On the distribution of bids for construction contract auctions

Abstract

The statistical distribution representing bid values constitutes an essential part of many auction models and has involved a wide range of assumptions, including the Uniform, Normal, Lognormal and Weibull densities. From a modelling point of view, its goodness is defined by how well it enables the probability of a particular bid value to be estimated -a past bid for ex-post analysis and a future bid for ex-ante (forecasting) analysis. However, there is no agreement to date of what is the most appropriate form and empirical work is sparse. Twelve extant construction data-sets from four continents over different time periods are analysed in this paper for their fit to a variety of candidate statistical distributions assuming homogeneity of bidders (ID not known). The results show there is no one single fit-all distribution, but that the 3p Log-Normal, Fréchet/2p Log-Normal, Normal, Gamma and Gumbel generally rank the best ex-post and the 2p Log-Normal, Normal, Gamma and Gumbel the best ex-ante -with ex-ante having around three to four times worse fit than ex-post. Final comments focus on the results relating to the third and fourth standardized moments of the bids and a post hoc rationalization of the empirical outcome of the analysis.

Finite-Sample Average Bid Auction

“…Friedman, 1956;Hossein Bor, 1977;Skitmore, 2014;Takano et al, 2014). In a more recent paper, Ballesteros-Pérez and Skitmore (2017) shows Gamma distribution is among the distributions that provide the best fit to the empirical auction data.…”

Standard Deviation of Bids for Construction Contract Auctions

“…The characteristics of these datasets are summarized in Table 1. Access to the raw data of all datasets is possible via the supplemental online material and from the original sources stated in the second column of Table 1 (Ballesteros-Pérez et al 2012a, 2015aBallesteros-Pérez and Skitmore 2017;Brown 1986;Drew 1995;Fu 2004;Shaffer and Micheau 1971;Skitmore 1991Skitmore , 1981Skitmore , 1986.…”

“…However, we are not interested here in inferring the profits from the submitted bids, but mostly in predicting the expected value of the bids. In this respect, there have been several empirical studies identifying a strong mathematical correlation between the bidders' cost estimates and the average bid of a past auction (Ballesteros-Pérez et al 2012a;Ballesteros-Pérez and Skitmore 2017). Figure 1 shows an example of this mathematical relationship in grey-colored dots and grey dashed regression lines.…”

“…Uniform, Normal, Weibull, Lognormal, and Gamma) (Skitmore 2014). However, Ballesteros and Skitmore (2017), in performing an extensive empirical study, demonstrated that the Lognormal distribution offers the best fit in most situations. Hence, this distribution should be the first choice when modelling the set of bids submitted by different bidders to a single auction.…”

Bidders Recommender for Public Procurement Auctions Using Machine Learning: Data Analysis, Algorithm, and Case Study with Tenders from Spain

“…ere is extensive literature about tender evaluation (also called bidding selection methods) for the selection of the optimal supplier in public procurement [33] with different techniques such as the economic scoring formulas [34], data envelopment analysis [35] or multicriteria decision making [36,37], and where multiple bidders are evaluated on the basis of price and quality [38]. In particular, the most studied public procurement auctions are related to construction, i.e., distribution of bids [39], bidding competitiveness and position performance [40], strategic bidding [41], tender evaluation and contractor selection [42,43], and empirical analysis in countries such as Slovakia [44]. ere are almost no studies which include all kinds of business sectors and a large volume of tenders.…”