Optimal control of an inventory system under whole sale price changes

¹ School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.
² Department of Mathematics, Kishore Bharati Bhagini Nivedita College, Ramkrishna Sarani, Behala, 700060 Kolkata, India.

^* Corresponding author: shib_sankar@yahoo.com, shibsankarsana@gmail.com

Received: 18 May 2019
Accepted: 14 August 2019

Abstract

Nowadays business owners use lots of incentive schemes to make customers buy more products. In this paper optimal ordering policy for customers is obtained when the manufacturer increases the purchasing price or temporary decreases it. Offering a special sale from the manufacturer is probabilistic and shortage occurs as partial backlogging. In this paper, the initial level of inventory when the purchasing price changes is not equal to zero. With respect to the assumptions, the amount of special order quantity, the shortage quantity, and the expected total saving from making an special order is optimized for the customer. The optimal amount of decision variables are obtained by maximizing the expected total saving function and a closed-form solution is derived. Several numerical examples are solved and sensitivity analysis is performed to prove the applicability of the proposed model. Finally, the impact of some parameters of the model including the demand, the probability of making a special order, the future prices, and the initial inventory is investigated. Optimal ordering policy for the customers is obtained in cases when an announced price increase occurs and when the prices temporarily decrease.