■ Sourcing professionals buy several trillion dol-lars worth of goods and services yearly. Weintroduced a new paradigm called expressivecommerce and applied it to sourcing. It combinesthe advantages of highly expressive humannegotiation with the advantages of electronicreverse auctions. The idea is that supply anddemand are expressed in drastically greaterdetail than in traditional electronic auctionsand are algorithmically cleared. This creates aPareto efficiency improvement in the allocation(a win-win between the buyer and the sellers),but the market-clearing problem is a highlycomplex combinatorial optimization problem.We developed the world’s fastest tree searchalgorithms for solving it. We have hosted $35billion of sourcing using the technology andcreated $4.4 billion of hard-dollar savings plusnumerous harder-to-quantify benefits. The sup-pliers also benefited by being able to expressproduction efficiencies and creativity, andthrough exposure problem removal. Supply net-works were redesigned, with quantitative under-standing of the trade-offs, and implemented inweeks instead of months.

Historical Backdrop on Sourcing Sourcing, the process by which companiesacquire goods and services for their operations,entails a complex interaction of prices, prefer-ences, and constraints. The buyer’s problem isto decide how to allocate the business acrossthe suppliers.

Traditionally, sourcing decisions have beenmade through manual, in-person negotiations.The advantage is that there is a very expressive

language for finding, and agreeing to, win-winsolutions between the supplier and the buyer.The solutions are implementable because oper-ational constraints can be expressed and takeninto account. On the downside, the process isslow, unstructured, and nontransparent. Fur-thermore, sequentially negotiating with thesuppliers is difficult and leads to suboptimaldecisions. (This is because what the buyershould agree to with a supplier depends onwhat other suppliers would have been willingto agree to in later negotiations.) The one-to-one nature of the process also curtails compe-tition.

These problems have been exacerbated by adramatic shift from plant-based sourcing toglobal corporatewide (category-based ratherthan plant-based) sourcing since the mid-1990s. This transition is motivated by a corpo-ration’s desire to leverage its spending acrossplants in order to get better pricing and betterunderstanding and control of the supply chainwhile at the same time improving supplier rela-tionships. (See, for example, Smock [2004].)This transition has yielded significantly largersourcing events that are inherently more com-plex.

During this transition, there has also been ashift to electronic sourcing where supplierssubmit offers electronically to the buyer. Thebuyer then decides, using software, how toallocate the business. Advantages of thisapproach include speed of the process, struc-ture and transparency, global competition, andsimultaneous negotiation with all suppliers(which removes the difficulties associated withthe speculation about later stages of the nego-tiation process, discussed above).

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FALL 2007 45Copyright © 2007, American Association for Artificial Intelligence. All rights reserved. ISSN 0738-4602

Expressive Commerce and Its Application to Sourcing:

How We Conducted $35 Billion of Generalized

Combinatorial Auctions

Tuomas Sandholm

AI Magazine Volume 28 Number 3 (2007) (© AAAI)

The most famous class of electronic sourcingsystems—which became popular in the mid-1990s through vendors such as FreeMarkets(now part of Ariba), Frictionless Commerce(now part of SAP), and Procuri—is a reverse auc-tion. The buyer groups the items into lots inadvance and conducts an electronic descend-ing-price auction for each lot. The lowest bid-der wins. (In some cases “lowness” is not meas-ured in terms of price but in terms of an ad hocscore that is a weighted function that takes intoaccount the price and some nonprice attributessuch as delivery time and reputation.)

Reverse auctions are not economically effi-cient; that is, they do not generally yield goodallocation decisions. This is because the opti-mal bundling of the items depends on the sup-pliers’ preferences (which arise, among otherconsiderations, from the set, type, and time-varying state of their production resources),which the buyer does not know at the time oflotting. Lotting by the buyer also hinders theability of small suppliers to compete. Further-more, reverse auctions do not support side con-straints, yielding two drastic deficiencies: (1)the buyer cannot express his or her businessrules; thus the allocation of the auction isunimplementable and the “screen savings” ofthe auction do not materialize in reality, and(2) the suppliers cannot express their produc-tion efficiencies (or differentiation), and areexposed to bidding risks (for example, if thebuyer’s desired package consists of multiplelots). In short, reverse auctions assume awaythe complexity that is inherent in the problemand dumb down the events rather thanembracing the complexity and viewing it as adriver of opportunity. It is therefore not sur-prising that there are strong broad-based signsthat reverse auctions have fallen in disfavor.

The New Paradigm: Expressive Commerce

In 1997 it dawned on me that it is possible toachieve the advantages of both manual negoti-ation and electronic auctions while avoidingthe disadvantages. The idea is to allow supplyand demand to be expressed in drasticallymore detail (as in manual negotiation) whileconducting the events in a structured electron-ic marketplace where the supply and demandare algorithmically matched (as in reverse auc-tions). The new paradigm, which we call expres-sive commerce™ (or expressive competition™),was so promising that I decided to found Com-bineNet, Inc., to commercialize it.

The finer-grained matching of supply anddemand yields Pareto improvements (that is,win-win solutions) between the buyer and thesuppliers. However, matching the drasticallymore detailed supply and demand is anextremely complex combinatorial optimiza-tion problem. We developed the world’s fastestalgorithms for optimally solving it. These algo-rithms are incorporated into the market-clear-ing engine, Clear Box™, at the core of our flag-ship product, the Advanced Sourcing ApplicationPlatform (ASAP).

Expressive commerce has two sides: expres-sive bidding™ and expressive allocation evaluation(also called expressive bid taking™) (Sandholmand Suri 2001).

Expressive BiddingWith expressive bidding, the suppliers canexpress their offers creatively, precisely, andconveniently using expressive and compactstatements that are natural in the suppliers’business. Our expressive bidding takes on sev-

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Figure 1. A Relatively Simple Discount Schedule.

This screenshot is from an actual sourcing event. The scope of the trigger of the discount (STEP 4) can be different than the scope of theitems to which the discount is to be applied (STEP 5).

eral forms. ASAP supports the following formsof expressive bidding, among others, all in thesame event. These forms will be explained inthe following paragraphs.

Bidding on an arbitrary number of self-con-structed packages of items (rather than beingrestricted to bidding on predetermined lots asin basic reverse auctions). The packages can beexpressed in more flexible and more usableforms than what is supported in vanilla com-binatorial auctions. For example, the biddercan specify different prices on the items if theitems get accepted in given proportions, andthe bidder can specify ranges for these propor-tions, thus allowing a huge space of packagesto be captured by one compact expression.

Conditional discount offers. The trigger condi-tions and the effects can be specified in highlyflexible ways.

Rich forms of discount schedules. (Simplerforms of discount schedules have already beenaddressed in the literature (Sandholm and Suri2001, Sandholm and Suri 2002, Hohner et al.2003).) Figure 1 shows a simple example. Rich-er forms allow the bidder to submit multiplediscount offers and to control whether andhow they can be combined (for example,sequenced in particular ways). Discount trig-gers can be expressed as dollars or units, and asa percentage or an absolute.

A broad variety of side constraints—such ascapacity constraints (Sandholm and Suri 2001).

Multiattribute bidding (Sandholm and Suri

2001). This allows the buyer to leave the itemspecification partially open, so the supplierscan pick values for the item attributes—such asmaterial, color, and delivery date—in a waythat matches their production efficiencies. Thisis one way in which the suppliers can alsoexpress alternate items.

Free-form expression of alternates. This fostersunconstrained creativity by the suppliers.

Expression of cost drivers. In many of ourevents, the buyer collects tens or hundreds ofcost drivers (sometimes per item) from the sup-pliers. By expressing cost drivers, the biddercan concisely implicitly price huge numbers ofitems and alternates. Figures 2 and 3 illustratebidding with attributes and cost drivers.

All of these expressive bidding features ofASAP have been extensively used by Com-bineNet’s customers. ASAP supports biddingthrough web-based interfaces and throughspreadsheets. In some cases, catalog prices fromdatabases have also been used.

CombineNet’s expressive bidding is flexiblein the sense that different suppliers can bid indifferent ways, using different offer constructs.In fact, some suppliers may not be sophisticat-ed enough to bid expressively at all, yet theycan participate in the same sourcing eventsusing traditional bidding constructs in thesame system. This paves a smooth road foradoption, which does not assume suddenprocess changes at the participating organiza-tions.

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Figure 2. A Simple Example of Bidding with Alternates, Cost Drivers, Attributes, and Constraints.

This piece of screen is from an actual event for sourcing truckload transportation. The figure shows part of the bid by one bidder on oneitem.

Benefits of Expressive Bidding. The mainbenefit of expressive bidding is that it leads toa Pareto improvement in the allocation. Inbusiness terms, it creates a win-win betweenthe buyer and the suppliers. There are severalreasons for this.

First, because the suppliers and the buyercan express their preferences completely (andeasily), the market mechanism can make better(economically more efficient and less wasteful)allocation decisions, which translates to high-er societal welfare. In other words, the methodyields better matching of supply and demand

because they are expressed in more detail. Thesavings do not come from lowering suppliermargins, but from reducing economic ineffi-ciency. With expressive bidding, the supplierscan offer specifically what they are good at,and at lower prices because they end up sup-plying in a way that is economical for them.(They can consider factors such as productioncosts and capacities, raw material inventories,market conditions, competitive pressures, andstrategic initiatives.) This creates a win-winsolution between the suppliers and the buyer.For example, in the sourcing of transportation

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Figure 3. An Example of Bidding with Cost Structures and Attributes.

These screens are part of an actual event where printed labels were sourced.

services, a substantial increase in economicefficiency comes from bundling multiple deliv-eries in one route (back-haul deliveries andmultileg routes). This reduces empty driving,leading to lower transportation costs and yield-ing environmental benefits as well: lower fuelconsumption, less driver time, less frequentneed to replace equipment, and less pollution.

Second, suppliers avoid exposure risks. Intraditional inexpressive markets, the suppliersface exposure problems when bidding. Thatmakes bidding difficult. To illustrate this point,consider a simple auction of two trucking tasks:the first from Pittsburgh to Los Angeles, andthe second from Los Angeles to Pittsburgh. If acarrier wins one of the tasks, the carrier has tofactor in the cost of driving the other directionempty. Say that the cost for the task then is$1.60 per mile. On the other hand, if the carri-er gets both tasks, the carrier does not have todrive empty, and the cost is $1.20 per mile.When bidding for the first task in an inexpres-sive auction, it is impossible to say where in the$1.20–$1.60 range the carrier should bid,because the cost for the first task depends onwhether the carrier gets the second task, whichin turn depends on how other carriers will bid.Any bid below $1.60 exposes the carrier to aloss in case the carrier cannot profitably winthe second task. Similarly, bidding above $1.20may cause the carrier to lose the deal on thefirst task although it would be profitable to takeon that task in case the carrier wins the secondtask. In an expressive auction, the buyer canprice each of the tasks separately, and price thepackage of them together, so there is no expo-sure problem. (For example, the buyer can bid$1.60 per mile for the first task, $1.60 per milefor the second task, and $1.20 per mile for thepackage of both tasks. Of course, the buyer canalso include a profit margin.) Therefore bid-ding is easier: the bidder does not have to spec-ulate what other suppliers will bid in the laterauctions. Also, the tasks get allocated optimal-ly because no bidder gets stuck with an unde-sirable bundle, or misses the opportunity towin when the bidder is the most efficient sup-plier. Furthermore, when there is an exposureproblem, the suppliers hedge against it byhigher prices. Removal of the bidders’ exposureproblems thus also lowers the buyer’s procure-ment cost.

Third, by expressive bidding with side con-straints (such as capacity constraints), eachsupplier can bid on all bundles of interest with-out being exposed to winning so much thathandling the business will be unprofitable oreven infeasible. This again makes bidding easi-er because—unlike in inexpressive markets—

the supplier does not have to guess whichpackages to commit his capacity to. (In aninexpressive market, making that guessrequires counterspeculating what the othersuppliers are going to bid, because that deter-mines the prices at which this supplier can windifferent alternative packages.) This also leadsto Pareto improvements in the allocation com-pared to inexpressive markets because in thosemarkets each bidder needs to make guesses asto what parts of the business the bidder shouldbid on, and those parts might not be the partsfor which the bidder really is the most efficientsupplier.

Fourth, expressive bidding allows morestraightforward participation in marketsbecause the strategic counterspeculation issuesthat are prevalent in noncombinatorial mar-kets are removed, as discussed above. This leadsto wider access of the benefits of e-commercebecause less experienced market participantsare raised to an equal playing field withexperts. This yields an increase in the numberof market participants, which itself leads to fur-ther economic efficiency and savings in sourc-ing costs. Broader access also stems from thebuyer not lotting the items and thus facilitat-ing competition from small suppliers as well.

Fifth, in basic reverse auctions, the buyer hasto prebundle items into lots, but the buyer can-not construct the optimal lotting because itdepends on the suppliers’ preferences. Withexpressive commerce, items do not have to beprebundled. Instead, the market determinesthe optimal lotting (specifically, the optimizerdetermines the optimal allocation based on theexpressive bids from the suppliers and theexpressions of constraints and preferencesfrom the buyer). This way, the economicallymost efficient bundling is reached, weeks arenot wasted on prebundling, and suppliers thatare interested in different bundles compete. Asa side effect, small suppliers’ bids together endup competing with large suppliers.

Sixth, expressive bidding fosters creativityand innovation by the suppliers. This aspect ishighly prized by both the suppliers and buyers.It can also yield drastic savings for the buyerdue to creative construction of lower-cost alter-nates.

Overall, expressive bidding yields both low-er prices and better supplier relationships. Inaddition to the buyers (our customers), alsosuppliers are providing very positive feedbackon the approach. They especially like (1) thatthey also benefit (unlike in traditional reverseauctions where their profit margins getsqueezed), (2) that they can express their pro-duction efficiencies, and (3) that they can

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express differentiation and creative offers. Infact, suppliers like expressive commerce somuch that they agree to participate in expres-sive commerce even in events that they boy-cotted when basic reverse auctions had beenattempted. Furthermore, perhaps the best indi-cation of supplier satisfaction is the fact thesuppliers are recommending the use of Com-bineNet to buyers.

The benefits of expressiveness can be furtherenhanced by multiple buyers conducting theirsourcing in the same event. This provides anopportunity for the bidders to bundle acrossthe demands of the buyers and also mitigatesthe exposure risks inherent in participating inseparate events. As an example, in Spring 2005CombineNet conducted an event where Proc-ter & Gamble and its two largest customers,Walmart and Target, jointly sourced theirNorth America–wide truckload transportationservices for the following year (Sandholm et al.2006). This enabled the carriers to constructbeneficial backhaul deliveries and multilegroutes by packaging trucking lanes across thedemand of the three buyers. (This was a hugeevent. Procter & Gamble’s volume aloneexceeded $885 million.)

Expressive Allocation EvaluationThe second half of expressive commerce isexpressive allocation evaluation, where thebuyer expresses preferences over allocationsusing a rich, precise, and compact languagethat is natural in the buyer’s business. It can beused to express legal constraints, business rules,prior contractual obligations, and strategicconsiderations.

In our experience, different types of sideconstraints are a powerful form of expressive-ness for this purpose. For example, the buyercan state: “I don’t want more than 200 winners(in order to avoid overhead costs),” “I don’twant any one supplier to win more than 15percent (in order to keep the supply chain com-petitive for the long term),” “I want minoritysuppliers to win at least 10 percent (becausethat is the law),” “Carrier X has to win at least$3 million (because I have already agreed tothat),” and so on. ASAP supports hundreds oftypes of side constraints.

ASAP also has a rich language for the buyerto express how item attributes (such as deliverydate or transshipment specifications) and sup-plier attributes (such as reputation) are to betaken into account when determining the allo-cation of business (Sandholm and Suri 2006).

A professional buyer—with potentially nobackground in optimization—can set up a sce-nario in ASAP by adding constraints and prefer-

ences through an easy-to-use web-based inter-face. (A simple example is shown in Figure 4.)To set up each such expression, the buyer firstchooses the template expression (for example,“I don’t want more than a certain number ofwinners,” or “I want to favor incumbent suppli-ers by some amount”) from a set of expressionsthat have been deemed potentially importantfor the event in question. The buyer then selectsthe scope to which that expression shouldapply: everywhere, or to a limited set of items,bid rounds, product groups, products, sites, andbusiness groups. Finally, the buyer selects theexact parameters of the constraint, for example,exactly how many winners are allowed. Con-straints and preferences can also be uploadedfrom business rule databases. Once the buyerhas defined the scenario consisting of side con-straints and preferences, the buyer calls the opti-mizer in ASAP to find the best allocation of busi-ness to suppliers under that scenario.

ASAP takes these high-level supply anddemand expressions, automatically convertsthem into an optimization model, and usessophisticated tree search algorithms to solvethe model. CombineNet has faced scenarioswith more than 2.6 million bids (on 160,000items, multiple units of each) and more than300,000 side constraints, and solved them tooptimality.

Benefits of Expressive Allocation Evalu-ation. Through side constraints and prefer-ence expressions, the buyer can include busi-ness rules, legal constraints, logisticalconstraints, and other operational considera-tions to be taken into account when determin-ing the allocation. This makes the auction’sallocation implementable in the real world: theplan and execution are aligned because theexecution considerations are captured in theplanning.

Second, the buyer can include prior (forexample, manually negotiated) contractualcommitments into the optimization. Thisbegets a sound hybrid between manual andelectronic negotiation. For example, the buyermay have the obligation that a certain supplierhas to be allocated at least 80 truckloads. Thebuyer can specify this as a side constraint inASAP, and ASAP will decide which 80 truck-loads (or more) are the best ones to allocate tothat supplier in light of all other offers, sideconstraints, and preferences. This again makesthe allocation implementable. (A poor person’sway of accomplishing that would be to manu-ally earmark some of the business to the priorcontracts. Naturally, allowing the system to dothat earmarking with all the pertinent infor-mation in hand yields better allocations.)

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Third, the buyer obtains a quantitativeunderstanding of the trade-offs in his supplychain by conducting what-if scenario naviga-tion; that is, by changing side constraints andpreferences and reoptimizing, the buyer canexplore the trade-offs in an objective manner.For example, the buyer may add the side con-straint that the supply base be rationalizedfrom 200 to 190. The resulting increase in pro-curement cost then gives the buyer an under-standing of the trade-off between cost andpractical implementability. As another exam-ple, the buyer might ask: If I wanted my aver-age supplier delivery-on-time rating to increaseto 99 percent, how much would that cost? As athird example, the buyer might see what wouldhappen if the buyer allowed a supplier to winup to 20 percent of the business instead of only15 percent. The system will tell the buyer how

much the procurement cost would decrease.The buyer can then decide whether the savingsoutweighs the added long-term strategic riskssuch as vulnerability to that supplier’s defaultand the long-term financial downside of allow-ing one supplier to become dominant. In ASAP,the buyer can change/add/delete any numberof side constraints and preferences in betweenoptimizations.

Fourth, quantitative understanding of thetrade-offs also fosters stakeholder alignment onthe procurement team, because the team mem-bers with different preferences can discussbased on facts rather than opinions, philoso-phies, and guesswork.

Time to Contract in Expressive CommerceThe time to contract is reduced from several

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Figure 4. A User Interface for Expressive Allocation Evaluation by the Bid Taker.

Every sourcing event has different expressiveness forms (selected from a library or preconfigured in a template). This particular sourcingevent was one of the simpler ones in that relatively few expressions of constraints and preferences were included in the user interface. Thebuyer uses the interface as follows. First, on the left (Step 1), the buyer selects which one of the expressiveness forms the buyer wants towork on and sets the parameters for that form. Then, on the right (Step 2) the buyer selects the scope to which this rule is to be applied. InStep 3, the buyer presses the “Add” button to add the rule, and a restatement of the rule appears in natural language for verification (notshown). The buyer can then add more rules to the same scenario by repeating this process. Finally, the buyer presses the “Optimize” but-ton (not shown) to find the optimal allocation for the scenario. This triggers the automated formulation of all these constraints and pref-erences—together with all the bid information that the bidders have submitted—into an optimization problem, and the solving of the prob-lem through advanced tree search.

months to weeks because no manual lotting isrequired, all suppliers can submit their offers inparallel, what-if scenarios can be rapidly gener-ated and analyzed, and the allocation is imple-mentable as is. This causes the cost savings tostart to accrue earlier, and decreases the humanhours invested.

Automated Item ConfigurationAn additional interesting aspect of biddingwith cost drivers and alternates (for example,using attributes) is that the market-clearing(aka winner determination) algorithm not onlydecides who wins but also ends up optimizingthe configuration (setting of attributes) foreach item. In deciding this, the optimizer, ofcourse, also takes into account the buyer’s con-straints and preferences.

Automated Supply Chain ConfigurationIn many sourcing events, the winner determi-nation also ends up optimizing the supplychain multiple levels upstream from the buyer.For example, in an event where Procter & Gam-ble sourced in-store displays using our hostingservice and technology, we sourced items fromdifferent levels of the supply chain in oneevent: buying colorants and cardboard of dif-ferent types, buying the service of printing,buying the transportation, buying the installa-tion service, and so on (Sandholm et al. 2006).Some suppliers made offers for some of thoseindividual items while others offered completeready-made displays (which are, in effect, pack-ages of the lower-level items), and some bid forpartial combinations. The market clearingdetermined the lowest-cost (adjusted for theProcter & Gamble’s constraints and prefer-ences) solution and thus, in effect, configuredthe supply chain multiple levels upstream.

Expressive Commerce as a Generalization of Combinatorial AuctionsA relatively simple early form of expressivecommerce was a combinatorial reverse auction(Sandholm et al. 2002), where the only form ofexpressiveness that the suppliers have is pack-age bidding, and the buyer has no expressive-ness. A predecessor of that was a combinatorialauction where the bidders are the buyers (andthere is only one unit of each item and no sideconstraints). Combinatorial auctions (Rassenti,Smith, and Bulfin 1982; Sandholm 1993; Sand-holm 2002b; Ledyard, Porter, and Rangel 1997;Rothkopf, Pekec, and Harstad 1998; Kwasnicaet al. 2005; Sandholm et al. 2005; Sandholmand Suri 2003; Hoos and Boutilier 2000;

Boutilier 2002; and deVries and Vohra 2003)enable bidders to express complementarityamong items (the value of a package beingmore than the sum of its parts) through pack-age bids. Substitutability (the value of a pack-age being less than the sum of its parts) canalso be expressed in some combinatorial auc-tions, usually using different languages forspecifying mutual exclusivity between bids(Sandholm 2002a; Fujishima, Leyton-Brown,and Shoham 1999; Sandholm 2002b; Nisan2000; and Hoos and Boutilier 2001).

Expressiveness leads to more economicalallocations of the items because bidders do notget stuck with partial bundles that are of lowvalue to them. This has been demonstrated, forexample, in auctions for bandwidth (McMillan1994, McAfee and McMillan 1996), transporta-tion services (Sandholm 1993, Sandholm 2000,Sandholm 1991, and Caplice and Sheffi 2003),pollution rights, airport landing slots (Rassen-ti, Smith, and Bulfin 1982), and carrier-of-last-resort responsibilities for universal services(Kelly and Steinberg 2000).

However, package bids and exclusivity con-straints are too impoverished a language forreal-world sourcing. While any mapping frombundles to real numbers can be expressed inthat language in principle, the real-world pref-erences in sourcing cannot be easily, naturally,and concisely expressed in it. Starting in 1997,we tackled this challenge and generalized theapproach to expressive commerce, with thelanguage constructs discussed above. Similarapproaches have recently been adopted byothers but only for drastically less complex(orders of magnitude smaller and less expres-sive) events (Hohner et al. 2003, Metty et al.2005).

The use of our richer expressiveness forms(rather than mere canonical package bids withexclusivity constraints) is of key importance forseveral reasons: (1) Bidders can express theirpreference in the language that is natural intheir domain. (2) Bidders can express theirpreferences concisely. To illustrate this point,consider the following simple example. A bid-der has no production efficiencies and thus hasa price for each item regardless of what otheritems the buyer produces. However, the bidderhas a capacity constraint. In our bidding lan-guage, the bidder can simply express a price foreach item and a capacity constraint. In con-trast, in the classical combinatorial auctionbidding languages, the supplier would have tosubmit bids for an exponential number ofpackages. (3) Due to the conciseness, the bidsare easy to communicate to the bid taker. (4)Our bidding constructs maintain the natural

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structure of the problem (rather than normal-izing the structure away into a format that onlyallows package bids with exclusivity con-straints). The clearing algorithms take advan-tage of that structure in many ways, for exam-ple, in generating cutting planes, decidingwhat variables to branch on, and so on.

Tree Search to Enable Expressive Commerce

A significant challenge in making expressivecommerce a reality is that the expressivenessmakes the problem of allocating the businessacross the suppliers an extremely complex com-binatorial optimization problem. Specifically,the clearing problem (aka winner determina-tion problem) is that of deciding which bids toaccept and reject (and to what extent in thecase of partially acceptable bids) so as to mini-mize sourcing cost (adjusted for preferences)subject to satisfying all the demand and all sideconstraints. Even in the vanilla combinatorialreverse auction where the only form of biddingis package bidding, and no side constraints orpreferences are allowed, the clearing problem isNP-complete and inapproximable in the worstcase in polynomial time (Sandholm et al. 2002).Expressive commerce is a much richer problem;thus the NP-hardness and inapproximabilitycarry over. (Müller, Lehmann, and Sandholm[2006] review the worst-case complexity of theclearing problem of different variants of combi-natorial auctions.) Thus sophisticated tech-niques are required.

In fact, prior to ASAP, no technology wascapable of solving clearing problems of thescale and expressiveness that our customerswanted to be able to support; for example,Hohner et al. (2003) found integer program-ming techniques to be effective for problemsonly as large as 500 items and 5000 bids. In2001, P&G gave us a trial instance of truckingservices sourcing that took a competing opti-mization product 30 minutes to solve. ASAPsolved it optimally in 9 seconds. While thatwas already a decisive speed difference, sincethat time our technology development hasyielded a further speed improvement of two tothree orders of magnitude.

There is significant structure in the expres-sive commerce problem instances, and it isparamount that the optimizer be able to takeadvantage of the structure. Mixed integer pro-gramming (MIP) techniques for tree search arequite good at this, and ASAP takes advantage ofthem. However, the techniques embodied inthe leading general-purpose MIP solvers aloneare not sufficient for the clearing problem.

ASAP uses sophisticated tree search to findthe optimal allocation. Given that the problemis NP-complete, in the worst case the run timeis superpolynomial in the size of the input(unless P = NP). However, in real-world sourc-ing optimization, the algorithms run extreme-ly fast: the median run time is less than a sec-ond, and the average is 20 seconds, with someinstances taking days. The algorithms are alsoanytime algorithms: they provide better andbetter solutions during the search process.

I began the algorithm development in 1997,and CombineNet now has 16 people workingon the algorithms, half of them full time. Theteam has tested hundreds of techniques (somefrom the AI and operations research literatureand some invented at CombineNet) to seewhich ones enhance speed on expressive com-merce clearing problems. Some of the tech-niques are specific to market clearing, whileothers apply to combinatorial optimizationmore broadly. We published the first genera-tions of our search algorithms (Sandholm2002a, Sandholm and Suri 2003, and Sand-holm et al. 2005). The new ideas in these algo-rithms included different formulations of thebasic combinatorial auction clearing problem(branching on items [Sandholm 2002a],branching on bids [Sandholm and Suri 2003,Sandholm et al. 2005], and multivariablebranching [Gilpin and Sandholm 2007]), upperand lower bounding across components indynamically detected decompositions (Sand-holm and Suri 2003, Sandholm et al. 2005),sophisticated strategies for branch questionselection (Sandholm 2006, Sandholm 2002a,Sandholm and Suri 2003, and Sandholm et al.2005), dynamically selecting the branch selec-tion strategy at each search node (Sandholm2006, Sandholm et al. 2005), the information-theoretic approach to branching in search(Gilpin and Sandholm 2007), sophisticatedlookahead techniques (Sandholm 2006, Gilpinand Sandholm 2007), solution seeding (Sand-holm 2006), primal heuristics (Sandholm 2006,Sandholm et al. 2005), identifying and solvingtractable cases at nodes (Sandholm and Suri2003; Sandholm et al. 2005; Sandholm 2006;and Conitzer, Derryberry, and Sandholm2004), techniques for exploiting part of theremaining problem falling into a tractable class(Sandholm 2006, Sandholm and Suri 2003),domain-specific preprocessing techniques(Sandholm 2002a), fast data structures (Sand-holm 2002a, Sandholm and Suri 2003, andSandholm et al. 2005), methods for handlingreserve prices (Sandholm 2002a, Sandholmand Suri 2003), and incremental winner deter-mination and quote computation techniques

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(Sandholm 2002a). Sandholm (2006) providesan overview of the techniques.

We have also invented a host of techniquesin the search algorithms that we have decidedto keep proprietary for now. They include dif-ferent formulations of the clearing problem,new branching strategies, custom cutting planefamilies, cutting plane generation and selec-tion techniques, and so on.

Since 2002 we have also been using machinelearning methods to predict how well differenttechniques will perform on the instance athand. (For this purpose, the instance is repre-sented by about 50 hand-selected numeric fea-tures.) This information can be used to dynam-ically select the technique for the instance athand, to give time estimates to the user, and soon. Our solver has several dozen importantparameters and each of them can take on sev-eral values. Therefore, our machine learningapproach of setting the parameters well on aninstance by instance basis is significantly morechallenging and more powerful than usingmachine learning to select among a handful ofhardwired solvers, an approach that has beensuccessfully pursued in academia in parallel(for example, Leyton-Brown, Nudelman, andShoham [2006]).

While the literature on combinatorial auc-tions has mainly focused on a variant wherethe only form of expressiveness is package bid-ding (sometimes supplemented with mutualexclusion constraints between bids), in ourexperience with sourcing problems the com-plexity is dominated by rich side constraints.Thus we have invested significant effort intodeveloping techniques that deal with side con-straints efficiently. CombineNet has faced sev-eral hundred different types of real-world sideconstraints. ASAP supports all of them. Weabstracted them into eight classes from an opti-mization perspective so the speed improve-ments that we build into the solver for a typeof side constraint get leveraged across all sideconstraint types within the class.

The resulting optimal search algorithms areoften 10,000 times faster than those of others.The main reason is that CombineNet special-izes on a subclass of MIP problems and has32,000 real-world instances on which toimprove its algorithms. The speed has allowedour customers to handle drastically larger andmore expressive sourcing events. The eventshave sometimes had more than 2.6 millionbids (on 160,000 items, multiple units of each)and more than 300,000 side constraints.

The state-of-the-art general-purpose MIPsolvers are inadequate, as is, also due to numer-ic instability. They err on feasibility, optimality,

or both, on about 4 percent of the sourcinginstances. We have invested significant efforton stability, yielding techniques that are sig-nificantly more robust.

Hosted Optimization forSourcing Professionals

CombineNet’s backend clearing engine, Clear-Box, is industry independent, and the interfaceto it is through our Combinatorial ExchangeDescription Language (CEDL), an XML-basedlanguage that allows ClearBox to be applied toa wide variety of applications by CombineNetand its partners (see figure 5).

Intuitive web-based interfaces designed forthe buyer and for the suppliers bring the pow-er of optimization to users with expertise insourcing, not in optimization. The usersexpress their preferences through interfacesthat use sourcing terminology. The interfacessupport simple click-through interaction ratherthan requiring the user to know any syntax.The approach allows sourcing professionals todo what they are best at (incorporating sourc-ing knowledge such as strategic and opera-tional considerations) and the optimizer to dowhat it is best at (sifting through huge numbersof allocations to pick the best one).

For every event, separate front-ends are con-figured that support only those bidding andallocation evaluation features that are appro-priate for that event. This makes the user inter-faces easier and more natural to use by sourcingprofessionals. User training typically takes afew hours. New front ends typically take froma few hours to a couple of weeks to go fromproject specification to deployment.

The user interfaces feed CEDL into ClearBox,and ClearBox then automatically formulatesthe optimization problem for the search algo-rithms. This contrasts with the traditionalmode of using optimization, where a consult-ant with optimization expertise builds themodel. The automated approach is drasticallyfaster (seconds rather than months) and avoidserrors.

Our web-based products and applicationservice provider (ASP) business model makeoptimization available on demand. No client-side software installation is necessary. This alsoavoids hardware investments by customers. Webuy the hardware and leverage it across cus-tomers, each with temporary load. (On manyinstances the search trees exceed 2 gigabytes ofRAM, rendering 32-bit architectures unusableand requiring a 64-bit architecture.) See figure6. The ASP model allows us quickly and trans-parently to tune our algorithms and to provide

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enhancements to all customers simultaneous-ly. We also offer the technology through con-sulting firms.

Market DesignWhile we attribute the bulk of the savings tothe application of optimization to sourcing,another important factor is market design:what forms of expressiveness are allowed, whatform of feedback is given to bidders during theevent, and so on. ASAP supports sealed bidevents (winners are determined at the end),events that have a (usually small) number ofrounds (winners are determined and feedbackprovided at the end of each round), and “live”events (winners are determined and feedbackprovided every time any participant expressesanything new).

Scenario NavigationThe buyer is typically not an individual but anorganization of several individuals with differ-ent preferences over allocations. Finance peo-ple want low sourcing cost, plant managerswant small numbers of suppliers, marketing

people want a high average carrier-delivery-on-time rating, and so on. ASAP enables the organ-ization to better understand the availabletrade-offs. Once the bids have been collected,the buyer conducts scenario navigation. Ateach step of that process, the buyer specifies aset of side constraints and preferences (thesedefine the scenario), and runs the optimizer tofind an optimal allocation for that scenario.This way the buyer obtains a quantitativeunderstanding of how different side con-straints and preferences affect the sourcing costand all other aspects of the allocation.

CombineNet has found that a buying organ-ization will navigate an average of 100 scenar-ios per sourcing event. (The maximum seen todate had 1107.) To navigate such large num-bers of scenarios, fast clearing is paramount.

Rapid clearing allows scenario navigation tobe driven by the actual data (offers). In con-trast, most prior approaches required the sce-nario (side constraints and preferences, if any)to be defined prior to analysis; there were insuf-ficient time and expert modeling resources totry even a small number of alternative scenar-ios. Data-driven approaches are clearly superi-or because the actual offers provide accuratecosts for the various alternative scenarios.

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Figure 5. Advanced Sourcing Application Platform (ASAP).

The platform is hosted on a server farm with multiple instantiations of each component. ASAP also includes modules for clearing manage-ment, server farm management, secure databases, and so on (not shown).

User Interface Application Event management by the buyer(s) Bidding by the suppliers Analysis by the buyer(s)

Industry-specific templateIndustry-specific template

Industry-specific template

Combinatorial Exchange DescriptionLanguage (CEDL™)

ClearBox™ (clearing engine) Automated problem formulation Sophisticated tree search

The next generation of ASAP will also sup-port automated scenario navigation. Comparedto basic scenario navigation, discussed above,it enables a more systematic and less wastefulnavigation of the scenario space. The systemqueries the sourcing team about their prefer-ences, using, for example, trade-off queries(“how much hassle would an extra supplier bein dollars?—give me an upper or lowerbound”) and comparison queries (“which ofthese two allocations do you prefer?”). The sys-tem decides the queries to pose in a data-direct-ed way so as to ask the team to refine its pref-erences only on an as-needed basis. (This isdesirable because internal negotiation in theteam is costly in terms of time and goodwill.)Specifically, based on all the offers that the sup-pliers have submitted, and all answers to previ-ous queries, the system strives to minimize

maximum regret. At each iteration of automat-ed scenario navigation, the system finds arobust solution that minimizes maximumregret (the regret is due to the fact that thesourcing team has not fully specified its prefer-ences, so for some preferences that are still con-sistent with the answers so far, the system’s rec-ommended allocation is not optimal). As theother step of each iteration, the system poses aquery to refine the team’s preferences in orderto be able to reduce the maximum regret fur-ther. The maximum regret also provides aquantitative measure of when further negotia-tion within the team is no longer worth it, andthe team should implement the current robustallocation. CombineNet pioneered automatedscenario navigation, including its differentdesign dimensions and algorithms (Boutilier,Sandholm, and Shields 2004). The optimiza-

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Figure 6. CombineNet’s Hosting Architecture Now Includes Hundreds of Computers, Hardware Load Balancers, Redundant Internet, and So On.

Other aspects of the hosting include 24/7 monitoring of the hosting infrastructure, backup power from a generator, measures against over-heating and fire, and physical security against unauthorized entry.

trade-offs in a data-driven way andalign the stakeholders in the buyingorganization. See also Sandholm et al.(2006) and case studies at www.Com-bineNet.com.

Today CombineNet employs 130full time (about half of them in engi-neering) and a dozen academics asadvisors. The company has operationson four continents. It is headquarteredin Pittsburgh, Pennsylvania, USA,with European headquarters in Berlin,Germany. It also has offices in Brus-sels, Belgium; Hamburg, Germany;Tokyo, Japan; and Beijing, China.

AcknowledgmentsI thank the CombineNet employeesfor helping make this vision a reality.Special thanks go to Subhash Suri,David Levine, Tony Bonidy, Paul Mar-tyn, Andrew Gilpin, Rob Shields,Bryan Bailey, Andrew Fuqua, DavidParkes, George Nemhauser, CraigBoutilier, and Egon Balas. Com-bineNet, Expressive Bidding, Expres-sive Competition, Expressive Com-merce, Expressive Bid Taking,ClearBox, Combinatorial ExchangeDescription Language, and CEDL aretrademarks of CombineNet, Inc.

ReferencesBoutilier, C. 2002. Solving ConciselyExpressed Combinatorial Auction Prob-lems. In Proceedings of the Eighteenth Nation-al Conference on Artificial Intelligence. MenloPark, CA: AAAI Press.

Boutilier, C.; Sandholm, T.; and Shields, R.2004. Eliciting Bid Taker Nonprice Prefer-ences in (Combinatorial) Auctions. In Pro-ceedings of the Nineteenth National Confer-ence on Artificial Intelligence. Menlo Park,CA: AAAI Press.

Caplice, C., and Sheffi, Y. 2003. Optimiza-tion-Based Procurement for TransportationServices. Journal of Business Logistics 24(2):109–128.

Conitzer, V.; Derryberry, J.; and Sandholm,T. 2004. Combinatorial Auctions withStructured Item Graphs. In Proceedings ofthe Nineteenth National Conference on Artifi-cial Intelligence. Menlo Park, CA: AAAI Press.

de Vries, S., and Vohra, R. 2003. Combina-torial Auctions: A Survey. INFORMS Journalon Computing 15(3): 284–309.

Fujishima, Y.; Leyton-Brown, K.; andShoham, Y. 1999. Taming the Computa-tional Complexity of Combinatorial Auc-tions: Optimal and ApproximateApproaches. In Proceedings of the Sixteenth

tion problem of finding the mostrobust allocation is even more com-plex than the clearing problem dis-cussed in most of this paper. We havedeveloped a prototype of automatedscenario navigation, and will solicitcustomer feedback soon.

ImpactThe new sourcing paradigm and tech-nology has already had significantimpact. The technology developmentbegan in 1997 and CombineNet wasfounded in 2000. Between December2001 and now (December 2006),CombineNet has used ASAP to host447 highly combinatorial procure-ment events, totaling a spend of $35billion. The 60 plus buyer companieswere mostly among the Global 1000.A total of more than 12,000 suppliercompanies bid in our system. Theindividual events ranged from $2 mil-lion to $1.6 billion, representing themost complex combinatorial auctionsever conducted. They spanned a broadrange of categories such as transporta-tion (truckload, less-than-truckload,ocean freight, dray, bulk, intermodal,small parcel, air freight, train, fleet,freight forwarding, and other), directmaterials (sugars and sweeteners,meat, vegetables, honey, starches, col-orants, fibers and nonwovens, steel,fasteners, solvents, chemicals, casings,resins, and polymers), packaging (cansand ends, corrugates, corrugated dis-plays, flexible film, folding cartons,labels, foam trays and pads, caps andclosures, shrink and stretch films,bags, pulp, pallets, and printedinstructions), indirect materials (man-agement, repair, and operations,[MRO] [electrical supplies, filters, pipesand valves and fittings, power trans-missions, pumps, safety supplies,office supplies, lab supplies, file fold-ers, solvents, and furnishings], chemi-cals [cylinder gasses, fuels, and other],technology [laptops and desktops andcameras], leased equipment, fleet vehi-cles, and promotional items, and serv-ices (security, janitorial, legal, patentand trademark, consulting, equipmentmaintenance, temp labor, marketing,customization, insurance, shuttlingand towing, warehousing, prepress,and advertising), and healthcare

(pharmaceuticals as well as medicaland surgical equipment and supplies),and telecommunication (sourcingwireless plans for employees of com-panies).

On the $35 billion spend, Com-bineNet delivered hard-dollar savingsof $4.4 billion to its customers in low-ered sourcing costs. The savings weremeasured compared to the prices thatthe buyer paid for the same items theprevious time the buyer sourced them(usually 12 months earlier). The $4.4billion is the implementable savingsthat the system yielded after the buy-er had applied side constraints andpreferences; the unconstrained sav-ings (that is, the savings arising fromexpressive bidding before the buyerexpresses constraints and preferences)was $5.4 billion. The savings figure isremarkable especially taking intoaccount that during the same timeperiod, the prices in the largest seg-ment, transportation, increased by 6–9 percent in the market overall.

The savings number does notinclude the savings obtained by sup-pliers, which are harder to measurebecause the suppliers’ true cost struc-tures are proprietary. However, there isstrong evidence that the suppliers alsobenefited, so a win-win was indeedachieved. First, suppliers that haveparticipated in expressive commerceevents are recommending the use ofthat approach to other buyers. Second,on numerous occasions, suppliers thatboycotted reverse auctions came backto the “negotiation table” once expres-sive commerce was introduced. Third,suppliers are giving very positive feed-back about their ability to express dif-ferentiation and provide creative alter-natives.

The savings number also does notinclude savings that stem fromreduced effort and compression of theevent timeline from months to weeksor even days.

The cost savings were achievedwhile at the same time achieving theother advantages of expressive com-merce discussed above, such as bettersupplier relationships (and better par-ticipation in the events), redesign ofthe supply chain, implementable solu-tions that satisfy operational consider-ations, and solutions that strike the

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Tuomas Sand-holm is a professorin the ComputerScience Depart-ment at CarnegieMellon Universityand founder, chair- man, and chief sci-entist of Com-

bineNet, Inc. He received Ph.D. and M.S.degrees in computer science from the Uni-versity of Massachusetts at Amherst in 1996and 1994. He earned an M.S. (B.S. included)with distinction in industrial engineeringand management science from the HelsinkiUniversity of Technology, Finland, in 1991.He has published more than 250 papers onelectronic commerce, game theory, artificialintelligence, multiagent systems, auctionsand exchanges, automated negotiation andcontracting, coalition formation, voting, safeexchange, normative models of boundedrationality, resource-bounded reasoning,machine learning, networks, and combina-torial optimization. Several of his systemshave been commercially fielded. He receivedthe NSF CAREER Award in 1997, the inaugu-ral ACM Autonomous Agents ResearchAward in 2001, the Alfred P. Sloan Founda-tion Fellowship in 2003, and the IJCAI Com-puters and Thought Award in 2003.

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