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A Two-Warehouse Inventory Model for Deteriorating Items with Capacity Constraints and Back-Ordering Under Financial Considerations

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Abstract

This paper investigated two warehouse inventory model for a single deteriorating items under the assumption of shortages and partial backlogging under payments delay and the effect of inflation and time value for money is also incorporated. Again, two warehouse capacity (owned and rented) have been considered over the finite horizon planning under which back-ordering is assumed. When the order quantity becomes higher than the storage capacity in own warehouse then the system involves two warehouse model. In this model, excess inventory are stored in rented warehouses which are assumed to charge higher unit holding costs than owned warehouses. Moreover, in rented warehouse item deteriorates with higher rates than in owned warehouse. At first own warehouse are filled out by its storage capacity and the rests are kept in rented warehouse. So, at first, the items in RW decreases due to demand and deterioration until it reaches to the level zero while on the other hand a portion on the inventory on OW is depleted due to deterioration only. Then, the inventory on OW decreases due to demand and deterioration until it reaches to the level zero. Finally, shortages start and backlogging rate is negative exponential of function waiting time. Here, the demand is used as exponential function of time and backlogging rate varies negative exponential function of waiting time. The total cost function is carried out under the effect of JIT setup cost. Two numerical examples are illustrated for the developed model and sensitivity analysis has been carried out to identify behaviour of model parameters.

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Acknowledgements

The authors wish to thank the anonymous referees for their helpful comments and suggestions which greatly improved the content of the article.

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Authors and Affiliations

  1. Department of Mathematics, Vidyasagar College for Women, 39, Sankar Ghosh Lane, Kolkata, 700006, India

    R. Chakrabarty & T. Roy

  2. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    K. S. Chaudhuri

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  1. R. Chakrabarty
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  2. T. Roy
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Correspondence to R. Chakrabarty.

Appendix A

Appendix A

From Eq. (3) we obtain order quantity \(Q=I(0)=\frac{a}{\alpha + b}(e^{(\alpha + b)t_{1}}-1)\) and if the order quantity \(Q\le W\) then it is unnecessary to rent any warehouse. Thus \(\frac{a}{\alpha + b}(e^{(\alpha + b)t_{1}}-1)\le W\) implies \(t_{1} \le \frac{1}{\alpha + b}log(1+\frac{(\alpha + b)W }{a})\). For simplicity, let \(t_{a}=\frac{1}{\alpha + b}log(1+\frac{(\alpha + b)W }{a})\). The inequality \(Q\le W\) holds if and only if \(t_{a}\ge t_{1}\). Therefore, the inequality \(Q>W\) holds if and only if \(t_{a}< t_{1}\) which implies that there are W units of items stored in OW and the remainder are despatched in RW.

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Chakrabarty, R., Roy, T. & Chaudhuri, K.S. A Two-Warehouse Inventory Model for Deteriorating Items with Capacity Constraints and Back-Ordering Under Financial Considerations. Int. J. Appl. Comput. Math 4, 58 (2018). https://doi.org/10.1007/s40819-018-0490-1

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