EOQ models for deteriorating items with substitutable and mutual complementary price, stock, and time-dependent demand

Abstract

The common assumption made in the classical economic order (EOQ) model is that an item has a finite life and with demand that is constant and independent. In practice, however, this is not always the case. The demand for an item may be dependent on other factors such as time, its stock level and price of other items such as its substitute and complement items. Moreover, some items deteriorate in nature and do not necessarily have a fixed shelf life as the classical EOQ model suggests. These inventory phenomena are apparent in most supply chains in today’s market and have added more complexity in management of these type of inventories. The characteristics displayed by these inventories has caught the attention of many researchers of lately.

In this dissertation two inventory models are developed where the second model is the extension of the first model. The first model is developed to find the optimal values of the selling price and cycle length that maximizes profit for two mutually complementary items, where these items are subject to deterioration. The demand for these items is given by the exponential function which is dependent on products selling prices, complement product selling price and time. Moreover, the ordering cost of the products is assumed to be made up of fixed and variable components.

The second model as the extension of the first model, considers a three-item EOQ policy, where Product 1 as the main item has a demand that is dependent on the following: its selling price and stock level, the selling price of the mutual complement (Product 2) as well as the selling price of its substitute (Product 3) and time. Product 2 has demand that is dependent on its selling price, the selling price of its complement (Product 1) and time. Product 3 has a demand that is dependent on its selling price, the selling price of its substitute (Product 1) and time. An example of a practical scenario for this model is in a perishable chicken feed supply chain between supplier of medicines used in chicken feed production and a manufacturer of animal feed. Typical in this node of the supply chain the manufacturer of animal feed may source a variety of medications from the same supplier. Due to certain nutritional specification of the feed formula, some of these medicines must be used together (complementarily) as part of the feed Bill of Material (BOM). Moreover, these complementary items can further be used interchangeably or substituted with an alternative item in an instance when there is stock out. Furthermore, stock display or availability at supplier of these medicines has a potential to stimulate demand as purchasing departments of animal feed manufactures are fond with stocking up on these medicines when there is more available.

The models presented in this dissertation can be said to be an extension of two models developed by other researchers namely Karaöz et al. (2011) and Ouyang et al. (2005), their models were developed for complementary and deterioration items, respectively. The two models are combined to address scenario presented in this study since there is currently limited or no study found by the researcher that addresses the combined effect of deteriorating items with substitutable and mutual complementary price-, stock-, and time-dependent demand in a single model. This research gap has given purpose to this dissertation. As such, the inventory models developed will contribute into the body of knowledge in the observed research gap. The models are aimed at generating an inventory replenishment policy that determines optimal selling prices, cycle length and order quantity that maximizes profit.

The numerical example and sensitivity analysis have been conducted to assess the effectiveness of the results generated by the inventory models. With the test of optimality condition for the models, the results obtained indicate that the profit maximising function is concave, that is, negative (semi)definite.

Findings from the two models developed shows that an increase in either holding or ordering cost results in reduction of profit. Similarly, higher deterioration rate leads to reduction in profit. In practice, these findings indication that these costs need to be constantly reviewed and improved for better profit results. The optimal selling prices have been generated by the models, where the sensitivity tests shows that a change in some parameters of the models may increase or decrease the selling price of an item.