Two-storage fuzzy inventory model with time dependent demand and holding cost under acceptable delay in payment
Abstract
If we observe a real business market, the demand for items in each cycle is not in the same pattern, that is, for specific business cycle it may increase, stable or decrease (for instance, cool drinks from end stage of the summer to winter; the demand goes on decreasing, and from the end of winter to peak time of summer; the demand goes on increasing). Also, if the supplier permits for delay in payment, retailer wishes to buy more goods, and for which the retailer may need extra storage (in terms of a rented warehouse). Moreover, the retailer has always wished to sell the items before they expire and accordingly order is placed. Mostly the parameters in a real world inventory model are imprecise. Thus, in the proposed study an inventory model having decreasing time dependent demand pattern with variable holding cost for TwoStorage facility under acceptable delay in payment has been developed. Mathematical model of the problem and its solution procedure is discussed for both crisp and fuzzy environment in order to obtain the optimal replenishment time and cost. Also, numerical examples are discussed to validate the study. Finally, sensitivity analysis is also studied to describe the fluctuating scenario of associated parameters.
Keyword : inventory model, two-storage facility, variable holding cost, time dependent demand, delay in payment, fuzzy inventory model, defuzzification, graded mean integration representation
How to Cite
Kumar, B. A., Paikray, S. K., & Mishra, U. (2020). Two-storage fuzzy inventory model with time dependent demand and holding cost under acceptable delay in payment. Mathematical Modelling and Analysis, 25(3), 441-460. https://doi.org/10.3846/mma.2020.10805
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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N. Misra and S. Mishra. Fuzzy inventory model with single item under constant demand and time dependent holding cost. J. progre. Res. Math., 7:949–961, 2016.
R.S. Rajan and R. Uthayakumar. A two-warehouse inventory model for deteriorating items with permissible delay under exponentially increasing demand. Int. J. Suppl. Oper. Manag., 2:662–682, 2015.
S.S. Routray, S.K. Paikray, S. Misra and U.K. Misra. Fuzzy inventory model with single item under time dependent demand and holding cost. Int. J. Adv. Res. Sci. Eng., 6:1604–1618, 2017.
B.K. Sett, B. Sarkar and A. Goswami. A two- warehouse inventory model with increasing demand and time varying deterioration. Sci. Iran., 19:1969–1977, 2012. https://doi.org/10.1016/j.scient.2012.10.040
S. Shabani, A. Mirzazadeh and E. Sharifi. A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment. J. Ind. Prod. Eng., 33(2):134–142, 2016. https://doi.org/10.1080/21681015.2015.1107859
D. Singh and A. Kumar. Two-warehouses partial backlogging inventory model for deteriorating items with selling price dependent demand under trade credit in the inflationary environment. Int. J. Pure Appl. Math., 118:1447–1457, 2018. https://doi.org/10.1504/IJOR.2011.040329
S.R. Singh, N. Kumar and R. Kumari. Two-warehouse fuzzy inventory model under the conditions of permissible delay in payments. Int. J. Oper. Res., 11(1):78–99, 2011.
S. Tiwari, L.E. Crdenas-Barrn, A. Khanna and C.K. Jaggi. Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment. Int. J. Prod. Econ., 176:154–169, 2016.
H-L. Yang. Two-warehouse partial backlogging inventory models with threeparameter weibull distribution deterioration under inflation. Int. J.Prod. Econ., 138(1):107–116, 2012. https://doi.org/10.1016/j.ijpe.2012.03.007
J.C.P. Yu. Optimizing a two-warehouse system under shortage backordering, trade credit, and decreasing rental conditions. Int. J.Prod. Econ., 209:147–155, 2019. https://doi.org/10.1016/j.ijpe.2018.06.003
S. Barik, S.K. Paikray, S. Mishra, B.A. Kumar and U.K. Misra. Optimal inventory model with single item under various demand conditions. Int. J. Adv. Res. Sci. Eng., 6:1577–1588, 2017.
S. Barik, S.K. Paikray, S. Mishra and U.K. Misra. Inventory models for deteriorating items for non linear holding cost with time dependant demand. J. Adv. Math., 9:2705–2709, 2014.
A.K. Bhunia, C.K. Jaggi, A. Sharma and R. Sharma. A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging. Appl. Math. Comput., 232(1):1125–1137, 2014. https://doi.org/10.1016/j.amc.2014.01.115
D. Chakraborty, D.K. Jana and T.K. Roy. Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments. Comput. Ind. Eng., 123:157–159, 2018. https://doi.org/10.1016/j.cie.2018.06.022
P. Guchhait, M.K. Maiti and M. Maiti. Two storage inventory model with fuzzy deterioration over a random planning horizon. Appl. Soft Comput., 13(1):428– 448, 2013. https://doi.org/10.1016/j.asoc.2012.07.028
C.W. Haley and H.K. Higgins. Inventory policy and trade credit financing. Manag. Sci., 20(4):464–471, 1973. https://doi.org/10.1287/mnsc.20.4.464
R.V. Hartley. Operations Research-A Managerial Emphasis. Good Year Publishing Company, California, 1976.
S. K. Indrajitsingha, P. N. Samanta and U.K. Misra. A fuzzy two-warehouse inventory model for single deteriorating item with selling-price-dependent demand and shortage under partial-backlogged condition. Appl. Appl. Math., 14:511–536, 2019.
C.K. Jaggi, L.E. Cárdenas-Barrón, S. Tiwari and A.A. Shafi. Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments. Sci. Iran. E., 24(1):390–412, 2017. https://doi.org/10.24200/sci.2017.4042
C.K. Jaggi, P. Gautam and A. Khanna. Inventory decisions for imperfect quality deteriorating items with exponential declining demand under trade credit and partially backlogged shortages. In P. Kapur, U. Kumar and A. Verma(Eds.), Quality, IT and Business Operations., Springer Proceedings in Business and Economics, pp. 213–229, Singapore, 2018.
C.K. Jaggi, S. Pareek, A. Khanna and R. Sharma. Credit financing in a twowarehouse environment for deteriorating items with price-sensitive demand and fully backlogged shortages. Appl. Math. Model., 38(21-22):5315–5333, 2014. https://doi.org/10.1016/j.apm.2014.04.025
C.K. Jaggi, S. Tiwari and S.K. Goel. Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities. Ann. Oper. Res., 248:253–280, 2017. https://doi.org/10.1007/s10479-016-2179-3
N.K. Kaliraman, R. Raj, S. Chandra and H. Chaudhary. Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment. Yugosl. J. Oper. Res., 27(1):109–124, 2017. https://doi.org/10.2298/YJOR150404007K
A. Khanna, M. Mittal P. Goutam and C.K. Jaggi. Credit financing for deteriorating imperfect quality items with allowable shortages. Decis. Sci. Lett., 5:45–60, 2016. https://doi.org/10.5267/j.dsl.2015.9.001
A. Khanna, P. Goutam and C.K. Jaggi. Inventory modeling for deteriorating imperfect quality items with selling price dependent demand and shortage backordering under credit financing. Int. J. Math. Eng. Manag. Sci., 2(2):110–124, 2017. https://doi.org/10.33889/IJMEMS.2017.2.2-010
D. Khurana. Two warehouse inventory model for deteriorating items with time dependent demand under inflation. Int. J. Comput. Appl., 114(7):34–38, 2015. https://doi.org/10.5120/19994-1738
Y. Liang and F. Zhou. A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment. Appl. Math. Model., 35(5):2221–2231, 2011. https://doi.org/10.1016/j.apm.2010.11.014
J-J. Liao, K-J. Chung and K-N. Huang. A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system. Int. J. Prod. Econ., 146(2):557–565, 2013. https://doi.org/10.1016/j.ijpe.2013.08.001
J-J. Liao, K-N. Huang and K-J. Chung. Lot-sizing decisions for deteriorating items with two warehouses under an order-size-dependent trade credit. Int. J. Prod. Econ., 137(1):102–115, 2012. https://doi.org/10.1016/j.ijpe.2012.01.020
N. Misra and S. Mishra. Fuzzy inventory model with single item under constant demand and time dependent holding cost. J. progre. Res. Math., 7:949–961, 2016.
R.S. Rajan and R. Uthayakumar. A two-warehouse inventory model for deteriorating items with permissible delay under exponentially increasing demand. Int. J. Suppl. Oper. Manag., 2:662–682, 2015.
S.S. Routray, S.K. Paikray, S. Misra and U.K. Misra. Fuzzy inventory model with single item under time dependent demand and holding cost. Int. J. Adv. Res. Sci. Eng., 6:1604–1618, 2017.
B.K. Sett, B. Sarkar and A. Goswami. A two- warehouse inventory model with increasing demand and time varying deterioration. Sci. Iran., 19:1969–1977, 2012. https://doi.org/10.1016/j.scient.2012.10.040
S. Shabani, A. Mirzazadeh and E. Sharifi. A two-warehouse inventory model with fuzzy deterioration rate and fuzzy demand rate under conditionally permissible delay in payment. J. Ind. Prod. Eng., 33(2):134–142, 2016. https://doi.org/10.1080/21681015.2015.1107859
D. Singh and A. Kumar. Two-warehouses partial backlogging inventory model for deteriorating items with selling price dependent demand under trade credit in the inflationary environment. Int. J. Pure Appl. Math., 118:1447–1457, 2018. https://doi.org/10.1504/IJOR.2011.040329
S.R. Singh, N. Kumar and R. Kumari. Two-warehouse fuzzy inventory model under the conditions of permissible delay in payments. Int. J. Oper. Res., 11(1):78–99, 2011.
S. Tiwari, L.E. Crdenas-Barrn, A. Khanna and C.K. Jaggi. Impact of trade credit and inflation on retailer’s ordering policies for non-instantaneous deteriorating items in a two-warehouse environment. Int. J. Prod. Econ., 176:154–169, 2016.
H-L. Yang. Two-warehouse partial backlogging inventory models with threeparameter weibull distribution deterioration under inflation. Int. J.Prod. Econ., 138(1):107–116, 2012. https://doi.org/10.1016/j.ijpe.2012.03.007
J.C.P. Yu. Optimizing a two-warehouse system under shortage backordering, trade credit, and decreasing rental conditions. Int. J.Prod. Econ., 209:147–155, 2019. https://doi.org/10.1016/j.ijpe.2018.06.003