Variable demand model for periodically reviewing with allowing refunding parts of the orders

Document Type : Original Article

Author

Higher Institute of Engineering and Technology, Tanta, Egypt.

Abstract

Depending on a feld study for one of the largest iron and paints warehouses in Egypt,
this paper presents a new multi-item periodic review inventory model considering the
refunding quantity cost. Through this feld study, we found that the inventory level is
monitored periodically at equal time intervals. Returning a part of the goods that were
previously ordered is permitted. Also, a shortage is permissible to occur despite having
orders, and it is a combination of the backorder and lost sales. This model has been
applied in both crisp and fuzzy environments since the fuzzy case is more suitable for
real-life than crisp. The Lagrange multiplier technique is used for solving the restricted
mathematical model. Here, the demand is a random variable that follows the normal
distribution with zero lead-time. Finally, the model is followed by a real application to
clarify the model and prove its efciency.

Keywords