An EOQ Model with Polynomial of Nth Degree Demand Rate, Constant Deterioration, Linear Holding Cost and Without Shortages under Inflation
IOSR Journal of Mathematics
In existing literature the inventory models are developed under the assumption of demand rate to be constant or linear or quadratic. In this paper, an inventory model is developed where demand rate is generalized as a polynomial of n th degree with constant deterioration rate. The holding cost is a linear function of time. Shortages are not allowed. A numerical example has been illustrated using MATLAB to describe the model and the sensitivity analysis of various parameters is carried out with
... raphical and tabular data. Keywords: Constant deterioration; Demand rate is a polynomial of n th degree; Inflation; Inventory; Time dependent holding cost I. Introduction Agrawal, R. (2009) developed the inventory model for integrated inventory system with the effect of inflation and credit period. Amutha R. et al (2013) worked on a model for constant demand with shortages under permissible delay in payments. He, Y. et al (2010) gave optimal production-inventory model for deteriorating items with multiple-market and Hou, K.L. et al (2009) developed the model the cash flow oriented EOQ model with deteriorating items under permissible delay in payments. Hung, K. (2011) discussed in inventory model with generalized type demand, deterioration and backorder. Jaggi, C.K. et al (2008) proposed a model for Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payment. Jain S. et al (2008) worked on a model with inventory level-dependent demand rate, deterioration, partial backlogging and decrease in demand and Khanr. S et al (2011) gave the idea of production model for a deteriorating item with shortage and time-dependent demand. Kumar Arya. et al (2012) developed a model for deteriorating items with time dependent demand and partial backlogging and Kumar M. et al (2012) gave the idea of deterministic model for deteriorating items with price dependent demand and time varying holding cost under trade credi, issue-1. Liao, J. (2008) developed an EOQ model with non instantaneous receipt and exponential deteriorating item under two-level trade credit and Mahata, G.C. et al (2009) worked on Optimal retailer's ordering policies in the EOQ model for deteriorating items under trade credit financing in supply chain. Mandal B. N. et al (1989) proposed an inventory model for deteriorating items and stock-dependent consumption rate and Mandal, B. (2010) developed an EOQ inventory model for Weibull distributed deteriorating items under ramp type demand and shortages. Meher, M. K. et al (2012) proposed model with weibull deterioration rate under the delay in payment in demand decling market and Mishra U. K. et al (2011) worked on model for weibull deteriorating items with permissible delay in payments under inflation. Mishra, V. et al (2011) gave model for ramp type demand, time dependent deteriorating items with salvage value and shortages. Mishra S. et al (2012) studied EOQ model with power demand of deteriorating items under the Influence of Inflation and Ouyang, L.Y. et al ( 2008) developed an economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. Ouyang, L.Y. et al (2009) proposed an economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. Panda, S. et al (2008) discussed an Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand Pareek, S. et al (2009) developed an inventory model for time dependent deteriorating item with salvage value and shortages and Patra, S.K. et al (2010) discussed an order level EOQ model for deteriorating items in a single warehouse system with price dependent demand in non-linear (quadratic) form and Soni, H. et al (2010) gave inventory models and trade credit a review". Skouri, K. et al (2009) developed Inventory models with ramp type demand rate, partial backlogging and weibull deterioration rate and Singh T. et al (2012) discussed an eoq model for a deteriorating item with time dependent exponentially declining demand under permissible delay in payment Tripathi R.P. et al (2010) A Cash flow oriented EOQ model under permissible delay in payments. Tripathi R.P., (2011) worked on Optimal pricing and ordering policy for inflation dependent demand rate under permissible delay in payments .Tripathy, C. K. et al (2010) discussed ordering policy for weibull deteriorating items for quadratic demand with permissible delay in payments Tripathi, R.P. et al (2011) www.iosrjournals.org 88 | Page proposed an inventory model with shortage, time-dependent demand rate and quantity dependent permissible delay in payment Tripathi, R.P. et al (2010) gave credit financing in economic ordering policies of nondeteriorating items with time-dependent demand rate Tripathy P.K, et al (2011) discussed an integrated partial backlogging model having weibull demand and variable deterioration rate with the effect of trade credit Yadav R. K. et al (2014) discussed deteriorating inventory model for quadratic demand and constant holding cost with partial backlogging and inflation Yadav R. K et al (2015) also proposed An Inventory model for variable demand, constant holding cost and without shortages Yadav, R.K et al (2013). The rest of this paper is organized as follows. Section II describes the assumptions used throughout this paper. In section III notations used in paper are listed. The mathematical formulation is given in section IV. Section V describes the mathematical solution of the problem formulated in section IV. The algorithm of the solution is provided in section VI. Concluding remarks and suggestions for future research are provided in Section VII while a numerical solution is mentioned in section VIII.