A game theoretical study on lead time, pricing and inventory decisions with price and inventory dependent demand

Open Access

Issue		RAIRO-Oper. Res. Volume 60, Number 3, May-June 2026


Page(s)		1357 - 1391
DOI		https://doi.org/10.1051/ro/2026029
Published online		20 May 2026

T. Avinadav, A. Herbon and U. Spiegel, Optimal ordering and pricing policy for demand functions those are separable into price and inventory age. Int. J. Prod. Econ. 155 (2014) 406–417. [Google Scholar]
M. Benioudakis, A. Burnetas and G. Ioannou, Lead-time quotations in unobservable make-to-order systems with strategic customers: risk aversion, load control and profit maximization. Eur. J. Oper. Res. 289 (2021) 165–176. [Google Scholar]
T. Boyaci and S. Ray, Product differentiation and capacity cost interaction in time and price sensitive markets. Manuf. Serv. Oper. Manage. 5 (2003) 18–36. [Google Scholar]
S.K. Chaharsooghi and J. Heydari, A study on the impact of lead time statistical specifications on supply chain performance under uncertainty. Int. J. Mech. Manuf. Syst. 4 (2011) 95–112. [Google Scholar]
X. Chen and P. Hu, Joint pricing and inventory management with deterministic demand and costly price adjustment. Oper. Res. Lett. 40 (2012) 385–389. [Google Scholar]
J.M. Chen, I.C. Lin and H.L. Cheng, Channel coordination under consignment and vendor managed inventory in a distribution system. Transp. Res. Part E: Logistics Transp. Rev. 46 (2010) 831–843. [Google Scholar]
J.M. Chen, H.L. Cheng and M.C. Chien, On channel coordination through revenue sharing contracts with price and shelf space dependent demand. Appl. Math. Model. 35 (2011) 4886–4901. [Google Scholar]
B.R. Cobb, A.W. Johnson, R. Rumí and A. Salmerón, Accurate lead time demand modeling and optimal inventory policies in continuous review systems. Int. J. Prod. Econ. 163 (2015) 124–136. [Google Scholar]
L. Devangan, R.K. Amit, P. Mehta, S. Swami and K. Shanker, Individually rational buyback contracts with inventory level dependent demand. Int. J. Prod. Econ. 143 (2013) 381–387. [Google Scholar]
M.A. Edalatpour and S.M.J. Mirzapour Al-e-Hashem, Simultaneous pricing and inventory decisions for substitute and complementary items with nonlinear holding cost. Prod. Eng. 13 (2019) 305–315. [Google Scholar]
M.A. Edalatpour, S.M.J. Mirzapour Al-e-Hashem and A.M. Fathollahi-Fard, Combination of pricing and inventory policies for deteriorating products with sustainability considerations. Environ. Dev. Sustain. 26 (2024) 6809–6849. [Google Scholar]
R. Guan and X. Zhao, Pricing and inventory management in a system with multiple competing retailers under (r,Q) policies. Comput. Oper. Res. 38 (2011) 1294–1304. [Google Scholar]
J. Heydari and Y. Norouzinasab, Coordination of pricing, ordering, and lead time decisions in a manufacturing supply chain. J. Ind. Syst. Eng. 9 (2016) 1–16. [Google Scholar]
W.A. Jauhari, S.C.N. Ramadhany, C.N. Rosyidi, U. Mishra and H. Hishamuddin, Pricing and green inventory decisions for a supply chain system with green investment and carbon tax regulation. J. Clean. Prod. 425 (2023) 138897. [Google Scholar]
S. Karray and G. Martín-Herrán, The effects of decision timing for pricing and marketing efforts in a supply chain with competing manufacturers. Int. Trans. Oper. Res. 31 (2024) 568–615. [Google Scholar]
A. Kausar, C.K. Jaggi and S. Maheshwari, Optimizing inventory and pricing decisions in a Closed-Loop Supply Chain: a sustainable approach towards manufacturing and remanufacturing. Clean. Logistics Supply Chain 16 (2025) 100223. [Google Scholar]
S. Kim, Y. Feng and J. Xu, Complementarity analysis of a multi-item inventory model with leading product pricing. Prod. Oper. Manage. 32 (2023) 4190–4211. [Google Scholar]
B.K. Kumar, D. Nagaraju and S. Narayanan, Optimality of cycle time and inventory decisions in a coordinated and non-coordinated three echelon supply chain under exponential price dependent demand. Int. J. Logistics Syst. Manage. 25 (2016) 199–226. [Google Scholar]
L. Kumar, K. Sharma and U.K. Khedlekar, Dynamic pricing strategies for efficient inventory management with auto-correlative stochastic demand forecasting using exponential smoothing method. Results Control Opt. 15 (2024) 100432. [Google Scholar]
J.Y. Lee, An incentive contract for lead time reduction in an (s – 1, s) inventory system. Comput. Oper. Res. 36 (2009) 1633–1638. [Google Scholar]
M. Leng and M. Parlar, Lead time reduction in a two level supply chain: non cooperative equilibria vs. coordination with a profit sharing contract. Int. J. Prod. Econ. 118 (2009) 521–544. [Google Scholar]
T. Li, X. Zhao and J. Xie, Inventory management for dual sales channels with inventory level dependent demand. J. Oper. Res. Soc. 66 (2015) 488–499. [Google Scholar]
J. Min and Y.W. Zhou, A perishable inventory model under stock dependent selling rate and shortage dependent partial backlogging with capacity constraint. Int. J. Syst. Sci. 40 (2009) 33–44. [Google Scholar]
C. Mondal and B.C. Giri, Pricing and bundling strategies for complementary products in a closed-loop green supply chain under manufacturers’ different behaviors. Expert Syst. Appl. 238 (2024) 121960. [Google Scholar]
S.K. Mukhopadhyay, X. Yue and X. Zhu, A Stackelberg model of pricing of complementary goods under information asymmetry. Int. J. Prod. Econ. 134 (2011) 424–433. [Google Scholar]
M. Noori, A.A. Taleizadeh and F. Jolai, Analyzing pricing, promised delivery lead time, supplier-selection, and ordering decisions of a multi-national supply chain under uncertain environment. Int. J. Prod. Econ. 209 (2019) 236–248. [Google Scholar]
V. Pando, J. García-Laguna and L.A. San-José, Optimal policy for profit maximizing in an EOQ model under non-linear holding cost and stock-dependent demand rate. Int. J. Syst. Sci. 43 (2011) 2160–2171. [Google Scholar]
P. Pekgün, P.M. Griffin and P. Keskinocak, Coordination of marketing and production for price and lead time decisions. IIE Trans. 40 (2008) 12–30. [Google Scholar]
S. Ray, Y. Gerchak and E.M. Jewkes, The effectiveness of investment in lead time reduction for a make to stock product. IIE Trans. 36 (2010) 333–344. [Google Scholar]
T. Roy and K.S. Chaudhuri, A production inventory model under stock-dependent demand, Weibull distribution deterioration and shortage. Int. Trans. Oper. Res. 16 (2009) 325–346. [Google Scholar]
S. Saha, I.E. Nielsen and I. Moon, Strategic inventory and pricing decision for substitutable products. Comput. Ind. Eng. 160 (2021) 107570. [Google Scholar]
P. Shi and X. Chen, Supply chain decision-making and coordination for joint investment in cost and carbon emission reduction. Int. J. Low-Carbon Technol. 18 (2023) 306–321. [Google Scholar]
C.K. Sivashankari, P. Vijayakumar and V. Choudri, Complementary products for imperfect production, reworking, scarp with advertisement-sales return–Bertrand’s price dependent demand. J. Control Decis. (2025) 1–17. [Google Scholar]
W. Soon, Investigation of Nash equilibrium existence involving complementarity constrained pricing models. Appl. Math. Comput. 218 (2011) 1553–1567. [Google Scholar]
Y. Sun, X. Zhang, X. Huang and W. Cao, Research on logistics service supply chain coordination in the context of Green Innovation. Sustainability 17 (2025) 646. [Google Scholar]
A.A. Taleizadeh, H. Moghadasi, S.T.A. Niaki and A.K. Eftekhari, An EOQ-joint replenishment policy to supply expensive imported raw materials with payment in advance. J. Appl. Sci. 8 (2009) 4263–4273. [Google Scholar]
A.A. Taleizadeh, S.T.A. Niaki and V. Hosseini, Optimizing multi product multi constraints bi-objective newsboy problem with discount by hybrid method of goal programming and genetic algorithm. Eng. Opt. 41 (2009) 437–457. [Google Scholar]
A.A. Taleizadeh, S.T.A. Niaki and M.B. Aryanezhad, Replenish-up-to multi chance-constraint inventory control system with stochastic period lengths and total discount under fuzzy purchasing price and holding costs. Int. J. Syst. Sci. 41 (2010) 1187–1200. [Google Scholar]
A.A. Taleizadeh, S.T.A. Niaki, N. Shafii, R. Ghavamizadeh-Meibodi and A. Jabbarzadeh, A particle swarm optimization approach for constraint joint single buyer single vendor inventory problem with changeable lead-time and (r,Q) policy in supply chain. Int. J. Adv. Manuf. Technol. 51 (2010) 1209–1223. [Google Scholar]
A.A. Taleizadeh, S.T.A. Niaki and F. Barzinpour, Multi-buyer multi-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead time. Appl. Math. Comput. 217 (2011) 9234–9253. [Google Scholar]
A.A. Taleizadeh, S.T.A. Niaki and A. Makui, Multi-product multi-chance constraint multi-buyer single-vendor supply chain problem with stochastic demand and variable lead time. Expert Syst. App. 39 (2012) 5338–5348. [Google Scholar]
A.A. Taleizadeh, S.T. Niaki and H.M. Wee, Joint single vendor–single buyer supply chain problem with stochastic demand and fuzzy lead-time. Knowl. Based Syst. 48 (2013) 1–9. [Google Scholar]
S. Transchel, S. Minner and D.F. Pyke, Capacity investment and pricing decisions in a single period two product problem, in Operation Research Proceedings, Selected Papers of the Annual International Conference of the German Operations Research Society (GOR). Springer (2007) 389–394. [Google Scholar]
S.D. Treville, N. Schurhoff, L. Trigeorgis and B. Avanzi, Optimal sourcing and lead time reduction under evolutionary demand risk. Prod. Oper. Manage. 23 (2014) 2103–2117. [Google Scholar]
Y. Wang and Y. Gerchak, Supply chain coordination when demand is shelf-space dependent. Manuf. Serv. Oper. Manage. 3 (2001) 82–87. [Google Scholar]
J. Wei, J. Zhao and Y. Li, Pricing decisions for complementary products with firms’ different market powers, Eur. J. Oper. Res. 224 (2013) 507–519. [Google Scholar]
Z. Wu, B. Kazaz, S. Webster and K.K. Yang, Ordering, pricing, and lead-time quotation under lead-time and demand uncertainty. Prod. Oper. Manage. 21 (2012) 576–589. [Google Scholar]
Z. Wu, Z. Liu and X. Zhai, Impacts of inventory billboard effect on RFID implementation strategy, in Enterprise Systems Conference (ES). IEEE (2014) 7–12. [Google Scholar]
Z. Wu, X. Zhai and Z. Liu, The inventory billboard effect on the lead time decision. Int. J. Prod. Econ. 170 (2015) 45–53. [Google Scholar]
Z. Xiang, J. Yang, M.H. Naseem and W. Ge, Research on dynamic cooperative replenishment optimization of shipbuilding enterprise inventory control under uncertainty. Sustainability 14 (2022) 2113. [Google Scholar]
T. Xiao and X. Qi, A two-stage supply chain with demand sensitive to price, delivery time, and reliability of delivery. Ann. Oper. Res. 241 (2016) 475–496. [Google Scholar]
T. Xiao, T.M. Choi and T.C.E. Cheng, Delivery lead time and channel structure decisions for make to order duopoly under different game scenarios. Transp. Rese. Part E: Logistics Transp. Rev. 87 (2016) 113–129. [Google Scholar]
X. Yue, S.K. Mukhopadhyay and X. Zhu, A Bertrand model of pricing of complementary goods under information asymmetry. J. Bus. Res. 59 (2006) 1182–1192. [Google Scholar]
Y. Zhai and T.C.E. Cheng, Lead-time quotation and hedging coordination in make-to-order supply chain. Eur. J. Oper. Res. 300 (2022) 449–460. [Google Scholar]
Y. Zhai, R.Y. Zhong, Z. Li and G. Huang, Production lead time hedging and coordination in prefabricated construction supply chain management. Int. J. Prod. Res. 54 (2016) 1–19. [Google Scholar]
S.X. Zhu, Integration of capacity, pricing, and lead time decisions in a decentralized supply chain. Int. J. Prod. Econ. 164 (2015) 14–23. [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.