Economic Order Quantity Model for Growing Items with Incremental Quantity Discounts, Capacitated Storage Facility, and Limited Budget

Abstract

The development of the inventory model started when Harris introduced the classic inventory model. It was firstly published by Wilson using the optimization method. He derived a mathematical equation model to obtain economic order quantities. Later, this model is known as the classic Economic Order Quantity (EOQ) or Wilson Model. The classic inventory EOQ model has some limitations. The model assumed that order items do not have physical changes during a planning period. This assumption becomes the weakness of the classical EOQ inventory model. Many items have material changes during a planning period, such as amelioration, deterioration, and growth. This research proposed a new mathematical model. The model relaxes three implicit assumptions of the classical EOQ: (1) the ordered items do not grow; (2) unlimited capacity; and (3) unlimited budget. A solution procedure to solve the model was developed and illustrated with a numerical example. A numerical example was performed to compare the result between the reference model and the new model. The number of ordered items per cycle time increased by 7%, and cycle time increased by 28%. It increased because the proposed model tends to choose large purchased quantities to get a cheap price. It caused the number of ordered items per cycle time to be larger and the cycle time to be smaller than the reference model. This research also provided sensitivity analysis. It showed the response of decision variables to some changes in input parameters.