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Research Article Open access CC BY 3.0

An Inventory Model for Deteriorating Items with Quadratic Demand and Partial Backlogging

R. Begum, S. K. Sahu, R. R. Sahoo

Current Journal of Applied Science and Technology · pp. 112–131 · Published 19 Apr 2012

10.9734/BJAST/2012/1180

Abstract

Aims: The scope of the model lies in its applicability in the management inventories of time-quadratic demand. It is also seen that large pile of goods displayed in a supermarket will motivate the customer to buy more. So the presence of inventory has a motivational effect on the people around it. Also there may be occasional shortages in inventory due to many reasons. Therefore, we develop an EOQ model for the inventory of a deteriorating item, taking demand rate and allowing shortages in inventory. Study Design: This paper presents an inventory model for deteriorating items with quadratic demand. In the model, shortages are allowed and partially backordered. The backlogging rate is a variable and dependent on the waiting time for the next replenishment. A numerical example is taken to illustrate the model and the sensitivity analysis is also studied.  Methodology: Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration.  Results: Convexity condition of the cost function is established to ensure the existence of unique point of minimum.  Conclusion: The proposed model can be extended in several ways. For instance, we may extend the demand function to stochastic fluctuating demand patterns or stock-dependent demand rate. Finally, we could extend the model to incorporate some more realistic features such as quantity discounts, permissible delay in payments, time value of money and inflation etc.

Inventory quadratic demand deteriorating items partial backlogging

References (38)

  1. 1 Recent trends in modeling of deteriorating inventory [DOI]
  2. 2 Inventory Replenishment Policy for a Linear Trend in Demand—An Analytical Solution [DOI]
  3. 3 (T, Si) Policy Inventory Model for Deteriorating Items with Time Proportional Demand [DOI]
  4. 4 A deterministic lot-size inventory model for deteriorating items with shortages and a declining market [DOI]
  5. 5 Optimal EOQ Models for Deteriorating Items with Time-Varying Demand [DOI]
  6. 6 Production/Operations Management: Contemporary Policy for Managing Operating Systems
  7. 7 An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand [DOI]
  8. 8 The Theory of Inventory Management [DOI]
  9. 9 Optimal selling price and lotsize with time varying deterioration and partial backlogging [DOI]
  10. 10 A note on an order-level inventory model for a deteriorating item with time-dependent quadratic demand [DOI]
  11. 11 Inventory replenishment policies for deteriorating items in a declining market [DOI]
  12. 12 Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand [DOI]
  13. 13 Replenishment Schedule for Deteriorating Items with Time-Proportional Demand [DOI]
  14. 14 An EOQ model for deteriorating items with a linear trend in demand and shortages in all cycles [DOI]
  15. 15 A Heuristic for Replenishment of Deteriorating Items with a Linear Trend in Demand [DOI]
  16. 16 An economic order quantity model of imperfect quality items with partial backlogging [DOI]
  17. 17 Demand influenced by enterprises’ initiatives — A multi-item EOQ model of deteriorating and ameliorating items [DOI]
  18. 18 An EOQ model for deteriorating items with time-varying demand and shortages [DOI]
  19. 19 EOQ model for an inventory with a linear trend in demand and finite rate of replenishment considering shortages [DOI]
  20. 20 An EOQ model for salesmen’s initiatives, stock and price sensitive demand of similar products – A dynamical system [DOI]
  21. 21 Structural properties of an inventory system with deterioration and trended demand [DOI]
  22. 22 The stochastic EOQ model with random sales price [DOI]
  23. 23 An EOQ model of homogeneous products while demand is salesmen’s initiatives and stock sensitive [DOI]
  24. 24 An EOQ model for perishable item with stock and price dependent demand rate [DOI]
  25. 25 The Finite Horizon Trended Inventory Replenishment Problem With Shortages [DOI]
  26. 26 A deterministic lot-size inventory model with shortages and a linear trend in demand [DOI]
  27. 27 Practical Inventory Replenishment Policies for a Linear Trend in Demand Followed by a Period of Steady Demand [DOI]
  28. 28 Stock Replenishment Quantities for Unbounded Linear Increasing Demand: An Interesting Consequence of the Optimal Policy [DOI]
  29. 29 A Replenishment Model for Radioactive Nuclide Generators [DOI]
  30. 30 ON A VOLUME FLEXIBLE PRODUCTION POLICY FOR A DETERIORATING ITEM WITH TIME-DEPENDENT DEMAND AND SHORTAGES
  31. 31 An EOQ Model for Deteriorating Items with Weibull Distribution Deterioration, Unit Production Cost with Quadratic Demand and Shortages
  32. 32 An EOQ model for imperfect quality products with partial backlogging – a comparative study [DOI]
  33. 33 Inventory Replenishment Policy for Linearly Increasing Demand Considering Shortages-An Optimal Solution [DOI]
  34. 34 On a Heuristic Inventory-replenishment Rule for Items with a Linearly Increasing Demand Incorporating Shortages [DOI]
  35. 35 Synchronized Production Policies for Deteriorating Items in a Declining Market [DOI]
  36. 36 A lot sizing heuristic for deteriorating items with shortages in growing and declining markets [DOI]
  37. 37 On improving replenishment policies for linear trend in demand [DOI]
  38. 38 An EOQ model for deteriorating items in a declining market with SFI policy [DOI]

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