Multi-Unit Combinatorial Auctions: an Exact Approach

In recent times combinatorial auctions have become an interesting domain for theoretical and applied developments of the electronic market technology. A combinatorial auction allows the simultaneous selling of several items and each participant to the auction may bid for bundles of items. When items in a bid are all different the auction is said a Single Unit Combinatorial Auction (SUCA), while when a bid may specify a number of units of a given item we call it a Multi-Unit Combinatorial Auction (MUCA). The bid taker’s objective is to find that set of bids which maximizes his total revenue. It has been shown that the problem, known as Winner Determination Problem, also for the special case in which each item is available in single units, is NP-hard ([4]). Up to now the bulk of research work on this subject has been focused on SUCA while a limited number of papers are available on the problem of Winner Determination in a MUCA (see, for instance, [2], [3] and [5]). For a complete survey on combinatorial auctions the reader is referred to [1]. From a practical point of view, the impact of auction increased importance is evident on the B2C (Business to Consumer) market (people taking part to on-line auctions organized by Ebay.com are increasing day by day). Less evident, but definitely not less important, is the impact of auctions development on the B2B (Business to Business) market, especially in the domain of supply logistics. We will focus our attention on a distribution problem which can be formulated as a Multi-Unit Combinatorial Auction. A transportation company provides a service of goods transshipment from some origins to different destinations. Each origin/destination pair is identified as a delivery route. For each route a given number of vehicles are made available for