On the hardness of pricing loss-leaders

Consider the problem of pricing n items under an unlimited supply with m buyers. Each buyer is interested in a bundle of at most k of the items. These buyers are single minded, which means each of them has a budget and they will either buy all the items if the total price is within their budget or they will buy none of the items. The goal is to price each item with profit margin p1, p2, ..., pn so as to maximize the overall profit. When k = 2, such a problem is called the graph-vertex-pricing problem. Another special case of the problem is the highwaypricing problem when the items (toll-booths) are arranged linearly on a line and each buyer (as a driver) is interested in paying for a path that consists of consecutive items. The goal again is to price the items (tolls) so as to maximize the total profits. There is an O(k)-approximation algorithm by [BB06] when the price on each item must be above its margin cost; i.e., pi > 0 for every i ∈ [n]. As for the highway problem, a PTAS i...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Preyas Popat, Yi Wu
• Keywords: Algorithms, Approximation Algorithm, Loss Leaders, SODA 2012, Toll Booths