In this paper, we have considered an EOQ inventory model with a price-dependent demand and time varying holding cost in fuzzy environments by employing trapezoidal fuzzy numbers. A fully-fuzzy inventory model is developed where the input parameters and decision variables are fuzzified. For this fuzzy model, an expected value method of defuzzification is employed to find the estimate of the profit function in the fuzzy sense. In addition, a rigorous methodology is constructed to examined for the optimal solution of fully-fuzzy inventory model. The optimal policy for the developed model is determined using the proposed algorithm after defuzzification of the profit function. Finally, a numerical example is provided in order to determine the sensitiveness in the decision variables with respect to fuzziness in the components.
KahramanC., GuilbayM., KabakO., Applications of fuzzy sets in industrial Engineering: A topical classification, Springer studfuzz201 (2006), 1–55.
2.
ZimmermannJ.H., Fuzzy set theory and its applications, second edition, Kluwer academic publishers, Boston, Dordrecht, London, 1991.
3.
AlfaresH.K., Inventory model with stock-level dependent demand rate and variable holding cost, International journal of production economics108 (2007), 2007.
4.
FergusonM., JayaramanV., SouzaG.C., Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables, European journal of operational research180 (2007), 2007.
5.
ZadehL., Fuzzy sets, Information and control8 (1965), 338–356.
6.
GhasemiN., Afshar NadjafiB., EOQ models with varying holding cost, Journal of industrial mathematics1 (2013), 1–7.
7.
KumarM., ChauhanA., KumarR., A deterministic inventory model for deteriorating items with price dependent demand and time varying holding cost under trade credit, International journal of soft computing and engineering1 (2013), 2231–2307.
8.
LeeY.P., DyeC.Y., An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate, Computers and industrial engineering63 (2012), 474–482.
9.
MinJ., ZhouY.W., A perishable inventory model under stock-dependent selling rate and shortage-dependent partial backlogging with capacity constraint, International Journal of Systems Science40 (2009), 33–44.
10.
ZhaoM., ZhongB., Inventory model with stock-level dependent demand rate and variable holding cost, Journal of Chongqing institute of technology (Natural Science)10 (2008), 10–23.
11.
ZhengpingD., An inventory coordination scheme of single-period products under price-dependent demand, In international conference on E-Product E-Service and E-Entertainment (ICEEE)1 (2010), 1–4.
12.
MandalS., MaitiM., Multi-item fuzzy EOQ models using genetic algorithm, Computers and industrial engineering44 (2003), 105–117.
13.
VijayanT., KumaranM., Inventory models with a mixture of back orders and lost sales under fuzzy cost, European Journal of operational research189 (2008), 105–119.
14.
KazemiN.,
EhsaniE and JaberY.M., An inventory model with back orders with fuzzy parameters and decision variables, International journal of approximate reasoning51 (2010), 964–972.
15.
MahataC.G., GoswamiA., Fuzzy inventory models for items with imperfect quality and shortage back ordering under crisp and fuzzy decision variables, Computers and industrial engineering64 (2013), 190–199.
16.
MahataG.C., MahataP., Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain, Mathematical and computer modeling53 (2011), 1621–1636.
17.
ChenC.Y., A probabilistic approach for traditional EOQ model, Journal of information optimization sciences24 (2003), 249–253.
18.
San-joseL.A., SiciliaJ., Garcia-LagunaJ., Analysis of an EOQ inventory model with partial back-ordering and non-linear unit holding cost, Omega54 (2015), 147–157.
19.
XuJ., ZhouX., A class of fuzzy expectation multi-objective model with chance constraints based on rough approximation and it’s application in allocation problem, Information sciences, Sichuan university research report180 (2010), 679–696.
20.
AlfaresK.H., GhaithanM.A., Inventory and pricing model with price-dependent demand, time -varying holding cost, and quantity discounts, Computer and industrial engineering94 (2016), 170–177.
21.
VijayanT., KumaranM., Fuzzy economic order time models with random demand, International journal of approximate reasoning50 (2009), 529–540.
22.
ChenH.S., WangC.C., Fuzzy economic production quantity model for items with imperfect quality, International journal of innovative computing3 (2007), 85–95.
23.
ChenH.S., WangC.C., ChangM.S., Optimization of fuzzy production inventory model with repairable defective products under crisp or fuzzy production quantity, International Journal of operations research2 (2005), 31–37.
24.
ChenH.S., ChangM.S., Optimization of fuzzy production inventory model with un-repairable defective products, International journal of production economics113 (2008), 887–894.
25.
BjorkM.K., An analytical solution to a fuzzy economic order quantity problem, International journal of approximate reasoning50 (2009), 485–493.
26.
MondalM., MaitiM.K., MaitiM., A two storage production-repairing model with fuzzy defective rate and displayed inventory dependent demand, Optimization and Engineering15 (2014), 751–772.
27.
RodriguezM.A., CorsanoG., VecchiettiA., MontagnaJ.M., Simultaneous optimization of production planning and inventory management of polyurethane foam plant, Optimization and Engineering19 (2018), 97–123.
28.
AgraA., ChristiansenM., DelgadoA., Discrete time and continuous time formulations for a short sea inventory routing problem, Optimization and Engineering18 (2017), 269–297.
29.
KunduA., GuchhaitP., PramanikP., MaitiM.K., MaitiM., A production inventory model with price discounted fuzzy demand using an interval compared hybrid algorithm, Swarm and Evolutionary computation34 (2017), 1–17.
30.
GaraiT., ChakabortyD., RoyT.K., Expected value of exponential fuzzy number and its application to multi-item deterministic inventory model for deteriorating items, Journal of Uncertainty Analysis and Applications5 (2017), 1–8.
31.
GaraiT., ChakabortyD., RoyT.K., A multi-item inventory model with fuzzy rough coefficients via fuzzy rough expectation, Conference Proceeding Mathematics & Statistics225 (2016), 377–394.
32.
GaraiT., ChakabortyD., RoyT.K., Possibility necessity credibility measures on generalized intuitionistic fuzzy number and its applications to multi-product manufacturing system, Journal of Granular Computing2 (2017), 1–15.
33.
BhuniaA.K., ShaikhA.A., Cardenas-BarronL.E., A partially integrated production-inventory model with interval valued inventory costs, variable demand and flexible reliability, Applied Soft Computing55 (2017), 491–502.
34.
MishraU., Cardenas-BarronL.E., TiwariS., ShaikhA.A., Trevino-GarzaG., An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment, Annals of Operations Research254 (2017), 165–190.
35.
FengL., ChanY.L., Cardenas-BarronL.E., Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date, International Journal of Production Economics185 (2017), 11–20.
36.
GaraiT., ChakabortyD., RoyT.K., A multi-item generalized intuiutionistic fuzzy inventory model with inventory level dependent demand using possibility mean, variance and covariance, Journal of Intelligent & Fuzzy System35 (2018), 1021–1036.
37.
GuoZ., LiuY., Modelling single-period inventory problem by distributionally robust fuzzy, Journal of Intelligent & Fuzzy System35 (2018), 1007–1019.
38.
WangZ., YangL., ZhaoL., CaoN., LuY., A dual-objective vendor-managed inventory model for a single-vendor multi-retailersupply chain with fuzzy random demand, Journal of Intelligent & Fuzzy System35 (2018), 211–222.
39.
GaraiT., ChakabortyD., RoyT.K., A fuzzy rough multi-objective multi-item inventory model with both stock-dependent demand and holding cost rate, Journal of Granular Computing3 (2018), 1–18.
40.
BatenA., andMd., KhalidR., Optimal production cycle time for inventory model with linear time dependent exponential distributed deterioration, Journal of Intelligent & Fuzzy System30 (2016), 1243–1248.
41.
KhalilA.M., HassanN., A note on “possibility multi-fuzzy soft set and its application in decision making”, Journal of Intelligent & Fuzzy System32 (2017), 2309–2314.
42.
Cardenas-BarronL.E., ChungK.J., Trevino-GarzaG., Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris, International, Journal of Production Economics155 (2014), 1–7.
43.
ChungK.J. and Cardenas-BarronL.E., The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management, Applied Mathematical Modelling37 (2013), 4653–4660.
