In this paper, a deterministic inventory model for deteriorating items with linear deterioration rate is proposed. Demand follows a power pattern. Shortages are permitted and partially backlogged. An optimal solution is derived to minimizes the total average cost. Numerical examples are given, and sensitivity analysis carried out to show how the optimal decisions are affected by changes in different parameters in the model. Graphical representation of the convexity of the total cost against the decision variables shows the efficiency and reliability of the model.
SahooA., IndrajitsinghaK., SamantaS.K., P. N. and MisraU.K., Selling price dependent demand with allowable shortages model under partially backlogged—deteriorating items, International Journal of Applied and Computational Mathematics5(4) (2019), 104.
2.
Olalekan AdaraniwonA. and Bin OmarM., An inventory model for delayed deteriorating items with power demand considering shortages and lost sales, Journal of Intelligent & Fuzzy Systems (36) (2019), 5397–5408.
3.
GiriB., GoswamiA. and ChaudhuriK., An eoq model fordeteriorating items with time varying demand and costs, Journal of the Operational Research Society47(11) (1996), 1398–1405.
4.
SarkarB. and SarkarS., An improved inventory model with partial backlogging, time varying deterioration and stockdependent demand, Economic Modelling30 (2013a), 924–932.
5.
SarkarB. and SarkarS., Variable deterioration and demand- an inventory model,b), Economic Modelling31 (2013), 548–556.
6.
DyeC.Y., ChangH.J. and TengJ.T., A deteriorating inventory model with time-varying demand and shortagedependent partial backlogging, European Journal of Operational Research172(2) (2006), 417–429.
7.
SilverE.A., A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment, Prod Inventory Manage2 (1973), 64–74.
8.
SilverE.A. and MealH.C., A simple modification of the eoq for the case of a varying demand rate, Production and Inventory Management10(4) (1969), 52–65.
9.
WeeH.M., Deteriorating inventory model with quantity discount, pricing and partial backordering, International Journal of Production Economics59(1-3) (1999), 511–518.
10.
SiciliaJ., Gonzalez-De-laM., Rosa Febles-AcostaJ. and Alcaide-Lopez-de PabloD., An inventory model for deteriorating items with shortages and time-varying demand, International Journal of Production Economics155 (2014), 155–162.
11.
JanssenL., ClausT. and SauerJ., Literature review of deteriorating inventory models by key topics from 2012 to 2015, International Journal of Production Economics182 (2016), 86–112.
12.
BenkheroufL., SkouriK. and KonstantarasI., Inventory decisions for a finite horizon problem with product substitution options and time varying demand, Applied Mathematical Modelling51 (2017), 669–685.
13.
BenkheroufL. and MahmoudM.G., On an inventory model for deteriorating items with increasing time-varying demand and shortages, Journal of the Operational Research Society47(1) (1996), 188–200.
14.
ChenL., ChenX., KeblisM.F. and LiG., Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand. Computers & Industrial Engineering. (2018).
15.
BatenM. and KhalidR., Optimal production cycle time for inventory model with linear time dependent exponential distributed deterioration, Journal of Intelligent & Fuzzy Systems30(2) (2016), 1243–1248.
16.
KhanlarzadeN., YeganeB., KamalabadiI. and FarughiH., Inventory control with deteriorating items: A stateof-the-art literature review, International Journal of Industrial Engineering Computations5(2) (2014), 179–198.
17.
RajeswariN. and IndraniK., Eoq policies for linearly time dependent deteriorating items with power demand and partial backlogging, International Journal of Mathematical Archive EISSN 2229-50466(2) (2015).
18.
AggrawalP. and SinghT., An EOQ model with ramp type demand rate, time dependent deterioration rate and shortages, Global Journal of Pure and Applied Mathematics13(7) (2017), 3381–3393.
19.
GhareP., A model for an exponentially decaying inventory, J ind Engng14 (1963), 238–243.
20.
ChenP.S., The impact of time-varying demand and production rates on determining inventory policy, Mathematical Methods of Operations Research54(3) (2001), 39–405.
21.
LiR., LanH. and MawhinneyJ.R., A review on deteriorating inventory study, Journal of Service Science and Management3(01) (2010), 117.
22.
VenkateswarluR. and MohanR., An inventory model for time varying deterioration and price dependent quadratic demand with salvage value, Journal of Computational and Applied Mathematics1(1) (2013), 21–27.
23.
BegumR., SahooR. and SahuS., A replenishment policy for items with price-dependent demand, time-proportional deterioration and no shortages, International Journal of Systems Science43(5) (2012), 903–910.
24.
MannaS.K. and ChaudhuriK., An eoq model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages, European Journal of Operational Research171(2) (2006), 557–566.
25.
SanaS.S., Optimal selling price and lotsize with time varying deterioration and partial backlogging, Applied Mathematics and Computation217(1) (2010), 185–194.
26.
SanniS. and ChukwuW., An economic order quantity model for items with three-parameter weibull distribution deterioration, ramp-type demand and shortages, Applied Mathematical Modelling37(23) (2013), 9698–9706.
27.
SenS. and ChakrabartyT., An order level inventory model with variable rate of deterioration and alternating replenishing rates considering shortages, Opsearch44(1) (2007), 17–26.
28.
SheikhS. and PatelR., Production inventory model with different deterioration rates under shortages and linear demand, International Refereed Journal of Engineering and Science5(3) (2016), 1–7.
29.
SinghT., MallickC. and SinghR.K., Formulating an Economic Order Quantity Model for Items withVariable Rate of Deterioration and Two-Component Demand. In Soft Computing for Problem Solving (2019), (pp. 273-282). Springer, Singapore.
30.
WhitinT.M., Theory of Inventory Management, Princeton University Press, 1957.
31.
SinghT. and PattnayakH., An eoq model for deteriorating items with linear demand,variable deterioration and partial backlogging, Journal of Service Science and Management6(02) (2013), 186.
32.
MishraV.K., Deteriorating inventory model with time dependent demand and partial backlogging, Applied Mathematical Sciences4(72) (2010), 3611–3619.
33.
DonaldsonW., Inventory replenishment policy for a linear trend in demand-an analytical solution, Journal of the Operational Research Society28(3) (1977), 663–670.
