Price Optimization Michel Bierlaire michel.bierlaire@epfl.ch - PowerPoint PPT Presentation

Price Optimization Michel Bierlaire michel.bierlaire@epfl.ch Transport and Mobility Laboratory Price Optimization – p. 1/9

Introduction • Choice model captures demand • Demand is elastic to price • Predicted demand varies with price, if it is a variable of the model • In principle, the probability to use/purchase an alternative decreases if the price increases. • The revenue per user increases if the price increases. • Question: what is the optimal price to optimize revenue? In short: • Price ↑⇒ profit/passenger ↑ and number of passengers ↓ • Price ↑⇒ profit/passenger ↓ and number of passengers ↑ • What is the best trade-off? Price Optimization – p. 2/9

Revenue calculation Number of persons choosing alternative i in the population � S ˆ N ( i ) = N s P ( i | x s , p is ) s =1 where • p s is the price of item i in segment s • x s gathers all other variables corresponding to segment s • the population is segmented into S homogeneous strata • P ( i | x s , p is ) is the choice model • N s is the number of individuals in segment s Price Optimization – p. 3/9

Revenue calculation The total revenue from i is therefore: S � R i = N s P ( i | x s , p is ) p is s =1 If the price is constant across segments, we have S � R i = p i N s P ( i | x s , p i ) s =1 Price Optimization – p. 4/9

Price optimization Optimizing the price of product i is solving the problem � S max N s P ( i | x s , p i ) p i p i s =1 Notes: • It assumes that everything else is equal • In practice, it is likely that the competition will also adjust the prices Price Optimization – p. 5/9

Illustrative example A binary logit model with = β p p 1 − 0 . 5 V 1 V 2 = β p p 2 so that e β p p 1 − 0 . 5 P (1 | p ) = e β p p 1 − 0 . 5 + e β p p 2 Two groups in the population: • Group 1: β p = − 2 , N s = 600 • Group 2: β p = − 0 . 1 , N s = 400 Assume that p 2 = 2 . Price Optimization – p. 6/9

Illustrative example 0.7 900 Share Revenues 850 0.6 800 0.5 750 0.4 Revenues Share 700 0.3 650 0.2 600 0.1 550 0 500 2 4 6 8 10 12 14 16 Price Price Optimization – p. 7/9

Sensitivity analysis • Parameters are estimated, we do not know the real value • 95% confidence interval: [ � β p − 1 . 96 σ, � β p + 1 . 96 σ ] • Perform a sensitivity analysis for β p in group 2 Price Optimization – p. 8/9

Sensitivity analysis 1800 1800 beta=-0.04 beta=-0.07 beta=-0.1 1600 beta=-0.13 1600 beta=-0.16 1400 1400 1200 1200 Revenues Share 1000 1000 800 800 600 600 400 400 200 200 2 4 6 8 10 12 14 16 Price Price Optimization – p. 9/9