A Multi Objective Offering Inventory Model with time Dependent Demand

Satya Kumar Das¹

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.1 , pp.11-16, Feb-2024

Online published on Feb 28, 2024

Copyright © Satya Kumar Das . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this article, I have presented a multi objective offering inventory model with limitation on initial invested money. Any offer on any things always attracts the customers so in this model to increase customer attraction, here purchase cost offering on quantity and demand is time dependent. Limitation is considered on set up cost and purchase cost. Costs are not specific so all cost parameters are considered as the generalized triangular fuzzy number. My formulated multi objective fuzzy inventory system has been solved by Fuzzy programming technique with hyperbolic membership function. A numerical example is taken to elaborate the inventory model. Sensitivity analysis and the graphical representations have been displayed to represent the truth of the model.

Key-Words / Index Term :
Inventory, offering, Multi-item, Fuzzy number, Fuzzy Technique.

References :
[1] F.J. Arcelus, N.H. Shah, G. Srinivasan, “Retailer’s pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives,”. Int. J. Prod. Econ., vol. 81-82, issue 1.153-162, 2003.
[2] Sana SS, “A deterministic EOQ model with delay in payments and time varying deterioration rate,” European Journal of Operational Research, 184(2), pp 509–533, 2008.
[3] Sarkar B, “An EOQ model with delay in payments and stock dependent demand in the presence of imperfect production,” Applied Mathematics and Computation, 218(17), pp 8295–8308, 2012.
[4] Mishra SS and Singh PK, “Computational approach to an inventory model with ramp-type demand and linear deterioration,” International Journal of Operational Research, 15(3), pp 337–357, 2012.
[5] Khanra S, Mandal B, & Sarkar B, An "inventory model with time dependent demand and shortages under trade-credit polic,“ Economic Modelling , 35, pp 349–355, 2013.
[6] Sarkar B, & Sarkar S, “Variable deterioration and demand-an inventory model, ” Economic Modelling, 31 pp 548–556, 2013.
[7] Alfares HK, Ghaithan AM, “Inventory and Pricing Model with Price-Dependent Demand, Time-Varying Holding Cost, and Quantity Discounts,” Computers & Industrial Engineering, 2016. http://dx.doi.org/10.1016/j.cie.2016.02.009.
[8] Liuxin C, Xian C, Keblis MF and Gen L, “Optimal pricing and replenishment policy for deteriorating inventory under stock-level-dependent, time-varying and price-dependent demand,” Comput. Ind. Eng, pp 1–15, 2018.
[9] Pando V, San-Jos´e LA, Garc´?a-Laguna J and Sicilia J, “Optimal lot-size policy for deteriorating items with stock-dependent demand considering profit maximization” Comput. Ind. Engin. 117 , pp 81–93, 2018.
[10] Mondal B, Garai A, Roy TK, “Optimization of generalized order-level inventory system under fully permissible delay in payment,” RAIRO--Operations Research, 2021. https://doi.org/10.1051/ro/2019079.
[11] R. Tersine, P.R. Leon. “Temporary price discount and EOQ,” J. Purchas. Mater. Manage., 17 (4), pp. 23- 27, 2010.
[12] R.C. Baker, N. Vilcassim, “Continuos review price change inventory model”, Prod. Invent. Manage., 4th Qtr, pp. 67-72, 1983.
[13] Monahan, J. P., “A quantity discount pricing model to increase vendor profits”, Management science, 30, 720–726, 1984.
[14] R. Davis, N. Gaither. “Optimal ordering policies under conditions of extended payment privileges Manage”. Sci., 31 (4), pp. 499-509, 1985.
[15] Lee, H. L., & Rosenblatt, M. J. , “A generalized quantity discount pricing model to increase supplier’s profits”. Management science, 32, pp 1177–1185, 1986.
[16] S.K. Goyal, “Economic ordering policy during special discount periods for dynamic inventory problems under certainty”. Eng. Costs Prod. Econ., 20 (1) , pp. 101-104, 1990.
[17] R. Tersine, S. Barman, “Economic purchasing strategies for temporary price discounts”. Eur. J. Oper. Res., 80 (2), pp. 328-343, 1995.
[18] H.M. Wee, J.Yu.“A deteriorating inventory model with a temporary price discount”, Int. J. Prod. Econ., 53 (1), pp. 81-90, 1997.
[19] F.J. Arcelus, G. Srinivasan. “Ordering policies under one time only discount and price sensitive demand”, IIE Trans., 30 (1), pp. 1057-1064, 1998.
[20] P. Chu, P.S. Chen, T. Niu, Note on supplier-restricted order quantity under temporary price discounts Math. Methods Oper. Res., 58 (1), pp. 141-147, 2003.
[21] B.R. Sarker, A.M. Kindi, “Optimal ordering policies in response to a discount offer”. Int. J. Prod. Econ., 100 (2), pp. 195-211, 2006.
[22] Lin, Y. J. (2008). “Minimax distribution free procedure with backorder price discount”, International Journal of Production Economics, 111, pp 118–128, 2008.
[23] L.E. Cárdenas-Barrón, “Optimal ordering policies in response to a discount offer: extensions”, Int. J. Prod. Econ. (in press b), doi:10.1016/j.ijpe.2009.05.003.
[24] Giri, B. C., & Roy, B., “A vendor–buyer integrated production–inventory model with quantity discount and unequal sized shipments”. International Journal of Operational Research, 16, pp 1–13, 2013.
[25] Payel Mandal & Bibhas Chandra Giri (2017): “A two-warehouse integrated inventory model with imperfect production process under stock-dependent demand and quantity discount offer”, International Journal of Systems Science: Operations & Logistics, DOI: 10.1080/23302674.2017.1335806.
[26] Shaikh AA, Khan MAA, Panda GC and Konstantaras I, “Price discount facility in an EOQ model for deteriorating items with stock-dependent demand and partial backlogging”, International Transactions in Operational Research, 26(4), pp 1365-1395, 2019.
[27] Roy TK, Maiti M, “Multi-Objective inventory models of deteriorating items with some constraints in a fuzzy environment”. Computers Ops Res, 25(12), pp1085-1095, 1998.
[28] Garai T, Chakraborty D, & Roy TK, “A Multi-item Inventory Model with Fuzzy Rough Coefficients via Fuzzy Rough Expectation”, Springer Proceedings in Mathematics & Statistics, 377– 394, 2018. https://doi.org/10.1007/978-981-10-7814-9_26.
[29] Garai T, Chakraborty D, Roy TK, “Multi-objective inventory model with both stock-dependent demand rate and holding cost rate under fuzzy random environment”. Ann Data Sci, 6, pp 61–81, 2019.
[30] Malik AI, Sarkar B, “Disruption management in a constrained multi-product imperfect production system.” Journal of manufacturing systems, 56, pp 227-240, 2020.
[31] Chakraborty D, Jana DK, Roy TK (2020) “Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under imprecise environment”. Soft Computing , 24 (19), pp 14471-14490, 2020.
[32] Das SK, “Multi item inventory model include lead time with demand dependent production cost and set-up-cost in fuzzy environment.” Journal of Fuzzy Extension and Applications, 1(3) pp 227- 243, 2020.
[33] Das SK, “A Fuzzy Multi Objective Inventory Model of Demand Dependent Deterioration Including Lead Time”, Journal of Fuzzy Extension and Applications, 3(1), pp 1-18, 2022.
[34] Garai T, Chakraborty D & Roy TK, “Expected Value of Exponential Fuzzy Number and Its Application to Multi-item Deterministic Inventory Model for Deteriorating Items”. J. Uncertain. Anal. Appl, 2017.https://doi.org/10.1186/s40467-017-0062-7.
[35] Soni HN, Suthar SN (2019)“EOQ model of deteriorating items for fuzzy demand and learning in fuzziness with finite horizon”. J. Control Decis. pp 1–14, 2019.
[36] Poswal P et al, “Investigation and analysis of fuzzy EOQ model for price sensitive and stock dependent demand under shortages”, 2022. https://doi.org/10.1016/j.matpr.2022.02.273.
[37] Roy TK & Maity M (1995) “A fuzzy inventory model with constraints”. Operation research, 32(4) pp 287- 298, 1995.
[38] Maity MK, “Fuzzy inventory model with two ware house under possibility measure in fuzzy goal”, Euro. J Oper. Res, 188, pp 746-774, 2008.
[39] Sarkar B (2012) “An EOQ model with delay in payments and time varying deterioration Rate”, Mathematical & Computer Modelling, 55(3-4), pp 367–377, 2012.
[40] Harris FW (1913) “How many parts to make at once factory.” Mag Mannage, 10(152), pp 135-136, 1913.
[41] Zadeh LA, “Fuzzy sets”. Information and Control 8, pp 338-353, 1965.
[42] Zimmermann HJ, “Application of fuzzy set theory to mathematical programming.” Information Science 36,pp 29-58, 1985.
[43] T. Bhosale and H. Umap (2023), “Evaluation And Selection Of Supplier In A Healthcare Supply Chain Using TOPSIS”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.46-50.
[44] R. M. Zulqarnain , M. Saeed , N. Ahmad , F. Dayan , B. Ahmad, “Application of TOPSIS Method for Decision Making”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.7, Issue.2, pp.76-81, 2020.
[45] Mohammed Alqatqat , Ma Tie Feng , Chandan Solanki, “ A Fuzzy Topsis Multiple-Attribute Decision Making for Production Electric upon Future Data” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.8, Issue.3, pp.12-23, 2021