In this article, an economic order quantity model has been studied in view of joint impacts of the memory and learning due to experiences on the decision-making process where demand is considered as price dependant function. The senses of memory and experience-based learning are accounted by the fractional calculus and dense fuzzy lock set respectively. Here, the physical scenario is mathematically captured and presented in terms of fuzzy fractional differential equation. The α-cut defuzzification technique is used for dealing with the crisp representative of the objective function. The main credit of this article is the introduction of a smart decision-making technique incorporating some advanced components like memory, self-learning and scopes for alternative decisions to be accessed simultaneously. Besides the dynamics of the EOQ model under uncertainty is described in terms of fuzzy fractional differential equation which directs toward a novel approach for dealing with the lot-sizing problem. From the comparison of the numerical results of different scenarios (as particular cases of the proposed model), it is perceived that strong memory and learning experiences with appropriate keys in the hand of the decision maker can boost up the profitability of the retailing process.
Keywords: Riemann–Liouville differentiability, Caputo differentiability, Laplace transformation, EOQ model, selling price, lock fuzzy dense, memory
@article{RO_2021__55_5_2991_0,
author = {Rahaman, Mostafijur and Mondal, Sankar Prasad and Alam, Shariful},
title = {An estimation of effects of memory and learning experience on the {EOQ} model with price dependent demand},
journal = {RAIRO. Operations Research},
pages = {2991--3020},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/ro/2021127},
mrnumber = {4323410},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021127/}
}
TY - JOUR AU - Rahaman, Mostafijur AU - Mondal, Sankar Prasad AU - Alam, Shariful TI - An estimation of effects of memory and learning experience on the EOQ model with price dependent demand JO - RAIRO. Operations Research PY - 2021 SP - 2991 EP - 3020 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021127/ DO - 10.1051/ro/2021127 LA - en ID - RO_2021__55_5_2991_0 ER -
%0 Journal Article %A Rahaman, Mostafijur %A Mondal, Sankar Prasad %A Alam, Shariful %T An estimation of effects of memory and learning experience on the EOQ model with price dependent demand %J RAIRO. Operations Research %D 2021 %P 2991-3020 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021127/ %R 10.1051/ro/2021127 %G en %F RO_2021__55_5_2991_0
Rahaman, Mostafijur; Mondal, Sankar Prasad; Alam, Shariful. An estimation of effects of memory and learning experience on the EOQ model with price dependent demand. RAIRO. Operations Research, Tome 55 (2021) no. 5, pp. 2991-3020. doi: 10.1051/ro/2021127
[1] , and , Fractional derivatives and their applications. Nonlinear Dyn. 38 (2004) 1–489.
[2] , and , On the concept of solutions for fractional differential equations with uncertainty. Non Linear Ann. 72 (2010) 2859–2862. | MR | Zbl | DOI
[3] and , Fuzzy Laplace transforms. Soft Comput. 14 (2010) 235–243. | Zbl | DOI
[4] , , and , A new method for solving fuzzy linear differential equations. Computing 92 (2011) 181–197. | MR | Zbl | DOI
[5] , and , Explicit solutions of fractional differential equations with uncertainty. Soft Comput. 16 (2012) 297–302. | Zbl | DOI
[6] and , Inventory and pricing model with price-dependent demand, time varying holding cost and quantity discounts. Comput. Ind. Eng. 94 (2016) 170–177. | DOI
[7] , and , First order linear fuzzy differential equations under generalized differentiability. Inf. Sci. 177 (2007) 1648–1662. | MR | Zbl | DOI
[8] , A note on “two-point boundary value problems associated with nonlinear fuzzy differential equations’’. Fuzzy Sets Syst. 157 (2006) 986–989. | MR | Zbl | DOI
[9] and , Decision making in a fuzzy environment. Manag. Sci. 17 (1970) 141–164. | MR | Zbl | DOI
[10] , , , and , Sensor-driven learning of time-dependent parameters for prescriptive analytics. IEEE Access 8 (2020) 92383–92392.
[11] and , Fuzzy initial value problem for -th order linear differential equations. Fuzzy Sets Syst. 121 (2001) 247–255. | MR | Zbl | DOI
[12] and , On fuzzy mapping and control. IEEE Trans. Syst. Man Cybern. 2 (1972) 30–34. | MR | Zbl | DOI
[13] , and , Backorder fuzzy inventory model under function principle. Inf. Sci. 95 (1996) 71–79. | DOI
[14] , and , Initial-valued first order fuzzy differential equation in bi-level inventory model with fuzzy demand. Math. Model. Anal. 13 (2008) 493–512. | MR | Zbl | DOI
[15] , Triangular dense fuzzy lock sets. Soft Comput. 22 (2017) 7243–7254.
[16] and , Triangular dense fuzzy sets and new defuzzification methods. J. Intell. Fuzzy Syst. 31 (2016) 469–477. | DOI
[17] , , and , An integrated inventory model involving discrete setup cost reduction, variable safety factor, selling price dependent demand and investment. RAIRO:OR 53 (2019) 39–57. | MR | DOI
[18] , and , Fractional Calculus: Models and Numerical Methods, World Scientific (2012). | Zbl
[19] , Inventory replenishment policy for a linear trend in demand – an analytic solution. Oper. Res. Quar. 28 (1977) 663–670. | Zbl | DOI
[20] , and , Pricing and lot-sizing policies for perishable goods when the demand depends on selling price, displayed stocks and expiration date. Int. J. Prod. Econ. 185 (2017) 11–20. | DOI
[21] , , and , An inventory model for deteriorating items with stock dependent demand rate. Eur. J. Oper. Res. 95 (1996) 604–610. | Zbl | DOI
[22] , and , A production inventory model with fuzzy production and demand using fuzzy differential equation: an interval compared genetic algorithm approach. Eng. Appl. Artif. Intell. 26 (2013) 766–778. | DOI
[23] , and , Inventory model of a deteriorating item with price and credit linked fuzzy demand: a Fuzzy differential equation approach. OPSEARCH 51 (2014) 321–353. | MR | DOI
[24] and , Analysis of Inventory Systems. Prentice-Hall, Englewood Cliffs, NJ (1963). | Zbl
[25] , How many parts to make at once. Factory Mag. Manag. 10 (1913) 135–136.
[26] , Optimal lot-size and price of perishable goods: a novel game-theoretic model using double interval grey numbers. Comput. Ind. Eng. 149 (2020) 106780. | DOI
[27] , , , and , Coordination and competition in two-echelon supply chain using grey revenue-sharing contracts. Grey Syst.: Theory App. (2020). DOI: . | DOI
[28] , and , A note on initial value problems for fractional fuzzy differential equations. Fuzzy Sets Syst. 347 (2018) 54–69. | MR | DOI
[29] , Bridging the gap between probabilistic and fuzzy-parameter EOQ models. Int. J. Prod. Econ. 91 (2004) 215–221. | DOI
[30] , Fuzzy differential equations. Fuzzy set Syst. 24 (1987) 301–317. | MR | Zbl | DOI
[31] , and , A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate. J. Clean. Prod. 154 (2017) 139–150. | DOI
[32] , and , A pollution sensitive remanufacturing model with waste items: triangular dense fuzzy lock set approach. J. Clean. Prod. 187 (2018) 789–803. | DOI
[33] , and , Incorporating human learning into afuzzy EOQ inventory model with backorders. Comput. Ind. Eng. 87 (2015) 540–542. | DOI
[34] , , and , Inventory system with expiration date: pricing and replenishment decisions. Comput. Ind. Eng. 132 (2019) 232–247. | DOI
[35] , , , and , Inventory models for perishable items with advanced payment, linearly time-dependent holding cost and demand dependent on advertisement and selling price. Int. J. Prod. Econ. 230 (2020) 107804. | DOI
[36] , , and , Optimal lot-size decision for deteriorating items with price-sensitive demand, linearly timedependent holding cost under all-units discount environment. Int. J. Syst. Sci.: Oper. Logist. (2020) 1–14. DOI: . | DOI
[37] , and , A optimal policy to increase supplier’s profit wit price dependent demand functions. Prod. Plan. Control 6 (1995) 45–50. | DOI
[38] , , and , A solution algorithm for integrated production-inventory-routing of perishable goods with transshipment and uncertain demand. Complex Intell. Syst. 7 (2021) 1349–1365. | DOI
[39] , , and , Application of Generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment. Oper. Res. Perspect. 3 (2016) 77–91. | MR
[40] , , and , A non instantaneous inventory model having different deterioration rates with stock and price dependent demand under partial backlogged shortage. Uncertain Supply Chain Manag. 6 (2018) 49–64. | DOI
[41] and , An Introduction to the Fractional Calculus and Differential Equations. John Wiley, New York (1993). | MR | Zbl
[42] , , , and , An inventory model under price and stock dependent demand for controllable deterioration rate with shortage and preservation technology investment. Ann. Oper. Res. 254 (2017) 165–190. | MR | DOI
[43] and , First order linear homogeneous fuzzy ordinary differential equation based on the Lagrange multiplier method. J. Soft Comput. Appl. 2013 (2013) 1–17.
[44] , and , A production-recycling model with variable demand, demand dependent fuzzy return rate: a fuzzy differential approach. Comput. Ind. Eng. 64 (2013) 318–332. | DOI
[45] , and , Joint pricing and ordering policy for a deteriorating inventory. Comput. Ind. Eng. 47 (2004) 339–349. | DOI
[46] , Inventory Systems. John Wiley, New York (1966).
[47] , and , Two echelon manufactures retailer supply chain strategies with price, quality and promotional effort sensitive demand. Int. Trans. Oper. Res. 22 (2015) 1071–1095. | MR | DOI
[48] , and , Application of memory effects in an inventory model with price dependent demand rate during shortage. Int. J. Edu. Manag. Eng. 3 (2019) 51–64.
[49] , Fuzzy-set theoretic interpretation of economic order quantity. IEEE Trans. Syst. Man Cybern. 17 (1987) 1082–1084. | DOI
[50] , Fractional Differential Equations. Academic Press, San Diego, CA (1999). | MR | Zbl
[51] and , Operational procurement policies under price dependent demand. Int. J. Prod. Eng. 65 (2000) 141–171. | DOI
[52] , , , , and , Arbitrary-order economic production quantity model with and without deterioration: generalized point of view. Adv. Differ. Equ. 2020 (2020). DOI: . | DOI | MR | Zbl
[53] , , , , , , and , Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model. Soft Comput. 24 (2020) 15341–15359. | Zbl | DOI
[54] , , , and , Interpretation of exact solution for fuzzy fractional non-homogeneous differential equation under the Riemann-Liouville sense and its application on the inventory management control problem. Granul. Comput. 6 (2021) 953–976. | DOI
[55] , , and , Synergetic study of inventory management problem in uncertain environment based on memory and learning effects. Sādhanā 46 (2021) 1–20. | MR | DOI
[56] , , and , Existence and uniqueness results for fractional differential equations with uncertainty. Adv. Diff. Equ. 2012 (2012). DOI: . | DOI | MR | Zbl
[57] , and , Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 1372–1381. | MR | Zbl | DOI
[58] , Price sensitive demand and random sales price – a news boy problem. Int. J. Syst. Sci. 43 (2012) 491–498. | MR | Zbl | DOI
[59] , , and , An economic order quantity modelconsidering different holding costs forimperfect quality items subject to fuzziness and learning. J. Intell. Fuzzy Syst. 30 (2016) 2985–2997. | Zbl | DOI
[60] , , and , Fuzzy inventory models: a comprehensive review. Appl. Soft Comput. 55 (2017) 588–621. | DOI
[61] and , A heuristic for selecting lot size quantities for the case of a deterministic time varying demand rate and discrete opportunities for replenishment. Prod. Inven. Manag. 14 (1973) 64–74.
[62] , and , Inventory formula when inventory cost is fuzzy. Int. J. Prod. Econ. 45 (1996) 499–504. | DOI
[63] , Fuzzy sets. Inf. Control 8 (1965) 338–356. | MR | Zbl | DOI
Cité par Sources :
