Abstract

This work investigates a deterministic inventory mathematical model for decaying items with a biquadratic demand function over time. Shortages are also allowed in the model. It also demonstrates that the biquadratic demand function is convex and provides the best solution. The convexity of this model is demonstrated via a three-dimensional graphical representation. To double-check the model, an illustration is made. The ideal solution has been subjected to a sensitivity analysis with regard to main parameters, and the results have been presented.

References

[1] Ajanta Roy, An Inventory model for deteriorating items with price dependent demand and time-varying holding cost, AMO- Advanced modeling and optimization, 10(1) (2008).
[2] Dr. Ravish Kumar Yadav, Ms. Pratibha Yadav, Volume Flexibility in Production Model with Cubic Demand Rate and Weibull Deterioration with partial backlogging, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728,p-ISSN: 2319-765X, 6(4) (2013) 29-34.
[3] Ganesh Kumar, Sunita and Ramesh Inaniyan, Cubical Polynomial Time Function Demand Rate and Pareto type Perishable rate based Inventory Model with Permissible delay in Payments under Partial Backlogging, Jnanabha, Vol. 50(1) (2020) 115-133.
[4] Garima Sharma and Bhawna Vyas, An Approach To Positive Reflectance On Inventory Cost By Developing EOQ Model With Linear Demand By Weibull Distribution Deteriorating Items And Partial Backlogging, ISSN 2231-5780 8(5) (2018) 125-133.
[5] Ghosh, S.K. and Chaudhuri, K.S., An order-level inventory model for a deteriorating item with Weibull distribution deterioration, time dependent quadratic demand and shortages’, International Journal of Advanced Modeling and Optimization, 6(1) (2004) 31-45.
[6] Goyal, S.K. and B.C. Giri, Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, 134 (2001) 1-16.
[7] G.P. Samanta and Ajanta Roy (2004), A Production Inventory model with deteriorating items and shortages, Yugoslav Journal of Operations research 14(2) (2004) 219-230.
[8] Roy A., An inventory model for deteriorating items with price dependent demand and time varying holding cost, Advanced Modeling and Optimization,10 (2008) 25–37, (2008).
[9] S.K. Goyal and B.C. Giri (, Recent trends in modelling of deteriorating inventory, European Journal of operational research 134 (2001) 1-16.
[10] Samanta, A., and Pal, M. Periodic review inventory policy for non-instantaneous deteriorating items with time-dependent deterioration rate. Pak. J. Stat. oper. Res. , 11(3) (2015) 409- 419
[11] Shah, N., and Munshi, M. M. An order-level lot size model for deteriorating items for two storage facilities when demand is exponentially declining. Revista Investigation Operational, 31 (3) (2010) 193-199.
[12] Vinod Kumar et.al. , An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging, Jour of Indus Engg Int., 9(4) (2013).
[13] Vashistha, P. K., and Gupta, V. S. An inventory model with Weibull distribution deterioration and time-dependent demand. International J. of Advances in Industrial Engineering Research, 2 (2011) 10.
[14] Ouyang, Wu and cheng, an inventory model for deteriorating items with exponential declining demand and partial backlogging, Yugoslav Journal of Operation Research, 15(2) (2005) 277-288.
[15] Yadav, R.K and Trivedi, R. A multi –echelon inventory models for deteriorating with partial backlogging, International journal of applied science and technology, (2013) 24-31.

[16] Yu, J. C , Cheng, S. J., Padilan, M., an d Wee, H. M. A two warehouse inventory model for deteriorating items with decreasing rental over time. Proc. of the Asia Pacific Industrial Engineering & Management Systems Conference, (Eds.), (2012) 2493-2505.