Research article Special Issues

Cost optimization model for items having fuzzy demand and deterioration with two-warehouse facility under the trade credit financing

  • Received: 28 September 2019 Accepted: 26 December 2019 Published: 05 February 2020
  • MSC : 90B05, 03E72

  • Most of the researchers developed their inventory models to forecast the optimal replenishment quantity and time in view of minimizing the total inventory cost by considering deterministic demand and the deterioration of the items. But, in real business these demands and deterioration are mostly fuzzy in nature due to many practical factors, such as increase or decrease in goodwill of the product, competition from the substitute products, scientific advancement in preserving facilities, change in environmental conditions and so on. So by following researcher's classical inventory model, retailer may order less or excess amount of items than the actual requirement. As a result, retailer may face loss in business or increase in cost. Moreover, in many cases, suppliers offer trade credit to increase their sales, and by availing the trade credit facility the retailer purchases a number of items more than the existing storage capacity (in own warehouse) in order to minimize the ordering cost and investment capital. To accommodate these excess amounts of items retailer may hire a warehouse on rent basis. In the light of these facts, we develop a cost optimization model for the inventory items having fuzzy demand and deterioration with two-warehouse facility under trade credit financing by considering triangular fuzzy numbers for the associated parameters. The Graded Mean Integration Representation defuzzification technique is used and numerical examples are provided to justify the validity of the proposed model. Finally, sensitivity analysis of major parameters has been incorporated to draw the managerial insight on optimal solution.

    Citation: Boina Anil Kumar, S. K. Paikray, Hemen Dutta. Cost optimization model for items having fuzzy demand and deterioration with two-warehouse facility under the trade credit financing[J]. AIMS Mathematics, 2020, 5(2): 1603-1620. doi: 10.3934/math.2020109

    Related Papers:

  • Most of the researchers developed their inventory models to forecast the optimal replenishment quantity and time in view of minimizing the total inventory cost by considering deterministic demand and the deterioration of the items. But, in real business these demands and deterioration are mostly fuzzy in nature due to many practical factors, such as increase or decrease in goodwill of the product, competition from the substitute products, scientific advancement in preserving facilities, change in environmental conditions and so on. So by following researcher's classical inventory model, retailer may order less or excess amount of items than the actual requirement. As a result, retailer may face loss in business or increase in cost. Moreover, in many cases, suppliers offer trade credit to increase their sales, and by availing the trade credit facility the retailer purchases a number of items more than the existing storage capacity (in own warehouse) in order to minimize the ordering cost and investment capital. To accommodate these excess amounts of items retailer may hire a warehouse on rent basis. In the light of these facts, we develop a cost optimization model for the inventory items having fuzzy demand and deterioration with two-warehouse facility under trade credit financing by considering triangular fuzzy numbers for the associated parameters. The Graded Mean Integration Representation defuzzification technique is used and numerical examples are provided to justify the validity of the proposed model. Finally, sensitivity analysis of major parameters has been incorporated to draw the managerial insight on optimal solution.


    加载中


    [1] P. M. Ghare, G. P. Schrader, A model for exponentially decaying inventory, J. Ind. Eng., 14 (1963), 238-243.
    [2] U. Mishra, L. E. Cárdenas-Barrón, S. Tiwari, et al., An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals Oper. Res., 254 (2017), 165-190. doi: 10.1007/s10479-017-2419-1
    [3] S. Benerjee, S. Agrawal, Inventory model for deteriorating items with freshness and price dependent demand: Optimal discounting and ordering policies, Appl. Math. Model., 52 (2017), 53-64. doi: 10.1016/j.apm.2017.07.020
    [4] S. Tiwari, L. E. Cárdenas-Barrón, M. Goh, et al., Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain, Int. J. Prod. Econ., 200 (2018), 16-36. doi: 10.1016/j.ijpe.2018.03.006
    [5] L. Chen, X. Chen, M. F. Keblis, et al., Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand, Comput. Ind. Eng., 135 (2019), 1294-1299. doi: 10.1016/j.cie.2018.06.005
    [6] Y. Zhang, Z. Wang, A joint ordering, pricing, and Freshness-Keeping policy for perishable inventory systems with random demand over infinite horizon, IEEE Rob. Autom. Lett., 4 (2019), 2707-2713. doi: 10.1109/LRA.2019.2916471
    [7] M. Braglia, D. Castellano, L. Marrazzini, et al., A continuous review, (Q, r) inventory model for a deteriorating item with random demand and positive lead time, Comput. Oper. Res., 109 (2019), 102-121. doi: 10.1016/j.cor.2019.04.019
    [8] J. A. L. Alvarez, P. Buijs, O. A. Kilic, et al., An inventory control policy for liquefied natural gas as a transportation fuel, Omega (United Kingdom), 90 (2020), Art. No. 101985.
    [9] A. A. Shaikh, L. E. Cárdenas-Barrón, A. K. Bhunia, et al., 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-Oper. Res., 53 (2019), 903-916. doi: 10.1051/ro/2017052
    [10] H. M. Lee, J. S. Yao, Economic production quantity for fuzzy demand and fuzzy production quantity, European J. Oper. Res., 109 (1998), 203-211. doi: 10.1016/S0377-2217(97)00200-2
    [11] C. Kao, WK. Hsu, A Single-Period inventory model with fuzzy demand, Comput. Math., 43 (2002), 841-848.
    [12] P. Dutta, D. Chakraborty, A. R. Roy, An inventory model for single-period products with reordering opportunities under fuzzy demand, Comput. Math. Appl., 53 (2007), 1502-1517. doi: 10.1016/j.camwa.2006.04.029
    [13] L. Wang, Q. L. Fu, Y. R. Zeng, Continuous review inventory models with a mixture of backorders and lost sales under fuzzy demand and different decision situations, Expert. Syst. Appl., 39 (2012), 4181-4189. doi: 10.1016/j.eswa.2011.09.116
    [14] J. Sadeghi, S. M. Mousavi, S. T. A. Niaki, Optimizing an inventory model with fuzzy demand, backordering, and discount using a hybrid imperialist competitive algorithm, Appl. Math. Model., 40 (2016), 7318-7335. doi: 10.1016/j.apm.2016.03.013
    [15] J. Sadeghi, S. T. A. Niaki, Two parameter tuned multi-objective evolutionary algorithms for abi-objective vendor managed inventory model with trapezoidal fuzzy demand, Appl. Soft comput., 30 (2015), 567-576. doi: 10.1016/j.asoc.2015.02.013
    [16] A. Kundu, P. Guchhait, P. Pramanik, et al., A production inventory model with price discounted fuzzy demand using an interval compared hybrid algorithm, Swarm. Evol. Comput., 34 (2017), 1-17. doi: 10.1016/j.swevo.2016.11.004
    [17] M. K. Maiti, M. Maiti, Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constaints via genetic algorithm, European J. Oper. Res., 179 (2007), 352-371. doi: 10.1016/j.ejor.2006.03.029
    [18] M. Rong, N. K. Mahapatra, M. Maiti, A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time, European J. Oper. Res., 189 (2008), 59-75. doi: 10.1016/j.ejor.2007.05.017
    [19] S. Shabani, A. Mirzazadeh, E. Sharifi, A two-warehouse inventory model with fuzzy deterioration and fuzzy demand rate under conditionally permissible delay in payment, J. Ind. Prod. Eng., 33 (2016), 134-142.
    [20] S. R. Singh, N. Kumar, R. Kumari, Two-warehouse fuzzy inventory model under the conditions of permissible delay in payments, Int. J. Oper. Res., 11 (2013), 78-99.
    [21] N. K. Samal, D. K. Pratihar, Optimization of variable demand fuzzy economic order quantity inventory models without and with backordering, Comput. Ind. Eng., 78 (2014), 148-162. doi: 10.1016/j.cie.2014.10.006
    [22] G. C. Mahata, P. Mahata, Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain, Math. Comput. Model., 53 (2011), 1621-1636. doi: 10.1016/j.mcm.2010.12.028
    [23] S. Jain, S. Tiwari, L. E. Cárdenas-Barrón, et al., A fuzzy imperfect production and repair inventory model with time dependent demand, production and repair rates under inflationary conditions, RAIRO-Oper. Res., 52 (2018), 217-239. doi: 10.1051/ro/2017070
    [24] A. A. Shaikh, L. E. Cárdenas-Barrón, L. Sahoo, A fuzzy inventory model for a deteriorating item with variable demand, permissible delay in payments and partial backlogging with shortage follows inventory (SFI) policy, Int. J. Fuzzy Syst., 20 (2018), 1606-1623. doi: 10.1007/s40815-018-0466-7
    [25] S. Pal, G. S. Mahapatra, G. P. Samanta, An EPQ model of ramptype demand with Weibull deterioration under inflation and finite horizon in crisp and fuzzy environment, Int. J. Prod. Econ., 156 (2014), 159-166. doi: 10.1016/j.ijpe.2014.05.007
    [26] R. V. Hartley, Operation Research-A mangerial Emphasis, Good Year Publishing Company, Calfornia, 1976.
    [27] K. V. S. Sarma, A deterministic order level inventory model for deteriorating items with two storage faclities, European J. Oper. Res., 29 (1987), 70-73. doi: 10.1016/0377-2217(87)90194-9
    [28] T. P. M. Pakkala, K. K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European J. Oper. Res., 57 (1992), 71-76. doi: 10.1016/0377-2217(92)90306-T
    [29] C. C. Lee, S-L Hsu, A two-warehouse production model for deteriorating inventory items with time-dependent demands, European J. Oper. Res., 194 (2009), 700-710. doi: 10.1016/j.ejor.2007.12.034
    [30] H-L. Yang, Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation, Int. J. Prod. Econ., 138 (2012), 107-116. doi: 10.1016/j.ijpe.2012.03.007
    [31] S. Agarwal, S. Banerjee, S. Papachristos, Inventory model with deteriorating items, ramp-type demand and partially backlogged shortages for a two warehouse system, Appl. Math. Model., 37 (2013), 8912-8929. doi: 10.1016/j.apm.2013.04.026
    [32] B. K. Sett, B. Sarkar, A. Goswami, A two-warehouse inventory model with increasing demand and time varying deterioration, Sci. Iran., 19 (2012), 1969-1977. doi: 10.1016/j.scient.2012.10.040
    [33] A. A. Shaikh, L. E. Cárdenas-Barrón, S. Tiwari, A two-warehouse inventory model for non-instantaneous deteriorating items with interval valued inventory costs and stock dependent demand under inflationary conditions, Neural Comput. Appl., 31 (2019), 1931-1948. doi: 10.1007/s00521-017-3168-4
    [34] C. W. Haley, R. C. Higgins, Inventory policy and trade credit financing, Manag. Sci., 20 (1973), 464-471. doi: 10.1287/mnsc.20.4.464
    [35] Y. Liang, F. Zhou, A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment, Appl. Math. Model., 35 (2011), 2221-2231. doi: 10.1016/j.apm.2010.11.014
    [36] J. J. Lia, K. N. Huang, K. J. Chung, Lot-sizing decisions for deteriorating items with two warehouses under an order-size-dependent trade credit, Int. J. Prod. Econ., 137 (2012), 102-115. doi: 10.1016/j.ijpe.2012.01.020
    [37] P. Guchhait, M. K. Maiti, M. Maiti, Two storage inventory model of a deteirorating item with variable demand under partial credit period, Appl. Soft Comput., 13 (2013), 428-448. doi: 10.1016/j.asoc.2012.07.028
    [38] J. J. Lio, K. J. Chung, K. N. Huang, A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system, In. J. Prod. Econ., 146 (2013), 557-565. doi: 10.1016/j.ijpe.2013.08.001
    [39] A. K. Bhunia, C. K. Jaggi, A. Sharma, et al., A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging, Appl. Math. Comput., 232 (2014), 1125-1137.
    [40] C. K. Jaggi, S. Pareek, A. Khanna, et al., Credit financing in a two-warehouse environment for deteriorating items with price-sensitive demand and fully backlogged shortages, Appl. Math. Model., 38 (2014), 5315-5333. doi: 10.1016/j.apm.2014.04.025
    [41] A. K. Bhunia, A. A. Shaikh, An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with different policies, Appl. Math. Comput., 256 (2015), 831-850.
    [42] S. Tiwari, L. E. Cárdenas-Barrón, A. Khanna, et al., 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 (2016), 156-169.
    [43] C. K. Jaggi, S. Tiwari, 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 (2017), 253-280. doi: 10.1007/s10479-016-2179-3
    [44] N. K. Kaliraman, R. Raj, S. Chandra, et al., Two warehouse inventroy model for deteriorating items with exponential demand rate and permissible delay in payment, Yugoslav J. Oper. Res., 27 (2017), 109-124. doi: 10.2298/YJOR150404007K
    [45] D. Chakraborty, D. K. Jana, 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 (2018), 157-179.
    [46] C. K. Jaggi, L. E. Cárdenas-Barrón, S. Tiwari, et al., Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments, Scientia Iranica, Trans. E. 24 (2017), 390-412. doi: 10.24200/sci.2017.4042
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3836) PDF downloads(480) Cited by(9)

Article outline

Figures and Tables

Figures(13)  /  Tables(7)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog