We study the problem when a firm sets prices for products based on past transaction data. We do not impose a model on the distribution of the customers' valuations and only assumes purchase choices satisfy incentive-compatible constraints. The valuation of each past customer can be encoded as a polyhedral set, and our approach maximizes the worst-case revenue. We show optimal prices in this setting can be approximated by solving a compact mixed-integer linear program.

We study a bundle pricing policy, Component Pricing with Bundle Size Discount (CPBSD). It sells bundles at the sum of component prices minus a discount depending on the bundle size. It subsumes many mechanisms including Component Pricing and Bundle Size Pricing. We show that CPBSD attains the optimal profit asymptotically among all pricing policies under a weak condition. We formulate MILP for the optimal CPBSD. Comprehensive numerical experiments demonstrate the good performance of CPBSD.

We consider a firm that sells some primary and ancillary products (services) to heterogeneous customers. The challenge is to determine the prices for all the products and services simultaneously, to optimize profits to the firm. We consider random utility model for customers' choice problem, and show that the choice model can be reformulated into a perturbed utility model (PUM) over the convex hull of the feasible solutions. Furthermore, we demonstrate how we can obtain a good approximation.