Quoting an Optimal Price

Suppose you are an eBay-like online store operator selling wonderful home furniture sets made in Indonesia. For example a typical sofa set you sell may consist of a central offering in the form of a large three-person couch that is accompanied by a couple of matching chairs and tables (sample picture from an online wholesale dealer below).



While the center-piece tends to catch the eye of couch potatoes, you would like your customers to also buy the accessory pieces that go with this core product to boost your margin. To make this an attractive proposition, you recognize that every customer has a different willingness to pay and budget in mind. So rather than employ an inflexible fixed-price all-or-nothing approach, or risk a full-blown auction, you keep prospective buyers interested by allowing them to buy what they like and even quote their own price that you either accept or counter with a higher price. Unlike you, the buyer cannot see the price offers accepted and rejected in the past. How should you price a customer request taking all this information into account?

This scenario, as many would recognize, is not uncommon at all and plays out across multiple industries in the real and virtual world. Practitioners of Operations Research and Business Analytics creatively design a variety of probabilistic optimization models that allow a seller to provide a real-time price quote to a prospective buyer that maximizes the statistical chance of a profitable sale while staying within a customer's intended budget. Such mathematical bid-pricing methods help create a win-win situation by matching a customer's willingness-to pay with a seller's willingness to sell. 

Where can you read more about such customized pricing models for bid response? A good start is the superb book on Pricing and Revenue Management by Robert Phillips or this pdf link. And if you are lucky enough to attend the Informs 2012 annual conference in Phoenix, AZ along with thousands of OR fans, a brilliant colleague of mine will be presenting a novel real-world instance not involving furniture, and talk about its tremendous business impact measured using non-monopoly currency. If real-life Integer Programming based probabilistic bid pricing can wake you up very very early in the morning, this talk is scheduled for 8 A.M, October 17.

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