Annals of Operations Research

, Volume 264, Issue 1–2, pp 459–476 | Cite as

Optimal inventory policies for deteriorating items with trapezoidal-type demand patterns and maximum lifetimes under upstream and downstream trade credits

Original Paper
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Abstract

In general, the demand rate moving through a product life cycle can be reasonably depicted by a trapezoidal-type pattern: it initially increases during the introduction and growth phases, then remains reasonably constant in the maturity phase, and finally decreases in the decline phase. It is evident that perishable products deteriorate continuously over time and can not be sold after its maximum lifetime. Thus, the deterioration rate of a product is increasing with time and closely related to its maximum lifetime. Furthermore, it has been hard to obtain loans from banks since the global financial meltdown in 2008. Hence, over 80% of firms in the United Kingdom and the United States sell their products on various short-term, interest-free loans (i.e., trade credit) to customers. To incorporate those important facts, we develop an inventory model by (1) assuming the demand pattern is trapezoidal, (2) extending the deterioration rate to 100% as its maximum lifetime is approaching, (3) using discounted cash-flow analysis to calculate all relevant costs considering the effects of upstream and downstream trade credits, and (4) including the costly purchase cost into the total cost, which is omitted in previous studies. Then, the order quantity that maximizes the present value of the profit is uniquely determined. Finally, through numerical examples, managerial insights are provided.

Keywords

Inventory control Trapezoidal-type demand Maximum lifetime Partial backlogging Trade credit 

Notes

Acknowledgements

The authors deeply appreciate Editor-in-Chief Endre Boros and three anonymous reviewers for their suggestions which significantly improve the paper.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of StatisticsSouthwestern University of Finance and EconomicsChengduChina
  2. 2.Department of Marketing and Management SciencesWilliam Paterson University of New JerseyWayneUSA
  3. 3.Department of MathematicsUniversity of IoanninaIoanninaGreece

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