Optimum pricing decision for the retailer with warranty and price-dependent variable demand

Open Access

Issue		RAIRO-Oper. Res. Volume 59, Number 3, May-June 2025


Page(s)		1419 - 1442
DOI		https://doi.org/10.1051/ro/2024219
Published online		14 May 2025

S.S. Ali, H. Barman, R. Kaur, H. Tomaskova and S.K. Roy, Multi-product multi echelon measurements of perishable supply chain: fuzzy non-linear programming approach. Mathematics 9 (2023) 2093. [Google Scholar]
M. Almasi, S. Khoshefetrat and M.R. Galankashi, Sustainable supplier selection and order allocation under risk and inflation condition. IEEE Trans. Eng. Manage. 68 (2021) 823–837. [CrossRef] [Google Scholar]
R. Amudha and E. Chandrasekaran, An EOQ model for deteriorating with quadratic demand and time-dependent holding cost. Int. J. Emer. Sci. Eng. 1 (2013) 5–6. [Google Scholar]
D.P. Andriani and F.S. Tseng, Coordinating a dual-channel supply chain with pricing and extended warranty strategies under demand substitution effects. East.-Eur. J. Enterp. Technol. 3 (2023) 45–56. [Google Scholar]
H. Barman, M. Pervin and S.K. Roy, Impacts of green and preservation technology investments on a sustainable EPQ model during COVID-19 pandemic. RAIRO-Oper. Res. 56 (2022) 2245–2275. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
H. Barman, M. Pervin, S.K. Roy and G.W. Weber, Analysis of a dual-channel green supply chain game-theoretical model under carbon policy. Int. J. Syst. Sci. Oper. Logist. 10 (2023a) 2242770. [Google Scholar]
H. Barman, S.K. Roy, L. Sakalauskas and G.W. Weber, Inventory model involving reworking of faulty products with three carbon policies under neutrosophic environment. Adv. Eng. Inf. 57 (2023b) 102081. [CrossRef] [Google Scholar]
L.E. Cárdenas-Barrón, A.A. Shaikh, S. Tiwari and G. Trevi˜no-Garza, An EOQ inventory model with non-linear stock-dependent holding cost, non-linear stock-dependent demand, and trade credit. Comp. Ind. Eng. 139 (2020) 105557. [CrossRef] [Google Scholar]
L.E. Cárdenas-Barrón, O.A. Marquez-Rios, I. Sanchez-Romero and B. Mandal, Optimizing price, lot size, and back ordering level for products with imperfect quality, different holding costs, and non-linear demand. Rev. de la Real Acad. de Ciencias Exactas Físicas y Nat. Ser. A Math. 116 (2022) 1–21. [CrossRef] [Google Scholar]
U.B. Chaudhari, N.H. Shah and M.Y. Jani, Inventory modelling of deteriorating item and preservation technology with advance payment scheme under quadratic demand. Opt. Inv. Manage. 3 (2020) 69–79. [Google Scholar]
M. Choudhury, C. Mahato and G.C. Mahata, An integrated inventory model with capacity constraint under ordersize dependent trade credit, all-unit discount and partial backordering. RAIRO-Oper. Res. 56 (2022) 1593–1622. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
C.J. Chung, G.A. Widyadana and H. Ming Wee, Economic production quantity model for deteriorating inventory with random machine unavailability and shortage. Int. J. Prod. Res. 49 (2011) 883–902. [CrossRef] [Google Scholar]
K.-J. Chung, J.-J. Liao, P.-S. Ting, S.-D. Lin and H.M. Srivastava, A unified presentation of inventory models under quantity discounts, trade credits, and cash discounts in the supply chain management. Rev. de la Real Acad. de Ciencias Exactas Físicas y Nat. Ser. A Math. 112 (2018) 509–538. [CrossRef] [Google Scholar]
S. Das, A.K. Manna, E.E. Mahmoud, K.M. Abualnaja, A.H. Abdel-Aty and A.A. Shaikh, Product replacement policy in a production inventory model with replacement period, stock, and price-dependent demand. J. Math. 2020 (2020) 6697279. [Google Scholar]
S. Das, M. Al-Amin Khan, E.E. Mahmoud, A.H. Abdel-Aty, K.M. Abualnaja and A.A. Shaikh, A production inventory model with partial trade credit policy and reliability. Alex. Eng. J. 60 (2021) 1325–1338. [CrossRef] [Google Scholar]
B. Sarkar, S. Sao, and S.K. Ghosh, Smart production and photocatalytic ultraviolet (PUV) wastewater treatment effect on a textile supply chain management. International J. Prod. Econ. 283 (2025) 109557. [CrossRef] [Google Scholar]
S. Kumar, M. Sigroha, N. Kumar, M. Kumari, and B. Sarkar, How does the retail price maintain trade-credit management with continuous investment to support the cash flow? J. Retail. Consum. Serv. 83 (2025) 104116. [CrossRef] [Google Scholar]
B.K. Dey, S. Pareek, M. Tayyab and B. Sarkar, Autonomation policy to control work-in-process inventory in a smart production system. Int. J. Prod. Res. 59 (2021) 1258–1280. [Google Scholar]
C.Y. Dye and T.P. Hsieh, An optimal replenishment policy for deteriorating items with effective investment in preservation technology. Eur. J. Oper. Res. 218 (2012) 106–112. [Google Scholar]
A. Garai and B. Sarkar, Economically independent reverse logistics of customer-centric closed-loop supply chain for herbal medicines and biofuel. J. Clean. Prod. 334 (2022) 129977. [CrossRef] [Google Scholar]
M.S. Habib, O. Asghar, A. Hussain, M. Imran, M.P. Mughal and B. Sarkar, A robust possibilistic programming approach toward animal fat-based biodiesel supply chain network design under uncertain environment. J. Clean. Prod. 278 (2021) 122403. [CrossRef] [Google Scholar]
M.S. Habib, M. Omair, M.B. Ramzan, T.N. Chaudhry, M. Farooq and B. Sarkar, A robust possibilistic flexible programming approach toward a resilient and cost-efficient biodiesel supply chain network. J. Clean. Prod. 366 (2022) 132752. [CrossRef] [Google Scholar]
M.A. Halim, A. Paul, M. Mahmoud, B. Alshahrani, A.Y. Alazzawi and G.M. Ismail, An overtime production inventory model for deteriorating items with nonlinear price and stock-dependent demand. Alex. Eng. J. 60 (2021) 2779–2786. [CrossRef] [Google Scholar]
K.L. Hou, H.M. Srivastava, L.C. Lin and S.H. Lee, The impact of system deterioration and product warranty on optimal lot-sizing with maintenance and shortages backordered. Rev. de la Real Acad. de Ciencias Exactas Físicas y Nat. Ser. A Math. 115 (2021) 103. [CrossRef] [Google Scholar]
C.K. Jaggi, A. Sharma and S. Tiwari, Credit financing in economic ordering policies for non-instantaneous deteriorating items with price-dependent demand under permissible delay in payments: a new approach. Int. J. Indus. Eng. Com. 6 (2015) 481–502. [Google Scholar]
S. Jain, S. Tiwari, L.E. Cárdenas-Barrón, A.A. Shaikh and S.R. Singh, 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. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
M.Y. Jani, N.H. Shah and U.B. Chaudhari, Inventory control policies for time-dependent deteriorating item with variable demand and two-level order linked trade credit. Opt. Inv. Manage. (2020) 55–67. [Google Scholar]
M.Y. Jani, M.R. Betheja, U. Chaudhari and B. Sarkar, Optimal investment in preservation technology for variable demand under trade-credit and shortages. Mathematics 9 (2021) 1301. [CrossRef] [Google Scholar]
B. Sarkar, B. Mridha, and S. Pareek, A sustainable smart multi-type biofuel manufacturing with the optimum energy utilization under flexible production. J. Clean. Prod. (2022) 129869. [CrossRef] [Google Scholar]
N. Jiang, L.L. Zhang and Y. Yu, Optimizing cooperative advertising, profit sharing, and inventory policies in a VMI supply chain: a Nash bargaining model and hybrid algorithm. IEEE Trans. Eng. Manage. 62 (2015) 449–461. [CrossRef] [Google Scholar]
S. Khalilpourazari and S.H.R. Pasandideh, Bi-objective optimization of multi-product EPQ model with backorders, rework process and random defective rate, in 2016 12th International Conference on Industrial Engineering (ICIE). IEEE (2016) 36–40. [Google Scholar]
S. Kumar, S.R. Singh and R.K. Sharma, Inventory models for non-instantaneous deterioration items with stock dependent demand under trade credit policy with inflation. Int. J. Eng. Sci. 11 (2022) 62–71. [Google Scholar]
S. Kumar, S.R. Singh, S. Agarwal and D. Yadav, Joint effect of selling price and promotional efforts on retailer’s inventory control policy with trade credit, time-dependent holding cost, and partial backlogging under inflation. RAIRO-Oper. Res. 57 (2023) 1491–1522. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
L. Lalremruati and A. Khanna, Analysing a lean manufacturing inventory system with price-sensitive demand and carbon control policies. RAIRO-Oper. Res. 57 (2023) 1797–1820. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
J.-J. Liao, K.-N. Huang, K.-J. Chung, S.-D. Lin, S.-T. Chuang and H.M. Srivastava, Optimal ordering policy in an economic order quantity (EOQ) model for non-instantaneous deteriorating items with defective quality and permissible delay in payments. Rev. de la Real Acad. de Ciencias Exactas Físicas y Nat. Ser. A Math. 114 (2020) 1–26. [CrossRef] [Google Scholar]
R.K. Mallick, K. Patra and S.K. Mondal, A new economic order quantity model for deteriorated items under the joint effects of stock dependent demand and inflation. Decis. Anal. 8 (2023) 100288. [Google Scholar]
A.K. Manna, J.K. Dey and S.K. Mondal, Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate. RAIRO-Oper. Res. 54 (2020) 1189–1213. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
J. Min, Y.W. Zhou, G.Q. Liu and S.D. Wang, An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments. Int. J. Sys. Sci. 43 (2012) 1039–1053. [CrossRef] [MathSciNet] [Google Scholar]
A.F. Momena, R. Haque, M. Rahaman and S.P. Mondal, A two-storage inventory model with trade credit policy and time-varying holding cost under quantity discounts. Logistics 7 (2023) 77. [CrossRef] [Google Scholar]
S.K. Mondal and B. Khara, Imperfect production inventory system considering effects of production reliability, in Fuzzy Optimization, Decision-making and Operations Research, edited by C. Jana, M. Pal, G. Muhiuddin and P. Liu. Springer, Cham (2023). DOI: 10.1007/978-3-031-35668-126. [Google Scholar]
A. Mondal and S.K. Roy, Multi-objective sustainable opened-and closed-loop supply chain under mixed uncertainty during COVID-19 pandemic situation. Comput. Ind. Eng. 159 (2021) 107453. [CrossRef] [Google Scholar]
A. Mondal, B.K. Giri, S.K. Roy, M. Deveci and D. Pamucar, Sustainable-resilient-responsive supply chain with demand prediction: an interval type-2 robust programming approach. Eng. Appl. Artif. Intell. 133 (2024) 108133. [CrossRef] [Google Scholar]
A. Paul, M. Pervin, S.K. Roy, G.W. Weber and A. Mirzazadeh, Effect of price-sensitive demand and default risk on optimal credit period and cycle time for a deteriorating inventory model. RAIRO-Oper. Res. 55 (2021) S2575–S2592. [CrossRef] [EDP Sciences] [Google Scholar]
M. Pervin, S.K. Roy and G.W. Weber, Deteriorating inventory with preservation technology under price and stock-sensitive demand. Am. Inst. Math. Sci. 16 (2020) 1582–1612. [Google Scholar]
Priyamvada, P. Gautam, A. Khanna and C.K. Jaggi, Preservation technology investment for an inventory system with variable deterioration rates under expiration dates and price-sensitive demand. Yugo. J. Oper. Res. 30 (2020) 289–305. [CrossRef] [MathSciNet] [Google Scholar]
C. Rout, D. Chakraborty and A. Goswami, A production inventory model for deteriorating items with backlog-dependent demand. RAIRO Oper. Res. 55 (2021) 549–570. [Google Scholar]
M. Saha and R.N. Giri, Consumers’ purchasing decisions of a dual-channel supply chain system under return and warranty policies. Int. J. Syst. Sci. Oper. Logist. 10 (2023) 2173990. [Google Scholar]
B. Samanta and B.C. Giri, A two-echelon supply chain model with price and warranty dependent demand and pro-rata warranty policy under cost-sharing contract. Decis. Making: Appl. Manage. Eng. 4 (2021) 47–75. [Google Scholar]
A. Datta, B.K. Dey, S. Bhuniya, I. Sangal, B. Mandal, M. Sarkar, R. Guchhait, B. Sarkar and B. Ganguly, Adaptation of e-commerce retailing to enhance customer satisfaction within a dynamical system under transfer of risk. J. Retail. Consum. Serv. 84 (2025) 104129. [CrossRef] [Google Scholar]
A. Sarkar, R. Guchhait, and B. Sarkar, Application of the artificial neural network with multithreading within an inventory model under uncertainty and inflation. Int. J. Fuzzy Syst. 24 (2022) 2318–2332. [CrossRef] [Google Scholar]
R. Guchhait and B. Sarkar, Economic evaluation of an outsourced fourth-party logistics (4PL) under a flexible production system. Int. J. Prod. Econ. 279 (2025) 109440. [CrossRef] [Google Scholar]
M. Sarkar and B. Sarkar, How does an industry reduce waste and consumed energy within a multi-stage smart sustainable biofuel production system? J. Clean. Prod. 262 (2020) 121200. [CrossRef] [Google Scholar]
B. Sarkar, M. Omair and N. Kim, A cooperative advertising collaboration policy in supply chain management under uncertain conditions. Appl. Soft Comput. 88 (2020) 105948. [CrossRef] [Google Scholar]
B. Sarkar, A. Debnath, A.S. Chiu and W. Ahmed, Circular economy-driven two-stage supply chain management for nullifying waste. J. Clean. Prod. 339 (2022) 130513. [CrossRef] [Google Scholar]
B. Sarkar, and S. Bhuniya, A sustainable flexible manufacturing-remanufacturing model with improved service and green investment under variable demand. Expert Syst. Appl. 202 (2022) 117154. [CrossRef] [Google Scholar]
W. Ahmed, M. Moazzam, B. Sarkar, and S.U. Rehman, Synergic effect of reworking for imperfect quality items with the integration of multi-period delay-in-payment and partial backordering in global supply chains. Engineering 7, (2021) 260–271. [CrossRef] [MathSciNet] [Google Scholar]
T. Sekar, R. Uthayakumar and P. Mythuradevi, A limited capacity storehouse inventory model for deteriorating items with preservation technology investment and partial backlogging under inflation. Comm. Appl. Anal. 21 (2017) 377–404. [Google Scholar]
M. Tayyab, J. Jemai, H. Lim, and B. Sarkar, A sustainable development framework for a cleaner multi-item multi-stage textile production system with a process improvement initiative. J. Clean. Prod. 246 (2020) 119055. [CrossRef] [Google Scholar]
N.H. Shah, Manufacturer–retailer inventory model for deteriorating items with price-sensitive credit-linked demand under two-level trade credit financing and profit-sharing contract. Cog. Eng. 2 (2015) 1012989. [CrossRef] [Google Scholar]
N.H. Shah and M.Y. Jani, Optimal ordering for deteriorating items of fixed-life with quadratic demand and two-level trade credit. Opt. Inv. Cont. Manage. Tech. (2016) 1–66. DOI: 10.4018/978-1-4666-9888-8.ch001. [Google Scholar]
N.H. Shah, U. Chaudhari and M.Y. Jani, An integrated production-inventory model with preservation technology investment for the time-varying deteriorating item under time and price-sensitive demand. Int. J. Invent. Res. 3 (2016) 81–98. [CrossRef] [Google Scholar]
N.H. Shah, U. Chaudhari and M.Y. Jani, An inventory model with an expiration date of items and deterioration under two-level trade credit and preservation technology investment for time and price-sensitive demand: DCF approach. Int. J. Logist. Syst. Manage. 27 (2017a) 420–437. [Google Scholar]
N.H. Shah, U.B. Chaudhari and M.Y. Jani, Optimal policies for a time-varying deteriorating item with preservation technology under selling price and trade credit-dependent quadratic demand in a supply chain. Int. J. Appl. Com. Math. 3 (2017b) 363–379. [CrossRef] [Google Scholar]
N.H. Shah, U. Chaudhari and L.E. Cárdenas-Barrón, Integrating credit and replenishment policies for deteriorating items under quadratic demand in a three-echelon supply chain. Int. J. Syst. Sci. Oper. Logist. 7 (2018a) 34–45. [Google Scholar]
N.H. Shah, M.Y. Jani and U. Chaudhari, Optimal replenishment time for a retailer under partial upstream prepayment and partial downstream overdue payment for quadratic demand. Math. Comput. Model. Dyn. Syst. 24 (2018b) 1–11. [CrossRef] [MathSciNet] [Google Scholar]
N.H. Shah, P.H. Shah and M.B. Patel, Retailer’s inventory decisions with exchange scheme under the effect of advertisement efforts. J. Ind. Prod. Eng. 39 (2022) 158–165. [Google Scholar]
S. Shee and T. Chakrabarti, An EPQ model for imperfect production system with deteriorating items, price-dependent demand, rework and lead time under markdown policy, in Data Analytics and Artificial Intelligence for Inventory and Supply Chain Management. Inventory Optimization, edited by D.K. Sharma and M. Jain. Springer, Singapore (2022). DOI: 10.1007/978-981-19-6337-75. [Google Scholar]
C. Singh and G.R. Ambedkar, Optimizing EOQ model for expiring items with stock, selling cost and lifetime dependent demand under inflation. OPSEARCH 60 (2023) 174–187. [CrossRef] [MathSciNet] [Google Scholar]
H.N. Soni, Optimal replenishment policies for non-instantaneous deterioration items with price and stock sensitive demand under permissible delay in payment. Int. J. Prod. Econ. 146 (2013) 259–268. [CrossRef] [Google Scholar]
H.M. Srivastava, K.-J. Chung, J.-J. Liao, S.-D. Lin and S.-F. Lee, An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits. Rev. de la Real Acad. de Ciencias Exactas Físicas y Nat. Ser. A Math. 115 (2021) 1–22. [CrossRef] [Google Scholar]
H.M. Srivastava, J.J. Liao, K.N. Huang, K.J. Chung, S.D. Lin and S.F. Lee, Supply chain inventory model for deteriorating products with maximum lifetime under trade-credit financing. TWMS J. Pure Appl. Math. 13 (2022) 53–71. [MathSciNet] [Google Scholar]
C. Stahl, N. Stein and C.M. Flath, Analytics applications in fashion supply chain management – a review of literature and practice. IEEE Trans. Eng. Manage. 70 (2021) 1258–1282. [Google Scholar]
A.A. Taleizadeh, H.M. Wee and S.G. Jalali-Naini, Economic production quantity model with repair failure and limited capacity. Appl. Math. Model. 37 (2013) 2765–2774. [Google Scholar]
A.A. Taleizadeh, M.S. Naghavi-Alhoseiny, L.E. Cardenas-Barron and A. Amjadian, Optimization of price, lot size and backordered level in an EPQ inventory model with rework process. RAIRO-Oper. Res. 58 (2024) 803–819. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
M. Tayyab and B. Sarkar, An interactive fuzzy programming approach for a sustainable supplier selection under textile supply chain management. Comput. Ind. Eng. 155 (2021) 107164. [CrossRef] [Google Scholar]
J.T. Teng and C.T. Chang, Economic production quantity models for deteriorating items with the price and stock-dependent demand. Comput. Oper. Res. 32 (2005) 297–308. [CrossRef] [MathSciNet] [Google Scholar]
R. Udayakumar, K.V. Geetha and S.S. Sana, Economic ordering policy for non-instantaneous deteriorating items with price and advertisement dependent demand and permissible delay in payment under inflation. Math. Methods Appl. Sci. 44 (2021) 7697–7721. [CrossRef] [MathSciNet] [Google Scholar]
B. Sarkar, A.S.H. Kugele and M. Sarkar, Two non-linear programming models for the multi-stage multi-cycle smart production system with autonomation and remanufacturing in same and different cycles to reduce wastes. J. Indust. Inform. Integ. 44 (2025) 100749. [Google Scholar]
M. Valliathal and R. Uthayakumar, Fuzzy economic production quantity model for Weibull deteriorating items with ramp type of demand. Int. J. Strat. Decis. Sci. 2 (2013) 55–90. [Google Scholar]
A.S. Mahapatra, S. Sengupta, A. Dasgupta, B. Sarkar and R.T. Goswami, What is the impact of demand patterns on integrated online-offline and buy-online-pickup in-store (BOPS) retail in a smart supply chain management? J. Retail. Consum. Serv. 82 (2025) 104093. [CrossRef] [Google Scholar]
R. Yadav, A.K. Sharma and P.T. Singh, A Production inventory model for fractionally time-dependent demand rate with weibull deterioration and partially backlogged items. Asian Res. J. Math. 20 (2024) 102–118. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.