate purchasing cost per item discount per item
the marginal cost of the Qsth item (when a special order is placed) is given by ðC dÞ þ iðC dÞQs =D. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Substituting Q by 2AD=iC in Eq. (1), of Sarker and Al Kindi (2006), which is the EOQ cost
0925-5273/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2007.10.004
ARTICLE IN PRESS S.K. Goyal, M.Y. Jaber / Int. J. Production Economics 112 (2008) 1000–1001
function, and dividing the result by D, the marginal cost of the Qsth item (when no special order is placed) is given by pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DC þ 2iDAC . D On equating the two types of marginal costs at Qs ¼ Qs , we get Qs ¼
Dð2A þ dQÞ . iQðC dÞ
1001
We leave it to the readers of the International Journal of Production Economics to decide for themselves between the two approaches they will prefer.
Reference Sarker, B.R., Al Kindi, M., 2006. Optimal ordering policies in response to a discount offer. International Journal of Production Economics 100 (2), 195–211.