Calorimetría diferencial de barrido (DSC, “Differential Scanning

In traditional auctions, as we know them, one item is auctioned at a time. However, in many auctions, bidders care in complex ways about the combination of items that they want to win. Imagine a buyer who wants to purchase a return ticket to a particular destination from an online auction site that sells airline tickets. In the traditional way of auctioning, she has to attend two separate auctions and win two tickets, one to and one from that destination. If she wins in only one of the auctions, she will end up with a one- way ticket which is of no value to her. Such a bidder strongly prefers an auction model that allows her to bid for the two items together as a bundle. In other words, the satisfaction of such a bidder is determined by the simultaneous allocation of the items.

In combinatorial auctions, multiple distinct items are simultaneously auctioned and the bidders can bid for any combination of items, or bundles. Bundling is particularly important when bidders have preferences not just for specific items but for bundles due to the complementarity or substitutability effects that exist among the items (de Vries and Vohra 2003).

Two items are said to be substitutes (have substitutability effect) if their combined value is less than the sum of their individual values (Shoham and Leyton-Brown 2009, p.362).

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An example of items being substitutes is two tickets to two movies which are shown at the same time.

Complementarity is the opposite effect of substitutability: two items are said to be complementary if their joint value exceeds the sum of their individual values (Shoham and Leyton-Brown 2009, p.362). As an example consider a left shoe and a right shoe. The combinatorial auctions where items to be bundles have complementarity effect have been categorized, based on the types of complementarity dependencies between items, into the following groups:

1. Path in space:

In this class, the bidders are interested in purchasing the connection between two points. The points are equivalent to the items under auction and they are connected to each other if they have accessibility relationship. Examples of auctions with this type of dependency are auctions to allocate truck routes, gas pipeline networks, network bandwidth and right to railway tracks.

2. Proximity in space:

Here, the complementarity arises from adjacency in two-dimensional space. Example of this class of auction includes: sale of adjacent pieces of real states, drilling right (in adjacent lots) and the spectrum auctions (to some extend).

3. Temporal matching:

Here, the complementarity arises from a temporal relationship between items. In the general temporal matching dependency with single quantity items, there are m distinct items, and each bidder wants 1 time slice from a set of j <= m items with some constraints over how the times of different items relate to one another. Example includes the auction over airport take-off and landing rights where j=2.

4. Temporal scheduling:

In this class, a bidder has a job, requiring some amount of one or more resources’ time, with a deadline by which the job should have been completed. The auction is over the time slots of the resources. Example includes distributed job-shop scheduling with one resource, and also allocating grid resources to the tasks.

25 5. Arbitrary dependencies:

In this category, the dependencies are due to some kind of regularity in the complementarity relationships between the items. Example includes any auction of different, indivisible goods which have dependencies to each other, such as semiconductor parts, or collectables, or the right to emit some quantity of different pollutants produced by the same industrial process. The combinatorial auction for procuring a composite service is another example in this group (Leyton-Brown et al. 2000).

Bundling of complementary or substitute items allows the bidders to more fully express their preferences which often leads to greater economic efficiency (allocating items to those who value them most) and greater auction revenue (Cramton et al. 2006, p.8).

Combinatorial auctions have been proposed and/or applied for practical applications in various industries. Examples include combinatorial auctions for supply chain management (industrial procurement) (Chen et al. 2011); procurement of school meals (Olivares et al. 2012); procuring transportation (logistics) services (Sheffi 2004; Srivastava et al. 2008); allocating bus routes to private operators (Cantillon and Pesendorfer 2006); allocating airport arrival and departure slots to competing airlines (Rassenti et al. 1982); and resource allocation in the cloud (Zaman and Grosu 2013).

Combinatorial auctions can be either direct or procurement auctions. In the direct combinatorial auction, there are multiple items or service for sale. While in the combinatorial procurement auction, there is a buyer who is interested in a combination of products or services and the sellers bid to provision these products or services.

In practice, combinatorial procurement auctions have been successfully applied by online platforms for industrial procurement. Examples of sourcing companies who have implemented combinatorial procurement auctions for strategic sourcing and supply chain include Logistics.com6, CombineNet now part of SciQuest7, and TradeExtensions8. The motivations behind designing a combinatorial procurement auction have been described as:

6 _{<http://www.logistics.com/>} 7 _{<http://www.sciquest.com/>} 8 _{<http://www.tradeextensions.com/>}

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1. Cost saving: Combinatorial bids represent the complementarity or substitutability effects among the items which lead to production and/or transportation cost savings for the bidders. This eventually improves the procurement cost for the bid-taker.

2. Time efficiency: Combinatorial bidding allows all sides to instantaneously express their complex preferences for the items through package bids and saves them from the need to attend different auctions to attain what they want.

3. Impacting on the market structure: In complex procurement scenarios with many items to be procured, refusing the combinatorial bids will restrict the competition to only big suppliers who are able to offer all the items. On the other hand, combinatorial auctions allow the splitting of a big contract into smaller parts thus making it possible for smaller suppliers to enter the competition. This, in turn, can lead to more cost saving for the bid-taker (Bichler et al. 2006).

The bid-taker of the combinatorial auction (buyer in a direct auction or the seller in a reverse or procurement auction) receives a set of price offers for various combinations of auctioned items and faces the problem of choosing the set of offers which maximizes the bid-taker’s revenue or economic efficiency, as will be discussed in more detail in subsection 2.4.2.2. This problem, known as the winner determination problem (WDP), is NP-complete in the general case and intractable (Sandholm 2002). We will discuss this aspect of combinatorial auctions later in subsection 7.2.1, when discussing the limitations of our proposed auction-based approach for composite service selection.