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Pricing Decision within an Inventory Model for Complementary and Substitutable Products

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  • Ata Allah Taleizadeh

    (School of Industrial Engineering, College of Engineering, University of Tehran, Tehran 456311155, Iran)

  • Masoumeh Sadat Babaei

    (Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran 1584743311, Iran)

  • Shib Sankar Sana

    (Principal, Kishore Bharati Bhagini Nivedita College, Ramkrishna Sarani, Behala, Kolkata 700060, India)

  • Biswajit Sarkar

    (Department of Industrial & Management Engineering, Hanyang University, Ansan, Gyeonggi-do 15588, Korea)

Abstract

A combination of substitutable and complementary products is very important for any business industry to make all-round profit from different aspects. How deterioration affects complementary products or substitutable products is discussed in this study. This study investigates the pricing and inventory decisions for complementary and substitutable items which are deteriorating in nature. Four models are analyzed where the demand of one product is dependent upon the selling price and the price of another product. This paper tries to compute the optimum prices and order quantities to optimize the total profit, which is the main aim. Theoretically, this model is solved by a classical optimization method. Numerical examples demonstrate the applicability of this model. Results conclude that the total profit is dependent on the degree of substitutability and complementarity. A sensitivity analysis of optimal solutions is given to test the stability of the proposed model.

Suggested Citation

  • Ata Allah Taleizadeh & Masoumeh Sadat Babaei & Shib Sankar Sana & Biswajit Sarkar, 2019. "Pricing Decision within an Inventory Model for Complementary and Substitutable Products," Mathematics, MDPI, vol. 7(7), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:568-:d:242923
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    References listed on IDEAS

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    1. S. Panda & S. Saha & M. Basu, 2009. "An EOQ model for perishable products with discounted selling price and stock dependent demand," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(1), pages 31-53, March.
    2. Stavrulaki, Euthemia, 2011. "Inventory decisions for substitutable products with stock-dependent demand," International Journal of Production Economics, Elsevier, vol. 129(1), pages 65-78, January.
    3. Luciano Salvietti & Neale R. Smith & Leopoldo Eduardo Cárdenas-Barrón, 2014. "A stochastic profit-maximising economic lot scheduling problem with price optimisation," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 8(2), pages 193-221.
    4. Sarkar, Biswajit & Saren, Sharmila & Wee, Hui-Ming, 2013. "An inventory model with variable demand, component cost and selling price for deteriorating items," Economic Modelling, Elsevier, vol. 30(C), pages 306-310.
    5. Barry A. Pasternack & Zvi Drezner, 1991. "Optimal inventory policies for substitutable commodities with stochastic demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(2), pages 221-240, April.
    6. Wei, Jie & Zhao, Jing & Li, Yongjian, 2013. "Pricing decisions for complementary products with firms’ different market powers," European Journal of Operational Research, Elsevier, vol. 224(3), pages 507-519.
    7. Neale R. Smith & Jorge Limón Robles & Leopoldo Eduardo Cárdenas-Barrón, 2009. "Optimal Pricing and Production Master Planning in a Multiperiod Horizon Considering Capacity and Inventory Constraints," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-15, August.
    8. Karakul, M. & Chan, L.M.A., 2010. "Joint pricing and procurement of substitutable products with random demands - A technical note," European Journal of Operational Research, Elsevier, vol. 201(1), pages 324-328, February.
    9. Zhang, Ren-Qian, 2012. "An extension of partial backordering EOQ with correlated demand caused by cross-selling considering multiple minor items," European Journal of Operational Research, Elsevier, vol. 220(3), pages 876-881.
    10. Serguei Netessine & Nils Rudi, 2003. "Centralized and Competitive Inventory Models with Demand Substitution," Operations Research, INFORMS, vol. 51(2), pages 329-335, April.
    11. Zhang, Ren-qian & Kaku, Ikou & Xiao, Yi-yong, 2011. "Deterministic EOQ with partial backordering and correlated demand caused by cross-selling," European Journal of Operational Research, Elsevier, vol. 210(3), pages 537-551, May.
    12. Karakul, M. & Chan, L.M.A., 2008. "Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem," European Journal of Operational Research, Elsevier, vol. 190(1), pages 179-204, October.
    13. Mehran Ullah & Biswajit Sarkar & Iqra Asghar, 2019. "Effects of Preservation Technology Investment on Waste Generation in a Two-Echelon Supply Chain Model," Mathematics, MDPI, vol. 7(2), pages 1-20, February.
    14. Dye, Chung-Yuan, 2007. "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging," Omega, Elsevier, vol. 35(2), pages 184-189, April.
    15. Xia, Yu, 2011. "Competitive strategies and market segmentation for suppliers with substitutable products," European Journal of Operational Research, Elsevier, vol. 210(2), pages 194-203, April.
    16. Anjos, Miguel F. & Cheng, Russell C. H. & Currie, Christine S. M., 2005. "Optimal pricing policies for perishable products," European Journal of Operational Research, Elsevier, vol. 166(1), pages 246-254, October.
    17. Abad, P. L., 2003. "Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale," European Journal of Operational Research, Elsevier, vol. 144(3), pages 677-685, February.
    18. Kim, Sang-Won & Bell, Peter C., 2011. "Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution," Omega, Elsevier, vol. 39(5), pages 528-538, October.
    19. Liu, Liming & Yuan, Xue-Ming, 2000. "Coordinated replenishments in inventory systems with correlated demands," European Journal of Operational Research, Elsevier, vol. 123(3), pages 490-503, June.
    20. Sudheer Gupta & Richard Loulou, 1998. "Process Innovation, Product Differentiation, and Channel Structure: Strategic Incentives in a Duopoly," Marketing Science, INFORMS, vol. 17(4), pages 301-316.
    21. Serguei Netessine & Gregory Dobson & Robert A. Shumsky, 2002. "Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation," Operations Research, INFORMS, vol. 50(2), pages 375-388, April.
    22. Yue, Xiaohang & Mukhopadhyay, Samar K. & Zhu, Xiaowei, 2006. "A Bertrand model of pricing of complementary goods under information asymmetry," Journal of Business Research, Elsevier, vol. 59(10-11), pages 1182-1192, October.
    23. Arunava Majumder & Rekha Guchhait & Biswajit Sarkar, 2017. "Manufacturing quality improvement and setup cost reduction in a vendor-buyer supply chain model," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 11(5), pages 588-612.
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