Efficient heuristic algorithms for maximum utility product pricing problems

• Very efficient implementations of Dobson-Kalish pricing heuristics and generalizations.
• Connections to Stackelberg Network pricing games, worst-case approximation ratios.
• Analysis of exchange properties leading to improved algorithms for optimal pricing.
• A new, lifted representation of a huge family of LP relaxations.
• Extensive computational tests, including huge data sets and real-world data.

We propose improvements to some of the best heuristic algorithms for optimal product pricing problem originally designed by Dobson and Kalish in the late 1980s and in the early 1990s. Our improvements are based on a detailed study of a fundamental decoupling structure of the underlying mixed integer programming (MIP) problem and on incorporating more recent ideas, some from the theoretical computer science literature, for closely related problems. We provide very efficient implementations of the algorithms of Dobson and Kalish as well as our new algorithms. We show that our improvements lead to algorithms which generate solutions with better objective values and that are more robust in overall performance. Our computational experiments indicate that our implementation of Dobson–Kalish heuristics and our new algorithms can provide good solutions for the underlying MIP problems where the typical LP relaxations would have more than a trillion variables and more than three trillion constraints.