
A Framework for Bidding in Procurement Auctions
by Jesús Palomo, David Rios Insua, Fabrizio Ruggeri
Increasing competition in the current economy is forcing companies to formally evaluate the risks of participating in an auction in order to avoid undercapitalisation. Scientists at the University Rey Juan Carlos, Madrid, and IMATICNR, have developed a general framework for addressing the issue of bid formulation in procurement auctions.
The Statistics and Decision Sciences group at the Rey Juan Carlos University (Spain) headed by Prof. David Ríos Insua, and the IMATICNR (Italy) headed by Prof. Fabrizio Ruggeri, have participated in the 'Metodi e sistemi di supporto alle decisioni' project with SnamprogettiENI, a company that frequently participates in auction processes to obtain construction contracts, eg for oil plants. The goal of this project is to improve their current approach to bid formulation by considering all the inherent uncertainties in the process. Among other things, this involves providing models for internal risks (cost uncertainty), external risks (abnormal unforseen events) and economic risks (uncertainty regarding winning the auction).
Auctions have become the most common market mechanism for allocating contracts in the modern economy. Auctions are seen as more democratic, and as such are particularly desirable for the dispersion of public contracts, and are also seen as more efficient, in the sense that the contract will be awarded to the company that values the contract most. We shall consider the case of pricesealed bid auctions, which is the type most commonly used in procurement processes.
The process currently used by the company involves numerous assumptions and allows too many decisions to rely on intuition. Furthermore, the accepted methods do not take advantage of information obtained from previous auctions (forecasting errors, experts' biases etc). These deficiencies have motivated the extension of traditional project management methods. For a given auction, the proposed framework is conceived as a sequential process, with the various uncertainties being modelled one at a time. We begin by estimating project costs with a dynamic model that allows for additional input from experts. Then, since abnormal events may arise during the development of the contract, thereby entailing additional project costs, we provide models to forecast the probability of such events, their effects, and their combined (interactive) effects. Having an appropriate cost (or sometimes duration, or performance) forecast, the company is then ready to submit a bid. As the company needs to win the auction to execute the project, a bidding strategy is developed to maximise the expected utility of the bidder. Finally, once the project is finished and the actual data arrive, we update the distributions using Bayes' rule, to incorporate the knowledge for iterations in future proposals.
The process therefore needs only to incorporate the following in order to significantly improve bid formulation:
 forecasting cost methods under normal circumstances
 forecasting cost methods under abnormal circumstances
 bidding methods.
The first step is to decompose the basic activity costs of a given project and to formulate a model for each accordingly; the project manager has beliefs about the activity cost, and asks for an expert's opinion about that cost. Specifically, the expert provides either a point estimation or an interval (symmetric or asymmetric). Using this information, the manager will then update his beliefs. The manager may also be curious about the expert's forecasting abilities, and who may need to produce a quantitative estimate of this success rate. The project cost forecasting distribution is obtained by aggregating the cost distributions of all the basic activities involved in the project.
So far, the estimation of the total cost only accounts for normal circumstances, but external risks such as labour strikes, storms and raw materials delays could also affect the project. The goal is to model the effect of such events on the basis of cost and duration, estimating the probability of the unforseen events and finding the distribution of the gravities together with their expected values. Next, we obtain the general or total gravity by combining, either according to the sum or maximum aggregation rule, these individual gravities. Finally, we estimate the additional cost due to these events. Again, the expert's opinion will be a valuable source of information, but there exist various ways in which the expert can convey his opinion, depending on project time constraints and his statistical training  from full specification of all intersections of possible events, to just specifying the most basic events.
Last, we must consider the economic risks associated with the auction process. We now apply game theory methodology to improve the bidder´s chances of winning the auction. We apply the project cost forecasting distribution obtained earlier, which accounts for internal and external risks, to formulate an optimal bidding strategy that will maximise the expected utility of the bidder. A unique Bayesian Nash equilibrium, assuming pure strategies, can be computed in the symmetric case, in the asymmetric case where bidders are risk neutral, and in the asymmetric case where bidders are risk averse, assuming an independent private values model.
This methodology has been successfully applied in offshore oil plant auctions and is currently being implemented in a decision support system with a userfriendly Web interface. We are currently working on extending the approach for duration estimates; a very relevant activity given that shorter delivery times are a key issue in assigning contracts, and control of the delivery time of subcontractors is important for companies.
Please contact:
Jesús Palomo, University Rey Juan Carlos/SpaRCIM
Tel: +34 91 6647475
Email: jpalomoescet.urjc.es
