This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory.

Keeping in view the concern about environmental protection, the study investigates effects of remanufacturing in an integrated production inventory model consisting of forward and reverse supply chain over infinite planning horizon. This article is developed for the deteriorating products with stock dependent demand under shortages. To make the model more realistic, flexibility of production system has been incorporated during forward manufacturing. We derive total cost function and using the results of calculus, optimum production policy is derived, which minimizes the total cost incurred. The results are discussed with a numerical example to illustrate the theory.

This paper derives a reverse logistic inventory model with imperfect production, stock-dependent demand, flexible manufacturing, and shortages over infinite planning horizon. The objective is to determine the joint policy for optimal production, amount of remanufacturing, collection of reusable items, and collection as well as disposal of defective items which minimizes the total cost of the inventory system under consideration. To make the model more realistic, both of the cases of linear and nonlinear holding costs have been discussed. The results are discussed with a numerical example to illustrate the theory.

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