How to Value Customer Transactions in Dynamic Pricing Situations?

Abstract

Problem definition: We study how to calculate the value, or profit, gained from a specific customer transaction in dynamic pricing situations with limited capacity. A popular cash-flow-based approach suggests that “profit=revenue-cost” but we show that it leads to a systematic bias, overvaluing high-price transactions and undervaluing low-price ones. We then present an intuitive refined approach to valuing customer transactions that corrects this bias.

Methodology/results: Using the seminal dynamic pricing model of Gallego and van Ryzin (1994), we evaluate the difference between the firm’s profit with and without a specific customer transaction – the value of an incremental customer transaction (VICT). Under the cash-flow-based approach, the value, or profit, increases in the price paid. We, however, show that a lower-priced transaction could have a higher VICT, that the expected VICT could be independent of, or even decrease in, the price paid. We prove that this depends on the elasticity properties of the demand function used by the firm’s dynamic pricing algorithms and more broadly, on how the shadow price on capacity changes over time. Building on that, we also show that certain non-stationary customer arrival patterns could restore the “intuitive” directional relationship that higher-priced transactions are more valuable.

Managerial implications: Our results have both short-term/operational and long-term/strategic implications. Operationally, because VICT reflects the value gained from a customer transaction, or, equivalently, the value lost if the transaction did not happen, VICT represents the maximum amount the firm is willing to spend on securing the transaction. Strategically, our results suggest that firms could encourage transactions at lower prices (yet at even lower shadow prices) as those generally bring more value.

Keywords: customer, transaction, value, dynamic pricing, limited capacity, shadow price, demand function