Cannibals and angels: price inventory management for substitute products

How do you price your hotel rooms to capture higher tier customers and encourage lower tier customers to buy add-ons such as meeting rooms and group catering? How do you manage leases so that your apartments stay vacant for as short a time as possible between tenancies? How do you price your hire cars to account for substitutions between different categories of car?

by Ioana Popescu, H. Ahmet Kuyumcu

There are many industries where available capacity has a primary influence on prices, and so both pricing and inventory strategy have important roles to play in profitability.

This paper, published in the Journal of Revenue and Pricing Management (January 2006) by H. Ahmet Kuyumcu, chief pricing scientist at Zilliant Inc, and Ioana Popescu, assistant professor of decision sciences at INSEAD, describes a model already used successfully to tackle the problem of balancing pricing with inventory control.

Kuyumcu and Popescu demonstrate that when demand is regular, maximising revenue is purely a pricing problem, but where demand is irregular and uncertain, other factors such as demand rationing come into the picture.

They delineate the interdependence of pricing and inventory strategies and propose a generic, static optimisation model that simultaneously considers pricing and inventory control with explicit demand rationing decisions. The authors formulate models for general pricing and inventory control that combine pricing and sales decisions, account for linear demand, and separate substitutable and non-substitutable products.

The practical application of the model is explored through a hotel pricing scenario, where the relationship between room hire and meeting-room hire is investigated. Examples of where this type of model has been used in real-life scenarios help to illustrate the adaptability and applicability of this method to a range of sectors. The smallest model in use involves 98 continuous variables and seven constraints. The largest involves 163,520 variables and 365 constraints.

The model proposed in this paper provides opportunities to investigate a wide variety of pricing and inventory control models, with a view to further examining the rationing strategies that best leverage product complementarities.

Cannibals and angels: price inventory management for substitutable products
H. Ahmet Kuyumcu and Ioana Popescu
Journal of Revenue and Pricing Management, January 2006

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