Annals of Operations Research

, Volume 260, Issue 1–2, pp 437–460 | Cite as

Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration

  • Magfura Pervin
  • Sankar Kumar Roy
  • Gerhard-Wilhelm Weber
S.I.: Advances of OR in Commodities and Financial Modelling


In this paper, a deterministic inventory control model with deterioration is developed. Here, the deterioration rate follows stochastic deterioration, especially Weibull distribution deterioration. A time-dependent demand approach is introduced to show the applicability of our proposed model and to be up-to-date with respect to time. The main purpose of the paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks. Keeping in mind the criterion of modern era, we consider that the holding cost is totally dependent on time, and shortages are allowed for this model. Subject to the formulated model, we minimize the total inventory cost. The mathematical model is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution with regard to important parameters is also carried out to elaborate the quality, e.g., stability, of our result and to possibly modify our model. The paper ends with a conclusion and an outlook to future studies.


Inventory Stochastic deterioration Shortage Time-dependent demand Time-varying holding cost Optimization 

Mathematics Subject Classification

90B05 91B70 91B24 



The first author is very much thankful to University Grants Commission (UGC) of India for providing financial support to continue this research work under [MANF(UGC)] scheme: Sanctioned letter number [F1-17.1/2012-13/MANF-2012-13-MUS-WES-19170 /(SA-III/Website)] dated 28/02/2013. The authors would like to express their cordial thanks to the Editor-in-Chief and anonymous reviewer for their valuable comments.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Magfura Pervin
    • 1
  • Sankar Kumar Roy
    • 1
  • Gerhard-Wilhelm Weber
    • 2
  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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