Exponentially backlogged shortage inventory model for deteriorating item with linear selling price of the product

Authors:

M. Mijanur Rahman,

DOI NO:

https://doi.org/10.26782/jmcms.2019.04.00023

Keywords:

Inventory,Weibul distributiondeterioration,linear price dependent demand,Partially backlogged shortage,

Abstract

This paper deals with an inventory model for deteriorating items with linear price and frequency of advertisement dependent demand and exponentially backlogged shortages. The deterioration rate follows three-parameter Weibull distribution. The corresponding non-linear problem have been formulated and solved. Numerical example has been considered to illustrate the model and the significant features of the result are discussed. Finally, we have performed the sensitivity analysis taking one or more parameters at a time.

Refference:

I.Abad, P.L.: Optimal pricing and lot-sizing under of conditions of perishability and partial backordering, Management Science, 42,1093-1104(1996).

II.Bhunia, A.K., Maiti, M.: An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand, Applied Mathematical Modelling,23, 301-308(1998).

III.Bhunia,A.K., Maiti, M.: Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level,Computers and Operations Research, 25,997-1006(1998).

IV.Bhunia, A.K., Shaikh, A.A, Dhaka, V., Pareek, S. An application of Genetic Algorithm and PSO in an inventory model for single deteriorating item with variable demand dependent on marketing strategy and displayed stock level, Scientica Iranica (in press) (2017)

V.Bhunia, A.K., Shaikh, A.A. A two-warehouse inventory model for deteriorating items with time dependent partial backlogging and variable demand dependent on marketing strategy and time, International Journal of Inventory Control and Management, 1(2), 95-110 (2011).

VI.Bhunia, A.K., Shaikh, A.A., A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration, International Journal of Industrial Engineering Computations (Growing Science), 5(3), 497–510(2014).

VII.Bhunia, A.K., Shaikh, A.A., A deterministic model for deteriorating items with displayed inventory level dependent demand rate incorporating marketing decision with transportationcost, International Journal of Industrial Engineering Computations, 2(3),547-562 (2011).

VIII.Bhunia, A.K., Shaikh, A.A., Cárdenas-Barrón, L.E., A partially integrated production inventory model with interval valued inventory costs, variable demand and flexible reliability, Applied Soft Computing, 55, 491-502 (2017).

IX.Bhunia, A.K., Shaikh, A.A., Gupta, R.K. A study on two warehouse partially backlogged deteriorating inventory models under inflation via particle swarm optimization, International Journal of System Science, 46(6), 1036–1050(2015).
X.Bhunia, A.K., Shaikh, A.A., Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm Optimization, Mathematical and Computer Modelling of Dynamical Systems, 22 (2), 160-179 (2016).
XI.Bhunia, A.K., Shaikh, A.A., Mahato, S.K., Jaggi, C.K. A deteriorating inventory model with displayed stock-level dependent demand and partially backlogged shortages with all unit discount facilities via Particle Swarm Optimization, International Journal of System Science: Operations and Logistics, 1(3), 164-180(2014).
XII.Bhunia, A.K., Shaikh, A.A., Maiti, A.K., Maiti, M., A two warehouse deterministic inventory model for deteriorating items with linear trend in time dependent demand over finite horizon by Elitist Real-Coded Genetic Algorithm, International Journal of Industrial Engineering Computations, 4(2), 241-258(2013).
XIII.Bhunia, A.K., Shaikh, A.A., Pareek, S., Dhaka, V. A memo on stock model with partial backlogging under delay in payments, Uncertain Supply Chain Management (Growing Science),3(1), 11-20(2015).
XIV.Bhunia, A.K., Shaikh, A.A., Sahoo, L. A two-warehouse inventory model for deteriorating items under permissible delay in payment via particle swarm optimization, International Journal of Logistics and Systems Management, 24(1), 45-68 (2015).
XV.Bhunia, A.K., Shaikh, A.A., Sharma, G, Pareek, S. A two-storage inventory model for deteriorating items with variable demand and partial backlogging, Journal of Industrial and Production Engineering, 32(4), 263-272 (2015).
XVI.Chakrabarty, T., Giri, B.C., Chaudhuri.,K.S.: An EOQ model for items with Weibull distribution deterioration, shortages and trend demand: An
extension of Philip’s model., Computers & Operations Research,25, 649-657(1998).
XVII.Covert, R.P., Philip, G.C.: An EOQ model for items with Weibull distribution deterioration,American Institute of Industrial Engineering Transactions,5, 323-326(1973).
XVIII.Deb, M., Chaudhuri, K.S.: An EOQ model for items with finite rate of production and variable rate of deterioration, Opsearch, 23, 175-181(1986).
XIX.Emmons, H.: A replenishment model for radioactive nuclide generators,Management Science,14, 263-273(1968).
XX.Ghare, P., Schrader, G.: A model for exponential decaying inventories,Journal of Industrial Engineering, 14, 238-243(1963).
XXI.Ghosh, S.K., Chaudhury, K.S.: An order-level inventory model for a deteriorating item withWeibull distribution deterioration, time-quadratic demand and shortages,International Journal ofAdvanced Modeling and Optimization,6(1),31-45(2004).
XXII.Giri, B.C. Jalan,A.K., Chaudhuri K.S.: Economic order quantity model with weibull deteriorating distribution, shortage and ram-type demand, International journal of SystemScience,34,237-243(2003).
XXIII.Giri, B.C. Pal, S., Goswami A., Chaudhuri K.S.: An inventory model for deteriorating items with stock-dependent demand rate, European Journal of Operational Research, 95, 604-610(1996).
XXIV.Giri, B.C., Chakrabarty,T., Chaudhuri K.S.: Retailer’s optimal policy for perishable product with shortages when supplier offers all-unit quantity and freight cost discounts,Proceeding ofNational Academy of Sciences,69(A), III, 315-326(1999).
XXV.Goswami, A., Chaudhuri, K. S.: An EOQ model for deteriorating items with shortage and a linear trend in demand,Journal of the Operational Research Society, 42, 1105-1110(1991).XXVI.Goyal, S.K., Gunasekaran, A.: An integrated production-inventory-marketing model for deteriorating items,Computers & Industrial Engineering, 28, 755-762(1995).
XXVII.Khan, M. A. A., Shaikh, A. A., Panda, G. C., & Konstantaras, I. (2018). Two-warehouse inventory model for deteriorating items with partial backlogging and advance payment scheme.RAIRO‐Operations Research.
XXVIII.Kotler, P.: Marketing Decision Making: A Model Building Approach, Holt. Rinehart, Winston, New York(1971).
XXIX.Ladany, S., Sternleib, A.: The intersection of economic ordering quantities and marketing policies,AIIE Trnsactions,6, 173-175(1974).
XXX.Luo, W.: An integrated inventory system for perishable goods with backordering, Computers &Industrial Engineering, 34, 685 –693(1998).
XXXI.Mandal, B. N., Phaujdar, S. An inventory model for deteriorating items and stock-dependent consumption rate, Journal of Operational Research Society, 40, 483 –488(1989a).
XXXII.Mandal, M., Maiti, M.: Inventory model for damageable items with stock-dependent demand and shortages, Opsearch, 34, 156-166(1997).
XXXIII.Mishra, U. Cardenas-Barron, L.E., Tivari, S., Shaikh, A.A., Gererdo, T.G., An inventory model under price and stock dependent demand for controllabledeterioration rate with shortages and preservation technology investment, Annals of Operational Research, 254 (1-2), 150-190 (2017).
XXXIV.Misra, R.B.: Optimum Production lot-size model for a system with deteriorating inventory, International Journal of Production Research, 13, 495-505(1975).
XXXV.Padmanabhan, G., Vrat, P.: EOQ models for perishable items under stock-dependent selling rate, European Journal of Operational Research, 86, 281-292(1995).
XXXVI.Pal, A.K., Bhunia, A.K., Mukherjee, R.N. Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering, European Journal of Operational Research, 175, 977-991(2006).
XXXVII.Pal, S., Goswami, A., Chaudhuri, K.S.: A deterministic inventory model for deteriorating items with stock-dependent demand rate,International Journal of Production Economics,32,291-299(1993).
XXXVIII.Panda, G. C., Khan, M. A. A., & Shaikh, A. A. (2018). A credit policy approach in a two-warehouse inventory model for deteriorating items with price-and stock-dependent demand under partial backlogging.Journal of Industrial Engineering International, 1-24.
XXXIX.Sana, S., Chaudhuri, K.S.: On a volume flexible production policy for deteriorating item with stock-dependent demand rate, Nonlinear Phenomena in Complex system,7(1),61-68(2004).
XL.Sana, S., Goyal, S.K., Chaudhuri, K.S.: A production-inventory model for a deteriorating item with trended demand and shortages,European Journal of Operation Research,157, 357-371(2004).
XLI.Sarkar, B.R., Mukherje,e. S., Balan, C.V.: An order-level lot-size inventory model with inventory-level dependent demand and deterioration,International Journal of Production Economics,48,227-236(1997).
XLII.Shaikh, A. A. (2017). An inventory model for deteriorating item with frequency of advertisement and selling price dependent demand under mixed type trade credit policy.International Journal of Logistics Systems and Management,28(3), 375-395.
XLIII.Shaikh, A. A., Khan, M. A. A., Panda, G. C., & Konstantaras, I. Price discount facility in an EOQ model for deteriorating items with stock‐dependent demand and partial backlogging.International Transactions in Operational Research. (in press)
XLIV.Shaikh, A.A. Cardenas-Barron, L.E., Bhunia, A.K., Tiwari, S. An inventory model of a three parameter Weibull distributed deteriorating item with variable demand dependent on price and frequency of advertisement under trade credit, Rairo-Operations research Journal (in press) (2017).
XLV.Shaikh, A.A., A two warehouse inventory model for deteriorating items with variable demand under alternative trade credit policy, International Journal of Logistics and Systems Management, 27 (1), 40-61(2017).
XLVI.Shaikh, A.A., Cardenas-Barron, L.E., Tiwari, S., A two-warehouse inventory model for non-instantaneous deteriorating items withinterval
valued inventory costs and stock dependent demand under inflationary conditions, Neural Computing and Applications (in press) (2017).
XLVII.Shaikh, A.A., Masud, Md. A, Uddin, Md, S., Khan, A. A., Non-instantaneous deterioration inventory model with price and stock dependent demand for fully backlogged shortages under inflation, International Journal of Business Forecasting and Marketing Intelligence(in press) (2017).
XLVIII.Shaikh, A.A., Panda,G.C., Sahu, S., Das, A.K.,Economic order quantity model for deteriorating item with preservation technology in time dependent demand with partial backlogging and trade credit,International Journal of Logistics and Systems Management, (in press) (2017).
XLIX.Subramanyam, S., Kumaraswamy, S.: EOQ formula under varying marketing policies and conditions, AIIE Transactions, 22, 312-314(1981).
L.Taleizadeh, A. A., Hadadpour, S., Cárdenas-Barrón, L. E., & Shaikh, A. A. (2017). Warranty and price optimization in a competitive duopoly supply chain with parallel importation.International Journal of Production Economics,185, 76-88.
LI.Tiwari, S., Jaggi, C.K., Bhunia, A.K., Shaikh, A.A., A two warehouse inventory model for Non-instantaneous Deteriorating Items with stock dependent demand under Inflationary Conditions using particle swarm optimization, Annals of Operational Research
LII.Urban, T.L.: Deterministic inventory models incorporating marketing decisions, Computers & Industrial Engineering, 22, 85-93(1992b).
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