This study develops a supply chain from the perspective of both the manufacturer and the retailer. The effect of imperfect production processes on lot-sizing is also considered. In this paper, a production model that takes into account volume flexibility, weibull distribution deterioration rate and inflation is proposed. Items of imperfect quality can be sold at a reduced selling price. The solution of the inventory system is illustrated with the help of a numerical example. The sensitivity of some variables to changes in the values of the parameters of the systems is also examined.

The issue of quality is mostly ignored in the classical inventory models. In other words, it implicitly assumes that the quality level is fixed at an optimal level and not subject to control. This means that sometimes defective items can also be produced during production in the real production environment. Empirical observations indicate that the production systems start producing imperfect units when the manufacturing companies increase the production run time. At the start of production, the production process is in control and the items produced are of acceptable quality. As the production run time increases, the machine gets out of control and this affects the quality of production. These defective items must be discarded, repaired, altered or if they have reached the customer, they are sold at reduced prices and hence extra costs are incurred. Therefore, in determining the optimal ordering policy, it is important to take the quality related costs into account. Assuming non-zero defective items, several authors like Proteous (1986) and Cheng (1991) extended the Economic Order Quantity (EOQ) models to imperfect production processes. The effect of defective items on lot size is noted in the works of Urban (1992), Anily (1995), Salama and Jaber (2000), Chang (2004) and Sana et al. (2007a).

In the above models, the rate of production is assumed to be inflexible. Schweitzer and Seidmann (1991) assumed that machine production rates can easily be changed. Khouja and Mehrez (1994) and Khouja (1995) extended the Embedded Platform Logistics System (EPLS) model to an imperfect production process with flexible production rates. Sana (2004) developed inventory models with volume flexible production for deteriorating items and shortage. Khouja and Mehrez (2005), Husseini et al. (2006), Sana et al. (2007a and 2007b) also discussed the volume of flexibility policy in production.

Traditionally, the supply chain inventory models consider different sub-systems. With the recent advances in communication and information technologies, the integration of these functions is a common phenomenon. Most enterprises are forced to extend supply chain that can respond rapidly to customer needs with minimum stock and maximum service level due to limited resources and globalization of market. The coordination among the producer and the retailer is the key to success in supply chain systems. Several researchers investigate integrated policies of the producers and the retailers. Rau et al. (2003) consider integrated models for deteriorating items with different demand
assumptions. Hans et al. (2006) developed new methodologies to obtain joint economic lot size in distribution system with a multiple shipment policy. Lo et al. (2007) developed the model with shortages. Singh and Singh (2008a) considered the supply chain model for deteriorating items and inflation. Singh and Singh (2008b) investigated the model with exponential increasing demand rate in a supply chain.

Supply Chain Management Journal, Supply Chain Models, Production Process, Inventory Systems, Embedded Platform Logistics System, Multiple Shipment Policy, Globalization, Information Technologies, Optimization Techniques, Production Inventory Models, Economic Order Quantity Models.