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Annals of Operations Research

, Volume 254, Issue 1–2, pp 165–190 | Cite as

An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment

  • Umakanta Mishra
  • Leopoldo Eduardo Cárdenas-BarrónEmail author
  • Sunil Tiwari
  • Ali Akbar Shaikh
  • Gerardo Treviño-Garza
Original Paper

Abstract

This paper develops an EOQ inventory model that considers the demand rate as a function of stock and selling price. Shortages are permitted and two cases are studied: (i) complete backordering and (ii) partial backordering. The inventory model is for a deteriorating seasonal product. The product’s deterioration rate is controlled by investing in the preservation technology. The main purpose of the inventory model is to determine the optimum selling price, ordering frequency and preservation technology investment that maximizes the total profit. Additionally, the paper proves that the total profit is a concave function of selling price, ordering frequency and preservation technology investment. Therefore, a simple algorithm is proposed to obtain the optimal values for the decision variables. Several numerical examples are solved and studied along with a sensitivity analysis.

Keywords

Controllable deterioration rate Price and stock dependent demand Preservation technology investment 

Mathematics Subject Classification

90B05 

Notes

Acknowledgements

The authors are thankful to the valuable, constructive and detailed suggestions provided by three anonymous referees. The second author was supported by the Tecnológico de Monterrey Research Group in Industrial Engineering and Numerical Methods 0822B01006. The third author is grateful to his parents, wife, children Aditi Tiwari and Aditya Tiwari for their valuable support during the development of this paper.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Umakanta Mishra
    • 1
  • Leopoldo Eduardo Cárdenas-Barrón
    • 2
    Email author
  • Sunil Tiwari
    • 3
  • Ali Akbar Shaikh
    • 2
  • Gerardo Treviño-Garza
    • 4
  1. 1.Faculty of Science and TechnologyICFAI University, TripuraWest TripuraIndia
  2. 2.School of Engineering and SciencesTecnológico de MonterreyMonterrey, NuevoMexico
  3. 3.Department of Operational Research, Faculty of Mathematical Sciences, New Academic BlockUniversity of DelhiDelhiIndia
  4. 4.BNSF Railway CompanyFort WothUSA

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