The development and application of inventory models for deteriorating items is one of the main concerns of the experts in the domain, since the number and variety of deteriorating products are dramatically increasing. Many types of products such as pharmaceuticals, health and cosmetics, foodstuffs, biotechnological, petrochemical and chemical materials are classified as deteriorating products. One of the major gaps in the deteriorating inventories literature is that researchers have not paid enough attention to two important features in their models : i) Considering stochastic conditions ; especially stochastic lead time is almost overlooked since makes the mathematical challenges complicated, ii) designing innovative inventory policies by taking into account the environmental issues and particularly the CO2 emission as a new objective in a multi-objective framework that is quite new. Today, the green principles have been expanded to many areas, including supply chains. It is obvious that much of the green legislation is relating to the type of product that is offered by supply chains. Accordingly, deteriorating products are more noticeable rather than infinite lifetime ones, because of : recycling process which is necessary for expired goods, special condition which exists for stocking and transporting, and even toxic effects of deteriorated products (for example in the case of radioactive substances). In this thesis, at first a comprehensive literature review is done. Then, the mathematical approaches for modeling deterioration process are identified and classified in three groups. Subsequently, we study replenishment policy for deteriorating products under stochastic conditions in form of three different problem areas. In the first one, we develop a continuous (r,Q) inventory model for a retailer that offers a deteriorating product by considering infinite planning horizon, stochastic lead time, constant demand rate and backordered shortages. For modeling the deterioration process, a non-linear holding cost is defined. Taking into consideration the stochastic lead time as well as a non-linear holding cost makes the mathematical model more complex. We therefore customize the proposed model for a uniform distribution function that could be tractable to solve optimally by an exact approach.

In second problem, we study the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously for a retailer that sells a deteriorating product. The inventory system is modeled as a continuous review system (r, Q) under stochastic lead time. We study two situations. In the first one, it is assumed that all the requirements are supplied by only one source, while in the second, two suppliers are available. Since the developed mathematical models are very complex, the Sequential Quadratic Programming (SQP) algorithm is used to solve the problems. Then, the situations in which each sourcing policy is the most economic are determined. Finally, in the last problem, we consider inventory and transportation costs, as well as the environmental impacts in a centralized supply chain by taking into account uncertain demand and partial backordered shortages. Due to the deterioration characteristic of products, a constant deterioration rate as well as a non-linear holding cost function is considered. In order to deal with demand uncertainty, a two stage stochastic programming approach is taken. Then, by considering transportation vehicles capacity, we develop a mixed integer mathematical model. In this way, the best transportation vehicles and replenishment policy are determined by finding a balance between financial and environmental criteria. A numerical example from the real world is also presented to show the applicability and effectiveness of the proposed model.