Imperfect Inventory Systems

In today’s manufacturing environment, managing inventories is one of the basic concerns of enterprises dealing with materials according to their activities, because material as the principal inventories of enterprises specially production ones composes the large portion of their assets. As a result, managing inventories influences directly financial, production, and marketing segments of enterprises so that efficient management of inventories leads to improving their profits. In addition, the effect of managing inventories on the selling prices of finished products is undeniable because more than half of production systems’ revenues are spent to buy materials or production components. On the other hand, customers expect to receive their orders at a lower price apace. So, an efficient managing inventories and production planning are key managerial and operational tools to achieve the main goals, which are satisfying the customers’ demand and becoming lower-cost producer, in order to increase market share.

Since the introduction of the economic order quantity (EOQ) model by Harris (1913), frequent contributions have been made in the literature toward the development of alternative models that overcome the unrealistic assumptions embedded in the EOQ formulation. For example, the assumption related to the perfect-quality items is technologically unattainable in most supply chain applications. In contrast, products can be categorized as “good quality,” “good quality after reworking,” “imperfect quality,” and “scrap” (Chan et al. 2003; Pal et al. 2013). In practice, the presence of defective items in raw material or finished product inventories may deeply affect supply chain coordination, and, consequently, the product flows among supply chain levels may become unreliable (Roy et al. 2015). In response to this concern, the enhancement of currently available production and inventory order quantity models, which accounts for imperfect items in their mathematical formulation, has become an operational priority in supply chain management (Khan et al. 2011). This enhancement may also include the knowledge transfer between supply chain entities in order to reduce the percentage of defective items.

As stated in Chap. 2, the economic order quantity (EOQ) model was first introduced in 1913. Seeking to minimize the total cost, the model generated a balance between holding and ordering costs and determined the optimal order size. Later, the EPQ model considered items produced by machines inside a manufacturing system with a limited production rate, rather than items purchased from outside the factory. Despite their age, both models are still widely used in major industries. Their conditions and assumptions, however, rarely pertain to current real-world environments. To make the models more applicable, different assumptions have been proposed in recent years, including random machine breakdowns, generation of imperfect and scrap items, and discrete shipment orders. The assumption of discrete shipments using multiple batches can make the EPQ model more applicable to real-world problems. The EPQ inventory models assume that all the items are manufactured with high quality and defective items are not produced. However, in fact, defective items appear in the most of manufacturing systems; in this sense, researchers have been developing EPQ inventory models for defective production systems. In these production systems, defective items are of two types: scrapped items and reworkable items.

Scrap and rework costs are a manufacturing reality impacting organizations across all industries and product lines. Scrap and rework costs are caused by many things—when the wrong parts are ordered, when engineering changes are not effectively communicated, or when designs are not properly executed on the manufacturing line. No matter why scrap and rework occurs, its impact on an organization is always the same—wasted time and money. And while no one, especially an operations manager, wants to admit it, these expenses add up quickly and negatively impact the bottom line.

The primary operation strategies and goals of most manufacturing firms are to seek a high satisfaction to customer’s demands and to become a low-cost producer. To achieve these goals, the company must be able to effectively utilize resources and minimize costs.

Traditional economic order quantity (EOQ) models offer a mathematical approach to determine the optimal number of items a buyer should order to a supplier each time. One major implicit assumption of these models is that all the items are of perfect quality (Rezaei and Salimi 2012). However, presence of defective products in manufacturing processes is inevitable. There is no production process which can guarantee that all its products would be perfect and free from defect. Hence, there is a yield for any production process. Basic and classical inventory control models usually ignore this fact. They assume all output products are perfect and with equal quality; however, due to the limitation of quality control procedures, among other factors, items of imperfect quality are often present. So it has given researchers the opportunity to relax this assumption and apply a yield to investigate and study its impact on several variables of inventory models such as order quantity and cycle time.

The role of the equipment condition in controlling quality and quantity is well known (Ben-Daya and Duffuaa 1995). Equipment must be maintained in top operating conditions through adequate maintenance programs. Despite the strong link between maintenance production and quality, these main aspects of any manufacturing system are traditionally modeled as separate problems. Few attempts have been made to integrate them in a single model that captures their underlying relationships.