The objective of this paper is to develop an integrated production inventory model for reworkable items with exponential demand rate. This is a three-layer supply chain model with perspectives of supplier, producer and retailer. Supplier delivers raw material to the producer and finished goods to the retailer. We consider perfect and imperfect quality products, product reliability and reworking of imperfect items. After screening, defective items reworked at a cost just after the regular manufacturing schedule. At the beginning, the manufacturing system starts produce perfect items, after some time the manufacturing system can undergo into “out-of-control” situation from “in-control” situation, which is controlled by reverse logistic technique. This paper deliberates the effects of business strategies like optimum order size of raw material, exponential demand rate, production rate is demand dependent, idle times and reverse logistics for an integrated marketing system. Mathematica is used to develop the optimal solution of production rate and raw material order for maximum expected average profit. A numerical example and sensitivity analysis is illustrated to validate the model.

In the global critical economic scenario, inflation plays a vital role in deciding optimal pricing of goods in any business entity. This article presents two single-vendor single-buyer integrated supply chain inventory models with inflation and time value of money. Shortage is allowed during the lead time and it is partially backlogged. Lead time is controllable and can be reduced using crashing cost. In the first model, we consider the demand of lead time follows a normal distribution, and in the second model, it is considered distribution-free. For both cases, our objective is to minimize the integrated system cost by simultaneously optimizing the order quantity, safety factor, lead time and number of lots. The discounted cash flow and classical optimization technique are used to derive the optimal solution for both cases. Numerical examples including the sensitivity analysis of system parameters is provided to validate the results of the supply chain models.

In this paper, an integrated production-inventory model with multi-item is developed from the perspectives of single producer, multiple suppliers and retailers. In this three-layer supply chain, the retailers are non-competing. Every supplier delivers only single type of raw material to the producer. The producer manufactures finished goods from the combination of fixed percentage of different types of raw materials. The producer manufactures various types of objects and supplies them to retailers according to the demand of multiple retailers. This paper studies the impact of different types of business policies such as exponential demand rate, demand dependent production rate, optimum order size of raw materials, and unit production cost at each stage of integrated marketing system. Mathematica is used to develop the model and to optimize the integrated profit function. A numerical example and sensitivity analysis is illustrated to justify the feasibility of the proposed model.