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An Integrated Production Inventory Model for Repairable Items with Uncertain Lead Time


  • Center for Mathematical Sciences, Banasthali University, Rajasthan, India
  • Department of Mathematics, C.C.S University, Meerut - 250001, Uttar Pradesh, India


Background/Objectives: The objective of this paper is to develop an integrated inventory model of deteriorating items with production and remanufacturing system for a single product under infinite time horizon. Methods/Statistical Analysis: Developed the mathematical equation of the inventory time behavior of the system during the remanufacturing cycle, production cycle and during the collection. After production or remanufacturing the items are supplied to the retailer in small shipments. The used products are collected from the market and a certain ratio of these products which is acceptable for remanufacturing is used for production and rest of all is salvaged. The remanufactured items are assumed to be equivalent to fresh produced items. We obtained an analytical solution which optimizes the total cost of the proposed inventory model. Findings: The model can be applied for optimizing the total inventory cost for the integrated system for such business enterprises where they follow closed loop supply chain. Applications/Improvements: The proposed model is effective as well as efficient for the business organization where they take initiative for remanufacturing/reparability after using the returned and used products from the market. This model further can be extended for inflation and effect of learning.


Closed Loop Supply Chain, Deterioration, Integrated Inventory Model, Reparability, Shortages, Uncertain Lead Time.

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