Bi-level pricing and inventory strategies for perishable products in a competitive supply chain
RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2395-2412

This paper aims to develop a new bi-level game model for joint pricing and inventory decisions in a competitive supply chain consisting of a dominant manufacturer, who produces single perishable product from deteriorating raw materials, and two follower retailers who face nonlinear price-dependent demand and operate under Cournot assumptions. Three levels of warehousing including raw material warehouse, final product warehouse, and retail warehouses with exponential deterioration rates are considered to explore the joint impact of deterioration rate and price elasticity on the equilibrium inventory decisions. A Stackelberg–Nash–Cournot model is developed to seek the equilibrium prices, quantities, and replenishment cycles and is solved through an exact methodology. A numerical example is presented to validate the proposed model and comprehensive sensitivity analyses are carried out to measure the impact of the model’s key parameters including the deterioration rate in the producer’s and the retailers’ warehouses, the retail and competitor price elasticity, and the market scale on the equilibrium.

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Accepté le :
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DOI : 10.1051/ro/2021106
Classification : 91A80
Keywords: Supply chain coordination, perishable products, inventory decisions, pricing, bi-level programming, Stackelberg–Nash–Cournot equilibrium
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Rajabi, Naser; Mozafari, Marzieh; Naimi-Sadigh, Ali. Bi-level pricing and inventory strategies for perishable products in a competitive supply chain. RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2395-2412. doi: 10.1051/ro/2021106

[1] G. Allon and A. Federgruen, Competition in service industries. Oper. Res. 55 (2007) 37–55. | MR | Zbl | DOI

[2] M. S. Bazaraa and C. M. Shetty, Nonlinear Programming. Theory and Algorithms. John Wiley & Sons (1979). | MR

[3] F. Bernstein and A. Federgruen, A general equilibrium model for industries with price and service competition. Oper. Res. 52 (2004) 868–886. | MR | Zbl | DOI

[4] 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. Appl. Math. Model. 39 (2015) 6725–6737. | MR | DOI

[5] K. Chen and T. Xiao, Pricing and replenishment policies in a supply chain with competing retailers under different retail behaviors. Comput. Ind. Eng. 103 (2017) 145–157. | DOI

[6] X. Chen, H. Zhang, M. Zhang and J. Chen, Optimal decisions in a retailer Stackelberg supply chain. Int. J. Prod. Econ. 187 (2017) 260–270. | DOI

[7] T. Chernonog, Inventory and marketing policy in a supply chain of a perishable product. Int. J. Prod. Econ. 219 (2020) 259–274. | DOI

[8] R. P. Covert and G. C. Philip, An EOQ model for items with Weibull distribution deterioration. AIIE Trans. 5 (1973) 323–326. | DOI

[9] W. A. Donaldson, Inventory replenishment policy for a linear trend in demand – an analytical solution. J. Oper. Res. Soc. 28 (1977) 663–670. | Zbl | DOI

[10] S. Eilon and R. V. Mallaya, Issuing and pricing policy of semi-perishables. In: Proceedings of the 4th International Conference on Operational Research. Wiley-Interscience (1966) 205–215.

[11] P. M. Ghare and G. H. Schrader, A model for exponentially decaying inventory system. J. Ind. Eng. 14 (1963) 238–243.

[12] H. Ghashghaei and M. Mozafari, A game theoretic approach to coordinate pricing, ordering and co-op advertising in supply chains with stochastic demand. Sci. Iran. 27 (2020) 3289–3304.

[13] D. Gligor, Re-examining supply chain fit: an assessment of moderating factors. J. Bus. Logistics 38 (2017) 253–265. | DOI

[14] A. Hafezalkotob, R. Mahmoudi, E. Hajisami and H. M. Wee, Wholesale-retail pricing strategies under market risk and uncertain demand in supply chain using evolutionary game theory. Kybernetes 47 (2018) 1178–1201. | DOI

[15] C. C. Hsieh and C. H. Wu, Capacity allocation, ordering, and pricing decisions in a supply chain with demand and supply uncertainties. Eur. J. Oper. Res. 184 (2008) 667–684. | MR | Zbl | DOI

[16] J. Huang, M. Leng and M. Parlar, Demand functions in decision modeling: a comprehensive survey and research directions. Decis. Sci. 44 (2013) 557–609. | DOI

[17] O. Kaya and A. L. Polat, Coordinated pricing and inventory decisions for perishable products. OR Spectr. 39 (2017) 589–606. | MR | DOI

[18] M. Kumar, P. Basu and B. Avittathur, Pricing and sourcing strategies for competing retailers in supply chains under disruption risk. Eur. J. Oper. Res. 265 (2018) 533–543. | MR | DOI

[19] B. Li, P. Chen, Q. Li and W. Wang, Dual-channel supply chain pricing decisions with a risk-averse retailer. Int. J. Prod. Res. 52 (2014) 7132–7147. | DOI

[20] B. Liu, R. Zhang and M. Xiao, Joint decision on production and pricing for online dual channel supply chain system. Appl. Math. Model. 34 (2010) 4208–4218. | MR | Zbl | DOI

[21] Z. Li, W. Yang, X. Liu and H. Taimoor, Coordination strategies in dual-channel supply chain considering innovation investment and different game ability. Kybernetes 49 (2019) 1581–1603. | DOI

[22] R. Maihami and I. Nakhai Kamalabadi, Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. Int. J. Prod. Econ. 136 (2012) 116–122. | DOI

[23] R. Maihami, B. Karimi and S. M. T. Fatemi Ghomi, Pricing and inventory control in a supply chain of deteriorating items: a non-cooperative strategy with probabilistic parameters. Int. J. Appl. Comput. Math. 3 (2017) 2477–2499. | MR | DOI

[24] S. Min, Z. G. Zacharia and C. D. Smith, Defining supply chain management: in the past, present, and future. J. Bus. Logistics 40 (2019) 44–55. | DOI

[25] J. Mo, F. Mi, F. Zhou and H. Pan, A note on an EOQ model with stock and price sensitive demand. Math. Comput. Model. 49 (2009) 2029–2036. | MR | Zbl | DOI

[26] M. Mokhlesian and S. H. Zegordi, Application of multidivisional bi-level programming to coordinate pricing and inventory decisions in a multiproduct competitive supply chain. Int. J. Adv. Manuf. Technol. 71 (2014) 1975–1989. | DOI

[27] H. Mokhtari, A. Naimi-Sadigh and A. Salmasnia, A computational approach to economic production quantity model for perishable products with backordering shortage and stock-dependent demand. Sci. Iran. Trans. E Ind. Eng. 24 (2017) 2138–2151.

[28] M. Mozafari, B. Karimi and M. Mahootchi, A differential Stackelberg game for pricing on a freight transportation network with one dominant shipper and multiple oligopolistic carriers. Sci. Iran. 23 (2016) 2391–2406.

[29] M. Mozafari, A. Naimi-Sadigh and A. H. Seddighi, Possibilistic cooperative advertising and pricing games for a two-echelon supply chain. Soft Comput. 25 (2021) 6957–6971. | DOI

[30] A. Naimi Sadigh, S. K. Chaharsooghi and M. Sheikhmohammady, Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain. Sci. Iran. 23 (2016) 1459–1473.

[31] A. Naimi-Sadigh, S. K. Chaharsooghi and M. Mozafari, Optimal pricing and advertising decisions with suppliers’ oligopoly competition: Stakelberg-Nash game structures. J. Ind. Manage. Optim. 17 (2021) 1423. | MR | DOI

[32] F. Otrodi, R. G. Yaghin and S. A. Torabi, Joint pricing and lot-sizing for a perishable item under two-level trade credit with multiple demand classes. Comput. Ind. Eng. 127 (2019) 761–777. | DOI

[33] A. Salmasnia and A. Talesh-Kazemi, Integrating inventory planning, pricing and maintenance for perishable products in a two-component parallel manufacturing system with common cause failures. Oper. Res. J. (2020). DOI: . | DOI

[34] H. D. Sherali, A. L. Soyster and F. H. Murphy, Stackelberg–Nash–Cournot equilibria: characterizations and computations. Oper. Res. 31 (1983) 253–276. | MR | Zbl | DOI

[35] D. Simchi-Levi, Designing and Managing The Supply Chain. Mcgraw-Hill College (2005).

[36] W. Soon, A review of multi-product pricing models. Appl. Math. Comput. 217 (2011) 8149–8165. | MR | Zbl

[37] A. A. Taleizadeh and M. Nematollahi, An inventory control problem for deteriorating items with back-ordering and financial considerations. Appl. Math. Modell. 38 (2014) 93–109. | MR | DOI

[38] M. Tavana, J. Prafulla and J. Rappaport, A comprehensive set of models of intra and inter-organizational coordination for marketing and inventory decisions in a supply chain. Int. J. Integr. Supply Manage. 2 (2006) 251–284. | DOI

[39] J. T. Wang, S. Zhang, C. H. Wu, J. J. Yu, C. B. Chen and S. B. Tsai, Time-sensitive markdown strategies for perishable products based on dynamic quality evaluation. Kybernetes 50 (2020) 165–180. | DOI

[40] T. M. Whitin, Inventory control and price theory. Manage. Sci. 2 (1955) 61–68. | DOI

[41] K. S. Wu, EOQ inventory model for items with Weibull distribution deterioration, time-varying demand and partial backlogging. Int. J. Syst. Sci. 33 (2002) 323–329. | MR | Zbl | DOI

[42] P. C. Yang and H. M. Wee, An integrated multi-lot-size production inventory model for deteriorating item. Comput. Oper. Res. 30 (2003) 671–682. | Zbl | DOI

[43] S. L. Yang and Y. W. Zhou, Two-echelon supply chain models: considering duopolistic retailers’ different competitive behaviors. Int. J. Prod. Econ. 103 (2006) 104–116. | DOI

[44] C. T. Yang, L. Y. Ouyang and H. H. Wu, Retailer’s optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging. Math. Prob. Eng. 2009 (2009) 1–18. | MR | Zbl

[45] P. C. Yang, S. L. Chung, H. M. Wee, E. Zahara and C. Y. Peng, Collaboration for a closed-loop deteriorating inventory supply chain with multi-retailer and price-sensitive demand. Int. J. Prod. Econ. 143 (2013) 557–566. | DOI

[46] R. Yin and K. Rajaram, Joint pricing and inventory control with a Markovian demand model. Eur. J. Oper. Res. 182 (2007) 113–126. | MR | Zbl | DOI

[47] J. L. Zhang, J. Chen and C. Y. Lee, Joint optimization on pricing, promotion and inventory control with stochastic demand. Int. J. Prod. Econ. 116 (2008) 190–198. | DOI

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