Document Type : Review Paper
Department of Mathematics, General Degree College at Gopiballavpur-II, Jhargram, West Bengal, India.
In this article, we have developed a deteriorated multi-item inventory model in a fuzzy environment. Here the demand rate is constant. Production cost and set-up cost are the most vital issue in the inventory system of the market world. Here production cost and set-up- cost are continuous functions of demand. Set-up-cost is also dependent on average inventory level. Deterioration cost is the most challenging issue in the business world. So here deterioration cost is dependent on inventory level and demand. Lead time crashing cost is considered the continuous function of leading time. In the real world all cost are not fixed. Due to uncertainty all cost parameters of the proposed model are taken as Generalized Triangular Fuzzy Number (GTFN). The formulated multi objective inventory problem has been solved by various techniques like as Geometric Programming (GP) technique, Fuzzy Programming Technique with Hyperbolic Membership Function (FPTHMF), Fuzzy Non-Linear Programming (FNLP) technique. Numerical example is taken to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.
- Abou-El-Ata, M. O., & Kotb, K. A. M. (1997). Multi-item EOQ inventory model with varying holding cost under two restrictions: a geometric programming approach. Production planning & control, 8(6), 608-611. https://doi.org/10.1080/095372897234948
- Aggarwal, S. P. (1978). A note on an order-level inventory model for a system with constant rate of deterioration. Opsearch, 15(4), 184-187.
- Bit, A. K. (2004). Fuzzy programming with hyperbolic membership functions for multiobjective capacitated transportation problem. Opsearch, 41(2), 106-120. https://doi.org/10.1007/BF03398837
- Ben-Daya, M. A., & Raouf, A. (1994). Inventory models involving lead time as a decision variable. Journal of the operational research society, 45(5), 579-582. https://doi.org/10.1057/jors.1994.85
- Beightler, C. S., & Phillips, D. T. (1976). Applied geometric programming. John Wiley & Sons.
- Biswal, M. P. (1992). Fuzzy programming technique to solve multi-objective geometric programming problems. Fuzzy sets and systems, 51(1), 67-71. https://doi.org/10.1016/0165-0114(92)90076-G
- Chakraborty, D., Jana, D. K., & Roy, T. K. (2018). Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments. Computers & industrial engineering, 123, 157-179. https://doi.org/10.1016/j.cie.2018.06.022
- Chen, C. K. (2000). Optimal determination of quality level, selling quantity and purchasing price for intermediate firms. Production planning & control, 11(7), 706-712. https://doi.org/10.1080/095372800432179
- Chuang, B. R., Ouyang, L. Y., & Chuang, K. W. (2004). A note on periodic review inventory model with controllable setup cost and lead time. Computers & operations research, 31(4), 549-561. https://doi.org/10.1016/S0305-0548(03)00013-3
- Dave, U., & Patel, L. K. (1981). (T, S i) policy inventory model for deteriorating items with time proportional demand. Journal of the operational research society, 32(2), 137-142. https://doi.org/10.1057/jors.1981.27
- Dave, U. (1986). An order-level inventory model for deteriorating items with variable instantaneous demand and discrete opportunities for replenishment. Opsearch, 23(1), 244-249.
- Duffin, R. J., Peterson, E. L., & Zener, C. (1967). Geometric programming: theory and application. John Wiley and Sons.
- Das, S. K., & Islam, S. (2018). Two warehouse inventory model for deteriorating items and stock dependent demand under conditionally permissible delay in payment. International journal of research on social and natural sciences, 3(1), 1-12.
- Das, K., Roy, T. K., & Maiti, M. (2000). Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: a geometric programming approach. Production planning & control, 11(8), 781-788. https://doi.org/10.1080/095372800750038382
- Das, S. K., & Islam, S. (2019). Multi-objective two echelon supply chain inventory model with lot size and customer demand dependent purchase cost and production rate dependent production cost. Pakistan journal of statistics and operation research, 15(4), 831-847. https://doi.org/10.18187/pjsor.v15i4.2929
- Chare, P., & Schrader, G. (1963). A model for exponentially decaying inventories. Journal of industrial engineering, 15, 238-243.
- Goyal, S. K., & Giri, B. C. (2001). Recent trends in modeling of deteriorating inventory. European journal of operational research, 134(1), 1-16. https://doi.org/10.1016/S0377-2217(00)00248-4
- Hariga, M., & Ben-Daya, M. (1999). Some stochastic inventory models with deterministic variable lead time. European journal of operational research, 113(1), 42-51. https://doi.org/10.1016/S0377-2217(97)00441-4
- Harri, F. (1913). How many parts to make at once factory. Mannage, 10, 135-136.
- Islam, S. (2010), Multi-objective geometric-programming problem and its application. Yugoslav journal of operations research, 20(2), 213-227. DOI: 2298/YJOR1002213I
- Islam, S. (2008). Multi-objective marketing planning inventory model: a geometric programming approach. Applied mathematics and computation, 205(1), 238-246. https://doi.org/10.1016/j.amc.2008.07.037
- Kotb, K. A., & Fergany, H. A. (2011). Multi-item EOQ model with both demand-dependent unit cost and varying leading time via geometric programming. Applied mathematics, 2(5), 551-555. DOI:4236/am.2011.25072
- Maiti, M. K. (2008). Fuzzy inventory model with two warehouses under possibility measure on fuzzy goal. European journal of operational research, 188(3), 746-774. https://doi.org/10.1016/j.ejor.2007.04.046
- Ouyang, L. Y., Yeh, N. C., & Wu, K. S. (1996). Mixture inventory model with backorders and lost sales for variable lead time. Journal of the operational research society, 47(6), 829-832. https://doi.org/10.1057/jors.1996.102
- Ouyang LY and Wu KS (1998). A min-max distribution free procedure for mixed inventory model with variable lead time. International journal of production economics, 56-57, 511-516. https://doi.org/10.1016/S0925-5273(97)00068-6
- Panda, G. C., Khan, M., & Shaikh, A. A. (2019). 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, 15(1), 147-170. https://doi.org/10.1007/s40092-018-0269-3
- Mandal, N. K., Roy, T. K., & Maiti, M. (2005). Multi-objective fuzzy inventory model with three constraints: a geometric programming approach. Fuzzy sets and systems, 150(1), 87-106. https://doi.org/10.1016/j.fss.2004.07.020
- Mandal, N. K., Roy, T. K., & Maiti, M. (2006). Inventory model of deteriorated items with a constraint: a geometric programming approach. European journal of operational research, 173(1), 199-210. https://doi.org/10.1016/j.ejor.2004.12.002
- Sarkar, B., Gupta, H., Chaudhuri, K., & Goyal, S. K. (2014). An integrated inventory model with variable lead time, defective units and delay in payments. Applied mathematics and computation, 237, 650-658. https://doi.org/10.1016/j.amc.2014.03.061
- Sarkar, B., Mandal, B., & Sarkar, S. (2015). Quality improvement and backorder price discount under controllable lead time in an inventory model. Journal of manufacturing systems, 35, 26-36. https://doi.org/10.1016/j.jmsy.2014.11.012
- Shaikh, A. A., Bhunia, A. K., Cárdenas-Barrón, L. E., Sahoo, L., & Tiwari, S. (2018). A fuzzy inventory model for a deteriorating item with variable demand, permissible delay in payments and partial backlogging with shortage follows inventory (SFI) policy. International journal of fuzzy systems, 20(5), 1606-1623. https://doi.org/10.1007/s40815-018-0466-7
- Tripathi, R. P., Pareek, S., & Kaur, M. (2017). Inventory model with exponential time-dependent demand rate, variable deterioration, shortages and production cost. International journal of applied and computational mathematics, 3(2), 1407-1419. https://doi.org/10.1007/s40819-016-0185-4
- Wee, H. M., Lo, C. C., & Hsu, P. H. (2009). A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment. European journal of operational research, 197(2), 620-631. https://doi.org/10.1016/j.ejor.2006.08.067
- Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
- Zimmermann, H. J. (1985). Applications of fuzzy set theory to mathematical programming. Information sciences, 36(1-2), 29-58. https://doi.org/10.1016/0020-0255(85)90025-8
- Saha, S., & Sen, N. (2017). A study on inventory model with negative exponential demand and probabilistic deterioration under backlogging. Uncertain supply chain management, 5(2), 77-88. DOI: 5267/j.uscm.2016.10.006
- Das, S. K. (2020). 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), 227-243. DOI: 22105/jfea.2020.254081.1025
- Bortlan, G., & Degani, R. (1985). A review of some methods for ranking fuzzy numbers. Fuzzy sets and systems, 15(1), 1-19. https://doi.org/10.1016/0165-0114(85)90012-0
- Barman, A., Das, R., & De, P. K. (2020). An analysis of retailer’s inventory in a two-echelon centralized supply chain co-ordination under price-sensitive demand. SN applied sciences, 2(12), 1-15. https://doi.org/10.1007/s42452-020-03966-7