A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand

This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to ob...

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Autores:: Salas-Navarro, Katherinne
Acevedo-Chedid, Jaime
Florez, Whady F
Ospina Mateus, Holman
Cárdenas-Barrón, Leopoldo Eduardo
Sankar Sana, Shib

Tipo de recurso:: Article of journal

Fecha de publicación:: 2020

Institución:: Corporación Universidad de la Costa

Repositorio:: REDICUC - Repositorio CUC

Idioma:: eng

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network_acronym_str	RCUC2
network_name_str	REDICUC - Repositorio CUC
repository_id_str
dc.title.spa.fl_str_mv	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
title	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
spellingShingle	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand Inventory supply chain collaboration multiple products marketing effort economic production quantity
title_short	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
title_full	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
title_fullStr	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
title_full_unstemmed	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
title_sort	A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand
dc.creator.fl_str_mv	Salas-Navarro, Katherinne Acevedo-Chedid, Jaime Florez, Whady F Ospina Mateus, Holman Cárdenas-Barrón, Leopoldo Eduardo Sankar Sana, Shib
dc.contributor.author.spa.fl_str_mv	Salas-Navarro, Katherinne Acevedo-Chedid, Jaime Florez, Whady F Ospina Mateus, Holman Cárdenas-Barrón, Leopoldo Eduardo Sankar Sana, Shib
dc.subject.spa.fl_str_mv	Inventory supply chain collaboration multiple products marketing effort economic production quantity
topic	Inventory supply chain collaboration multiple products marketing effort economic production quantity
description	This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to obtain the optimal production lot size and the optimal marketing effort in order to achieve the maximum profits. Some numerical examples are illustrated to justify the model. Moreover, a sensitivity analysis is well done in order to analysis the effect of the changes of key parameters of inventory model on the the maximum benefits of all members of the chain.
publishDate	2020
dc.date.issued.none.fl_str_mv	2020
dc.date.accessioned.none.fl_str_mv	2021-02-03T13:59:47Z
dc.date.available.none.fl_str_mv	2021-02-03T13:59:47Z
dc.type.spa.fl_str_mv	Artículo de revista
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dc.type.content.spa.fl_str_mv	Text
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/article
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dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
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dc.identifier.uri.spa.fl_str_mv	https://hdl.handle.net/11323/7821
dc.identifier.doi.spa.fl_str_mv	10.3934/jimo.2019020
dc.identifier.instname.spa.fl_str_mv	Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv	REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.cuc.edu.co/
url	https://hdl.handle.net/11323/7821 https://repositorio.cuc.edu.co/
identifier_str_mv	10.3934/jimo.2019020 Corporación Universidad de la Costa REDICUC - Repositorio CUC
dc.language.iso.none.fl_str_mv	eng
language	eng
dc.relation.references.spa.fl_str_mv	[1] H. M. Abdelsalam and M. M. Elassal, Joint economic lot sizing problem for a three-Layer supply chain with stochastic demand, International Journal of Production Economics, 155 (2014), 272-283. [2] A. Ahmadi-Javid and P. Hoseinpour, A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints, Transportation Research Part E: Logistics and Transportation Review, 82 (2015), 238-255. [3] F. Alawneh and G. Zhang, Dual-channel warehouse and inventory management with stochastic demand, Transportation Research Part E: Logistics and Transportation Review, 112 (2018), 84-106. [4] M. Ben-Daya, R. Asád and M. Seliaman, An integrated production inventory model with raw material replenishment considerations in a three layer supply chain, International Journal of Production Economics, 143 (2013), 53-61 [5] L. E. Cárdenas-Barrón and S. S. Sana, A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives, International Journal of Production Economics, 155 (2014), 249-258. [6] L. E. Cárdenas-Barrón and S. S. Sana, Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort, Applied Mathematical Modelling, 39 (2015), 6725-6737. [7] L. E. Cárdenas-Barrón, J. T. Teng, G. Trevino-Garza, H. M. Wee and K. R. Lou, An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain, International Journal of Production Economics, 136 (2012), 384-388. [8] Z. Dai, F. Aqlan and K. Gao, Optimizing multi-echelon inventory with three types of demand in supply chain, Transportation Research Part E: Logistics and Transportation Review, 107 (2017), 141-177. [9] S. K. De and S. S. Sana, The (p, q, r, l) mode l fo r stochastic demand unde r Intuitionistic fuzzy agg regation with Bonferroni mean, Journal of Intelligent Manufacturing, check (2016), 1-19. [10] J. P. Dube, Multiple discreteness and product differentiation: Demand for carbonated soft drinks, Marketing Science, 23 (2004), 66-81. [11] B. C. Giri and S. Bardhan, Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production, International, Journal of Production Economics, 191 (2017), 66-73 [12] S. K. Goyal and C. T. Chang, Optimal ordering and transfer policy for an inventory with stock dependent demand, European Journal of Operational Research, 196 (2009), 177-185. [13] S. K. Goyal and A. Gunasekaran, An integrated production-inventory-marketing model for deteriorating items, Computers & Industrial Engineering, 28 (1995), 755-762 [14] K. L. Hou and L. C. Lin, An EOQ model for deteriorating items with price-and stock-dependent selling rate under inflation and time value of money, International Journal of Systems Science, 37 (2006), 1131-1139. [15] M. Johari, S. M. Hosseini-Motlagh, M. Nematollahi, M. Goh and J. Ignatius, Bi-level credit period coordination for periodic review inventory system with price-credit dependent demand under time value of money, Transportation Research Part E: Logistics and Transportation Review, 114 (2018), 270-291. [16] S. Karray, Periodicity of pricing and marketing efforts in a distribution channel, European Journal of Operational Research, 228 (2013), 635-647. [17] S. Kim and D. I. Gilliland, Working more or working less? Contingent allocation of reseller effort in distribution channels, Industrial Marketing Management, 64 (2017), 44-56. [18] H. Krishnan, R. Kapusciniski and D. A. Butz, Coordinating contracts for decentralized supply chain with retailer promotional effect, Management Science, 50 (2004), 48-63 [19] W. Lee, S. P. Wang and W. C. Chen, Forward and backward stocking policies for a two-level supply chain with consignment stock agreement and stock-dependent demand, European Journal of Operational Research, 256 (2017), 830-840. [20] P. Ma, H. Wnag and J. Shang, Supply chain chanel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581 [21] P. Ma, H. Wang and J. Shang, Contract design for two-stage supply chain coordination: Integrating manufacturer-quality and retailer-marketing efforts, International Journal of Production Economics, 146 (2013), 745-755. [22] J. Min, Y. W. Zhou and J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Applied Mathematical Modelling, 34 (2010), 3273-3285. [23] N. M. Modak, S. Panda and S. S. Sana, Pricing policy and coordination for a two-layer supply chain of duopolistic retailers and socially responsible manufacturer, International Journal of Logistic: Research and Applications, 19 (2015), 487-508. [24] N. M. Modak, S. Panda and S. S. Sana, Two-echelon supply chain coordination among manufacturer and duopolies retailers with recycling facility, International Journal of Advanced Manufacturing Technology, 87 (2016), 1531-1546. [25] P. A. Naik, K. Raman and R. S. Winer, Planning marketing-mix strategies in the presence of interaction effects, Marketing Science, 24 (2005), 25-34. [26] M. G. Nagler, An exploratory analysis of the determinants of cooperative advertising participation rates, Marketing Letters, 17 (2006), 91-102. [27] T. Paksoy, N. Y. Pehlivan and E. Ozceylan, A new tradeoff model for fuzzy supply chain network design and optimization, Human and Ecological Risk Assessment: An International Journal, 19 (2013), 492-514. [28] T. Paksoy, E. Ozceylan and G. W. Weber, Profit oriented supply chain network optimization, Central European Journal of Operations Research, 21 (2013), 455-478. [29] B. Pal, S. S. Sana and K. Chaudhuri, Three-layer supply chain – A production-inventory model for reworkable items, Applied Mathematics and Computation, 219 (2012), 530-543. [30] S. Panda, N. M. Modak, M. Basu and S. K. Goyal, Channel coordination and profit distribution in a social responsible three-layer supply chain, International Journal of Production Economics, 168 (2015), 224-233. [31] S. Panda, S. Saha and S. K. Goyal, Dilema of rented warehouse and shelf for inventory systems with displayed stock level dependent demand, Economic Modelling, 32 (2013), 452-462. [32] S. Panda, N. M. Modak, S. S. Sana and M. Basu, Pricing and replenishment policies in dual-channel supply chain under continuous unit cost decrease, Applied Mathematics and Computation, 256 (2015), 913-929. [33] M. Pervin, S. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460. [34] M. Pervin, S. K. Roy and G. W. Weber, A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control & Optimization, 7 (2017), 21-50. [35] M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control & Optimization, 8 (2018), 169-19 [36] M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, Journal of Industrial & Management Optimization, (2018) [37] X. Pu, L. Gong and G. Han, A feasible incentive contract between a manufacturer and his fairness-sensitive retailer engaged in strategic marketing efforts, Journal of Intelligent Manufacturing, 30 (2019), 193-206. [38] A. Roy, S. S. Sana and K. Chaudhuri, A joint venturing of single supplier and single retailer under variable price, promotional effort and service level, Pacific Science Review B: Humanities and Social Sciences, 1 (2015), 8-14. [39] A. Roy, S. S. Sana and K. Chaudhuri, Optimal replenishment order for uncertain demand in three layer supply chain, Economic Modelling, 29 (2012), 2274-2282. [40] K. Salas-Navarro, J. Acevedo-Chedid, N. Mercado-Caruso and S. S. Sana, An inventory model of three-layer supply chain of wood and furniture industry in the Caribbean region of Colombia, Internarional Journal of Systems Science: Operations and Logistics, 5 (2018), 69-86. [41] S. S. Sana, An EOQ model for salesmen's initiatives, stock and price sensitive demand of similar products – A dynamical system, Applied Mathematics and Computation, 218 (2011), 3277-3288. [42] S. S. Sana, Optimal contract strategies for two stage supply chain, Economic Modelling, 30 (2013), 253-260. [43] S. S. Sana, J. Acevedo-Chedid and K. Salas-Navarro, A three layer supply chain model with multiple suppliers, manufacturers and retailers for multiple items, Applied Mathematics and Computation, 229 (2014), 139-150. [44] S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decision Support Systems, 50 (2011), 539-547. [45] S. S. Sana, Sales team's initiatives and stock sensitive demand – A production control policy, Economic Modelling, 31 (2013), 783-788 [46] J. Song, F. Li, D. D. Wu, L. Liang and A. Dolgui, Supply chain coordination through integration of innovation effort and advertising support, Applied Mathematical Modelling, 49 (2017), 108-123. [47] H. Soni and N. H. Shah, Optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 184 (2008), 91-100. [48] Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878 [49] S. Zhao and Q. Zhu, A risk-averse marketing strategy and its effect on coordination activities in a remanufacturing supply chain under market fluctuation, Journal of Cleaner Production, 171 (2018), 1290-1299.
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spelling	Salas-Navarro, Katherinne43bd8765374e373d1c885d3059a927d3Acevedo-Chedid, Jaime464ab66215e948ca83508aeace5e4a5dFlorez, Whady F305237a2649bd4eef52bd29581602044Ospina Mateus, Holman9ca115ead2308e90de7504122610ec81Cárdenas-Barrón, Leopoldo Eduardo8e50003a3472ecccad6660b78b020cebSankar Sana, Shib909fdc49ed1513b1cd8a228dfb1fe9952021-02-03T13:59:47Z2021-02-03T13:59:47Z2020https://hdl.handle.net/11323/782110.3934/jimo.2019020Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to obtain the optimal production lot size and the optimal marketing effort in order to achieve the maximum profits. Some numerical examples are illustrated to justify the model. Moreover, a sensitivity analysis is well done in order to analysis the effect of the changes of key parameters of inventory model on the the maximum benefits of all members of the chain.application/pdfengCorporación Universidad de la CostaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2American Institute Of Mathematical Scienseshttps://www.aimsciences.org/article/doi/10.3934/jimo.2019020Inventorysupply chain collaborationmultiple productsmarketing efforteconomic production quantityA collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demandArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion[1] H. M. Abdelsalam and M. M. Elassal, Joint economic lot sizing problem for a three-Layer supply chain with stochastic demand, International Journal of Production Economics, 155 (2014), 272-283.[2] A. Ahmadi-Javid and P. Hoseinpour, A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints, Transportation Research Part E: Logistics and Transportation Review, 82 (2015), 238-255.[3] F. Alawneh and G. Zhang, Dual-channel warehouse and inventory management with stochastic demand, Transportation Research Part E: Logistics and Transportation Review, 112 (2018), 84-106.[4] M. Ben-Daya, R. Asád and M. Seliaman, An integrated production inventory model with raw material replenishment considerations in a three layer supply chain, International Journal of Production Economics, 143 (2013), 53-61[5] L. E. Cárdenas-Barrón and S. S. Sana, A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives, International Journal of Production Economics, 155 (2014), 249-258.[6] L. E. Cárdenas-Barrón and S. S. Sana, Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort, Applied Mathematical Modelling, 39 (2015), 6725-6737.[7] L. E. Cárdenas-Barrón, J. T. Teng, G. Trevino-Garza, H. M. Wee and K. R. Lou, An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain, International Journal of Production Economics, 136 (2012), 384-388.[8] Z. Dai, F. Aqlan and K. Gao, Optimizing multi-echelon inventory with three types of demand in supply chain, Transportation Research Part E: Logistics and Transportation Review, 107 (2017), 141-177.[9] S. K. De and S. S. Sana, The (p, q, r, l) mode l fo r stochastic demand unde r Intuitionistic fuzzy agg regation with Bonferroni mean, Journal of Intelligent Manufacturing, check (2016), 1-19.[10] J. P. Dube, Multiple discreteness and product differentiation: Demand for carbonated soft drinks, Marketing Science, 23 (2004), 66-81.[11] B. C. Giri and S. Bardhan, Sub-supply chain coordination in a three-layer chain under demand uncertainty and random yield in production, International, Journal of Production Economics, 191 (2017), 66-73[12] S. K. Goyal and C. T. Chang, Optimal ordering and transfer policy for an inventory with stock dependent demand, European Journal of Operational Research, 196 (2009), 177-185.[13] S. K. Goyal and A. Gunasekaran, An integrated production-inventory-marketing model for deteriorating items, Computers & Industrial Engineering, 28 (1995), 755-762[14] K. L. Hou and L. C. Lin, An EOQ model for deteriorating items with price-and stock-dependent selling rate under inflation and time value of money, International Journal of Systems Science, 37 (2006), 1131-1139.[15] M. Johari, S. M. Hosseini-Motlagh, M. Nematollahi, M. Goh and J. Ignatius, Bi-level credit period coordination for periodic review inventory system with price-credit dependent demand under time value of money, Transportation Research Part E: Logistics and Transportation Review, 114 (2018), 270-291.[16] S. Karray, Periodicity of pricing and marketing efforts in a distribution channel, European Journal of Operational Research, 228 (2013), 635-647.[17] S. Kim and D. I. Gilliland, Working more or working less? Contingent allocation of reseller effort in distribution channels, Industrial Marketing Management, 64 (2017), 44-56.[18] H. Krishnan, R. Kapusciniski and D. A. Butz, Coordinating contracts for decentralized supply chain with retailer promotional effect, Management Science, 50 (2004), 48-63[19] W. Lee, S. P. Wang and W. C. Chen, Forward and backward stocking policies for a two-level supply chain with consignment stock agreement and stock-dependent demand, European Journal of Operational Research, 256 (2017), 830-840.[20] P. Ma, H. Wnag and J. Shang, Supply chain chanel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581[21] P. Ma, H. Wang and J. Shang, Contract design for two-stage supply chain coordination: Integrating manufacturer-quality and retailer-marketing efforts, International Journal of Production Economics, 146 (2013), 745-755.[22] J. Min, Y. W. Zhou and J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Applied Mathematical Modelling, 34 (2010), 3273-3285.[23] N. M. Modak, S. Panda and S. S. Sana, Pricing policy and coordination for a two-layer supply chain of duopolistic retailers and socially responsible manufacturer, International Journal of Logistic: Research and Applications, 19 (2015), 487-508.[24] N. M. Modak, S. Panda and S. S. Sana, Two-echelon supply chain coordination among manufacturer and duopolies retailers with recycling facility, International Journal of Advanced Manufacturing Technology, 87 (2016), 1531-1546.[25] P. A. Naik, K. Raman and R. S. Winer, Planning marketing-mix strategies in the presence of interaction effects, Marketing Science, 24 (2005), 25-34.[26] M. G. Nagler, An exploratory analysis of the determinants of cooperative advertising participation rates, Marketing Letters, 17 (2006), 91-102.[27] T. Paksoy, N. Y. Pehlivan and E. Ozceylan, A new tradeoff model for fuzzy supply chain network design and optimization, Human and Ecological Risk Assessment: An International Journal, 19 (2013), 492-514.[28] T. Paksoy, E. Ozceylan and G. W. Weber, Profit oriented supply chain network optimization, Central European Journal of Operations Research, 21 (2013), 455-478.[29] B. Pal, S. S. Sana and K. Chaudhuri, Three-layer supply chain – A production-inventory model for reworkable items, Applied Mathematics and Computation, 219 (2012), 530-543.[30] S. Panda, N. M. Modak, M. Basu and S. K. Goyal, Channel coordination and profit distribution in a social responsible three-layer supply chain, International Journal of Production Economics, 168 (2015), 224-233.[31] S. Panda, S. Saha and S. K. Goyal, Dilema of rented warehouse and shelf for inventory systems with displayed stock level dependent demand, Economic Modelling, 32 (2013), 452-462.[32] S. Panda, N. M. Modak, S. S. Sana and M. Basu, Pricing and replenishment policies in dual-channel supply chain under continuous unit cost decrease, Applied Mathematics and Computation, 256 (2015), 913-929.[33] M. Pervin, S. K. Roy and G. W. Weber, Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration, Annals of Operations Research, 260 (2018), 437-460.[34] M. Pervin, S. K. Roy and G. W. Weber, A Two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items, Numerical Algebra, Control & Optimization, 7 (2017), 21-50.[35] M. Pervin, S. K. Roy and G. W. Weber, An integrated inventory model with variable holding cost under two levels of trade-credit policy, Numerical Algebra, Control & Optimization, 8 (2018), 169-19[36] M. Pervin, S. K. Roy and G. W. Weber, Multi-item deteriorating two-echelon inventory model with price-and stock-dependent demand: A trade-credit policy, Journal of Industrial & Management Optimization, (2018)[37] X. Pu, L. Gong and G. Han, A feasible incentive contract between a manufacturer and his fairness-sensitive retailer engaged in strategic marketing efforts, Journal of Intelligent Manufacturing, 30 (2019), 193-206.[38] A. Roy, S. S. Sana and K. Chaudhuri, A joint venturing of single supplier and single retailer under variable price, promotional effort and service level, Pacific Science Review B: Humanities and Social Sciences, 1 (2015), 8-14.[39] A. Roy, S. S. Sana and K. Chaudhuri, Optimal replenishment order for uncertain demand in three layer supply chain, Economic Modelling, 29 (2012), 2274-2282.[40] K. Salas-Navarro, J. Acevedo-Chedid, N. Mercado-Caruso and S. S. Sana, An inventory model of three-layer supply chain of wood and furniture industry in the Caribbean region of Colombia, Internarional Journal of Systems Science: Operations and Logistics, 5 (2018), 69-86.[41] S. S. Sana, An EOQ model for salesmen's initiatives, stock and price sensitive demand of similar products – A dynamical system, Applied Mathematics and Computation, 218 (2011), 3277-3288.[42] S. S. Sana, Optimal contract strategies for two stage supply chain, Economic Modelling, 30 (2013), 253-260.[43] S. S. Sana, J. Acevedo-Chedid and K. Salas-Navarro, A three layer supply chain model with multiple suppliers, manufacturers and retailers for multiple items, Applied Mathematics and Computation, 229 (2014), 139-150.[44] S. S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decision Support Systems, 50 (2011), 539-547.[45] S. S. Sana, Sales team's initiatives and stock sensitive demand – A production control policy, Economic Modelling, 31 (2013), 783-788[46] J. Song, F. Li, D. D. Wu, L. Liang and A. Dolgui, Supply chain coordination through integration of innovation effort and advertising support, Applied Mathematical Modelling, 49 (2017), 108-123.[47] H. Soni and N. H. Shah, Optimal ordering policy for stock-dependent demand under progressive payment scheme, European Journal of Operational Research, 184 (2008), 91-100.[48] Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878[49] S. Zhao and Q. 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A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand

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