Abstract
In this paper, we propose an exact solution approach to solve a joint product line selection and pricing problem with a fixed cost factor. We adopt the multinomial logit model to estimate the sales of each marketed product, and suppose that the introduction of each product to the market incurs some constant fixed costs. Utilizing an implicit function form of the optimal price, we transform the original problem into the one with the decision variables for the product introduction only. The efficiency of the proposed transformation approach is demonstrated through simulations. We further discuss its applicability to generalized problems.
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Notes
Gallego and Wang [10] studied a generalized pricing problem in which the price sensitivity may vary at the product level. Due to the nature of the product line selection problem, however, utilizing the characterization of Gallego and Wang can be limited. For example, we may need to estimate the price sensitivity of a potential product which has not been introduced to the market, which brings another challenge. For simplicity, we assume that the price sensitivities of the consumers within a segment are the same for each product.
Due to a technical issue, we could not run this simulation with the same computational environment of the numerical study provided in Sect. 4. The new environment has stronger computing power in which the mean computation time for a single segment case, \(I=1\), became two thirds of that of the original.
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Acknowledgements
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (No. NRF-2015R1A2A2A04007359).
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Park, J., Mo, J. An efficient method for joint product line selection and pricing with fixed costs. Optim Lett 13, 367–378 (2019). https://doi.org/10.1007/s11590-018-1356-5
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DOI: https://doi.org/10.1007/s11590-018-1356-5