The previous efforts toward single period inventory problem with price-dependent demand only investigate the optimal order quantity to minimize the total inventory costs; however, there is no method in the literature to avoid unwanted costs due to the deviation between the actual demand and the previously estimated demand. To fill this gap, the present paper supposes that stochastic demand rate with normal distribution is sensitive to the selling price; this means that increasing the selling price would decrease the demand rate and vice versa. After monitoring the consumption trend within a section of the period, a new selling price is implemented to change the demand rate and reduce the shortage or salvage costs at the end of the period. Three functions were suggested to represent the demand rate as a function of selling price, and the numerical analysis was implemented to solve the proposed problem. Finally, an illustrative numerical example was solved for different configurations in order to show the advantages of the proposed model. The results revealed that there is a significant improvement in the system costs when price revision is considered. 1. Introduction Inventory management is an important task in the business operations. The classical single period problem (SPP) deals with the purchasing inventory problem for single-period products, such as perishable or seasonal goods. The SPP has been popularly researched in the last decade, because of its extensive application in the inventory management of the products with short life cycles (e.g., fashion clothes and electronic products [1]). The authors made extensions to incorporate real world situations in SPP (for further information refer to Khouja [2]); however, there are two important problems in SPP; the first one is how to be in front of demand’s uncertainty in the real dynamic global condition and the other one is how to deal with the demand pattern which is dependent to the selling price. For the price-dependent demand background, Whitin [3] assumed that the expected demand is a function of price, and by using incremental analysis, he derived the necessary optimality condition. Whitin then provided closed-form expressions for the optimal price, which is used to find the optimal order quantity for a demand with a rectangular distribution. Mills [4] assumed demand to be a random variable with an expected value that is decreasing in price and with constant variance. Mills derived the necessary optimality conditions and provided further analysis for the case of demand with rectangular
References
[1]
J. L. Zhang, C. Y. Lee, and J. Chen, “Inventory control problem with freight cost and stochastic demand,” Operations Research Letters, vol. 37, no. 6, pp. 443–446, 2009.
[2]
M. Khouja, “The single-period (news-vendor) problem: literature review and suggestions for future research,” Omega, vol. 27, no. 5, pp. 537–553, 1999.
[3]
T. M. Whitin, “Inventory control and price theory,” Management Science, vol. 2, pp. 61–68, 1955.
[4]
E. S. Mills, “Uncertainty and price theory,” The Quarterly Journal of Economics, vol. 73, pp. 116–130, 1959.
[5]
S. Karlin and C. R. Carr, “Prices and optimal inventory policy,” in Studies in Applied Probability and Management Science, K. J. Arrow and H. Scarf, Eds., pp. 159–172, Stanford University Press, Stanford, Calif, USA, 1962.
[6]
A. H. L. Lau and H. S. Lau, “The newsboy problem with price-dependent demand distribution,” IIE Transactions, vol. 20, no. 2, pp. 168–175, 1988.
[7]
L. H. Polatoglu, “Optimal order quantity and pricing decisions in single-period inventory systems,” International Journal of Production Economics, vol. 23, no. 1–3, pp. 175–185, 1991.
[8]
H. Polatoglu and I. Sahin, “Optimal procurement policies under price-dependent demand,” International Journal of Production Economics, vol. 65, no. 2, pp. 141–171, 2000.
[9]
P. L. Abad and C. K. Jaggi, “A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive,” International Journal of Production Economics, vol. 183, pp. 115–122, 2003.
[10]
A. H. L. Lau and H. S. Lau, “Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model,” European Journal of Operational Research, vol. 147, no. 3, pp. 530–548, 2003.
[11]
S. Banerjee and A. Sharma, “Optimal procurement and pricing policies for inventory models with price and time dependent seasonal demand,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 700–714, 2010.
[12]
G. R. Bitran and S. V. Mondschein, “Periodic pricing of seasonal products in retailing,” Management Science, vol. 43, no. 1, pp. 64–79, 1997.
[13]
M. J. Khouja, “Optimal ordering, discounting, and pricing in the single-period problem,” International Journal of Production Economics, vol. 65, no. 2, pp. 201–216, 2000.
[14]
A. ？en and A. X. Zhang, “The newsboy problem with multiple demand classes,” IIE Transactions, vol. 31, no. 5, pp. 431–444, 1999.
[15]
Y. Feng and B. Xiao, “Optimal policies of yield management with multiple predetermined prices,” Operations Research, vol. 48, no. 2, pp. 332–343, 2000.
[16]
N. C. Petruzzi and M. Dada, “Dynamic pricing and inventory control with learning,” Naval Research Logistics, vol. 49, no. 3, pp. 303–325, 2002.
[17]
C. S. Chung, J. Flynn, and J. Zhu, “The newsvendor problem with an in-season price adjustment,” European Journal of Operational Research, vol. 198, no. 1, pp. 148–156, 2009.
[18]
P. S. You and T. C. Chen, “Dynamic pricing of seasonal goods with spot and forward purchase demands,” Computers and Mathematics with Applications, vol. 54, no. 4, pp. 490–498, 2007.
[19]
J. Mo, F. Mi, F. Zhou, and H. Pan, “A note on an EOQ model with stock and price sensitive demand,” Mathematical and Computer Modelling, vol. 49, no. 9-10, pp. 2029–2036, 2009.
[20]
S. Sinha and S. P. Sarmah, “Single-vendor multi-buyer discount pricing model under stochastic demand environment,” Computers and Industrial Engineering, vol. 59, pp. 945–953, 2010.
[21]
H. Chen, Y. Chen, C. H. Chiu, T. M. Choi, and S. Sethi, “Coordination mechanism for the supply chain with leadtime consideration and price-dependent demand,” European Journal of Operational Research, vol. 203, no. 1, pp. 70–80, 2010.
[22]
C. H. Chiu, T. M. Choi, and C. S. Tang, “Price, rebate, and returns supply contracts for coordinating supply chains with price-dependent demands,” Production and Operations Management, vol. 20, no. 1, pp. 81–91, 2011.
