Studies on Some Inventory Model for Deteriorating Items with Weibull Replinishment and Generalised Pareto Decay Having Demands as Function of on Hand Inventory

Lakshmana Rao, A; Srinivasa Rao, K

doi:10.22034/2014.4.02

Studies on Some Inventory Model for Deteriorating Items with Weibull Replinishment and Generalised Pareto Decay Having Demands as Function of on Hand Inventory

Document Type : Research Paper

Authors

A Lakshmana Rao ¹
K Srinivasa Rao ²

¹ Aditya Institute of Technology and Management, Tekkali, Srikakulam- Dist, India

² Department of Statistics, Andhra University, Visakhapatnam, India

10.22034/2014.4.02

Abstract

Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., Hence, it is needed to develop inventory models with random replenishment. In this paper, an EPQ model for deteriorating items is developed and analyzed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalized Pareto distribution and demand is a function of on hand inventory. Using the differential equations, the instantaneous state of inventory is derived. With suitable cost considerations, the total cost function is obtained. By minimizing the total cost function, the optimal ordering policies are derived. Through numerical illustrations, the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significant influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.

Keywords

Main Subjects

production & inventory management

References

Arya, R.K., Singh S.R. and Shakya, S.K. (2009) ‘An order level inventory model for perishable items with stock dependent demand and partial backlogging’, International Journal of Communicational and Applied Mathematics, Vol.4(1), pp. 19-28.

Banker, R.C. and Urban, T.L. (1988) ‘A deterministic inventory system with an inventory-level-dependent demand rate’, Journal of Operational Research Society, Vol.39 (9), pp. 823-831.

Datta, T.K. and Pal, A.K. (1988) ‘Order level inventory systems with power demand pattern for items with variable rate of deterioration’, Indian Journal of Pure and Applied Mathematics, Vol.19 (1), pp. 1043-1053.

Gupta, R. and Vrat, P. (1986) ‘Inventory model for stock dependent consumption rate’, OPSEARCH, Vol. 23, pp. 19-24.

Jasvinder, Rajendra Sharma and A. P. Singh (2013) ‘An optimal ordering policy for inventory model with Non – Instantaneous deteriorating items and stock-dependent demand’, Applied Mathematical Science, Vol.7 (82), pp. 4073 – 4080.

Levin, R.I., McLaughlin, C.P., Lamone, R.P. and Kottas, J.F. (1972) ‘Production operations management, contemporary policy for managing operating systems’, MCGraw-Hill, New-York.

Mahata, G.C. and Goswami, A. (2009a) ‘Fuzzy EOQ models for deteriorating items with stock dependent demand non-linear holding costs’, International Journal of Applied Mathematics and Computer Science, Vol.5(2), pp. 94-98.

Mandal, B.N. and Phaujdar, S. (1989) ‘An inventory model for deteriorating items and stock-dependent consumption rate’, Journal of Operational Research Society, Vol.40(5), pp. 483-488.

Panda, S., Senapati, S. and Basu, M. (2009c) ‘A single cycle perishable inventory model with time dependent quadratic ramp-type demand and partial backlogging’, International Journal of Operational Research, Vol.5(1), pp. 110-129.

Roy, A., Maitai, M.K., Kar, S. and Maiti, M. (2009) ‘An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon’, Applied Mathematical Modelling, Vol.33(2), pp. 744-759.

Santanu Kumar Ghosh, Jamia Sarkar and Kripasindhu (2015) ‘A Multi items inventory model for deteriorating items in limited storage space with stock dependent demand’ , American Journal of Mathematical and Management Sciences, Vol 34(2), pp. 147-161.

Silver, E.A. and Peterson, R. (1985) ‘Decision systems for inventory management and production planning’, 2nd Edition, John Wiley & Sons, New-York.

Sridevi, G., Nirupama Devi, K. and Srinivasa Rao, K. (2010) ‘Inventory model for deteriorating items with Weibull rate of replenishment and selling price dependent demand, International Journal of Operational Research, Vol. 9(3), pp. 329-349.

Srinivasa Rao, K. and Begum, K.J (2007) ‘Inventory models with generalized Pareto decay and finite rate of production’, Stochastic Modelling and Application, Vol.10 (1 and 2), pp. 13-27.

Srinivasa Rao, K. and Essay, K.M (2012) ‘ Inventory model for deteriorating items with stock dependent production rate and Weibull decay’ , International Journal of Mathematical Archive, Vol. 3(10), pp. 3709-3723.

Srinivasa Rao, K. and Eswara Rao, S (2015) ‘ Inventory model under permissible delay in payments and inflation with generalized Pareto lifetime’, International Journal of Production Management, Vol. 8 (1 and 2), pp. 202-226.

Srinivasa Rao, K., Vevekananda Murty, M. and Eswara Rao. S. (2005) ‘Optimal ordering and pricing policies of inventory models for deteriorating items with generalized Pareto lifetime’, Journal of Stochastic Process and its Applications, Vol.8 (1), pp. 59-72.

Teng, J.T. and Chang, C.T. (2005) ‘EPQ models for deteriorating items with price and stock-dependent demand’, Computers Operations Research, Vol. 32(2), pp. 297-308.

Uma Maheswara Rao, S.V., Venkata Subbaiah, K. and Srinivasa Rao. K. (2010) ‘Production inventory models for deteriorating items with stock dependent demand and Weibull decay’, IST Transaction of Mechanical Systems-Theory and Applications, Vol.1, No.1 (2), pp. 13-23.

Venkata Subbaiah, K., Srinivasa Rao, K. and Satyanarayana, B. (2004) ‘Inventory models for perishable item having demand rate dependent on stock level’, OPSEARCH, Vol.41, pp. 222-235.

Yang, H.L., Teng, J.T. and Chern, M.S. (2010) ‘An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages’, International Journal of Production Economics, Vol.123(1), pp. 8-19.

ang, C.T., Ouyang, L.Y., Wu, K.S. and Yen, H.F. (2011) ‘An optimal replenishment policy for deteriorating items with stock-dependent demand and relaxed terminal condition under limited shortage space’, Central European Journal of Operational Research, Vol.19(1), pp. 139-153.