A numerical optimization approach for pricing components in customer defined bundles in a B2B market

This research examines the problem of pricing products in multi-product, multi-quantity bundles in a business-to-business market setting in which customers’ valuation of products diminishes with the size of the bundle. The framework developed in this paper consists of three steps: (i) estimation of diminished valuation of each product based on their stand-alone valuations and bundle composition, (ii) maximization of expected profit of the firm to obtain the optimal bundle price, and (iii) maximization of customer satisfaction to obtain the optimal split of the bundle price into component prices. A Nelder–Mead optimization based method is proposed as a solution approach, which leverages an importance sampling based Monte Carlo integration method to approximate the quantities of interests in the model. The framework is also used to analyze the behavior of the model for quantity increase. Results indicate that the price per unit of each product decreases when the quantity of any of the products is increased. However, the rate of decrement is the least for the product whose quantity is incremented. Additional results show that fixing prices (and not re-optimizing), when the bundle composition changes, can significantly reduce the firm's profit.