تشخیص مناقصه غیرعادی در مزایده های تأمین تجهیزات

Procurement auctions may be affected by abnormally low bids, whose acceptance may have negative consequences on the auctioneer. A method, based on the average submitted bid, is considered to detect such anomalous bids and aid the auctioneer in the possible rejection decision. Analytical expressions or simulation results are provided for the detection probability and for the false alarm probability. The performances heavily depend on the number of tenderers and on the dispersion of bid values. Both performance indices improve as the number of tenderers grows and generally degrade as the dispersion grows. The presence of multiple anomalous bids leads to a significant worsening of the performance, while courtesy bids raise both the false alarm probability and the detection probability. The use of the average-bid criterion, though officially endorsed in national legislations, is therefore recommended as a strongly precautionary criterion, i.e. when the need to avoid anomalous bids is considered much more relevant than the costs associated to deeper investigation of anomalous bids or to the erroneous rejection of regular bids.

Procurement of goods, services, or public works is often accomplished by reverse auctions, where suppliers provide their competitive biddings to a buyer [7] and [8]. Each supplier indicates the minimum price at which it is willing to undertake the work or provide the goods/services. Through this competition auctions appear as an effective way of reducing prices for the buyer. Since the assignment is typically awarded to the supplier providing the lowest bid, each tenderer is spurred to provide the lowest possible bid, taking into account the expected level of competition and its expected rate of return (we assume anyway that competitors are not informed of the bids of one another, which could lead to forms of cheating as described in [27]). However, in some circumstances the behaviour of the tenderer may deviate from these guidelines. For example, it may be in desperate need of obtaining a contract, though it may turn into a financial loss. Or it may aim at ousting a potential competitor (the phenomenon of predatory bidding [1]). In some cases it may even present a non-competitive bid, i.e. a bid just a bit higher than the expected competitors so to have a very small probability of winning (the phenomenon of cover pricing), with the aim of staying in favour with the auctioneer by showing interest in the auction (hence such bids are also known as courtesy bids) [31]. In all these cases the tenderer presents an anomalous bid, whose value has been set by a line of reasoning different from that of regular competitors. Such anomalous bids represent a distortion in the regular execution of an auction. In particular, abnormally low bids, leading to awarding the contract to a supplier that could end up not providing the goods/services, are a cause of deep concern and have come to the attention of the European Union [13]. The negative consequences on the auctioneer's activity can be avoided if the anomalous bids are detected and their submitters subject to a deeper investigation, hence the need for a criterion to identify anomalous bids and support the auctioneer in the rejection decision. Decision support systems are an established tool to aid the auctioneer in auction operations such as this [25]. In the statistical literature observations that stand outside the bulk of the data (a characteristic common to both abnormally low bids and courtesy bids) are typically designated as outliers. Many statistical tests have been proposed for the general problem of identifying and removing outliers. Two surveys of such methods can be found in [2] and [34], while the most prominent one is described in the seminal paper by Grubbs [16] and [35]. In addition, some tests have been devised for the specific purpose of detecting bids due to cover pricing (i.e. abnormally high) and have been examined e.g. in [19], [30], [31] and [33]. Instead a number of schemes, typically different from the ones above mentioned, have been introduced in the grey literature for the detection of abnormally low bids. Examples are the national regulations in Spain [20] and [21], Italy [28], Germany, and Turkey [37]. However, the introduction of these schemes has not been accompanied by a proper evaluation of their performances, namely of their capability to detect anomalous bids without declaring as anomalous otherwise regular bids (which we may call a false alarm). In this paper we provide analytical expressions and simulation results for two performance indices of detection schemes: the detection probability and the false alarm probability. We focus on a class of detection schemes for abnormally low bids (hereafter we will use the generic term of anomalous bids), based on the use of the average bid. A particular version of such scheme has been officially adopted by public bodies in Spain and Italy. Its relevance lies in its official endorsement, though it has so far escaped a proper evaluation. Some background information on procurement auctions is provided in Section 2, while the average-bid detection scheme itself is described in Section 5. The reference model for the bid distribution needed to perform our evaluation is provided in Section 3, while the performance indices are defined in Section 4. The evaluation is finally conducted in Sections 6 (detection probability) and 7 (false alarm probability) for the case of a single anomalous bid. The case of multiple anomalous bids is instead studied in Section 8. In addition, the influence of the presence of courtesy bids (abnormally high) on the detection of abnormally low bids is evaluated in Section 9.

An average bid based method has been presented for the detection of abnormally low bids in procurement auctions. Two performance indices have been selected for its evaluation: the detection probability and the false alarm probability, whose dependence on the number of tenderers, the dispersion of bids, and the rebating factor of the anomalous bid has been investigated. A large number of participants has always a positive effect on the performance of the method. Instead, a larger dispersion of bids contributes to lower the detection probability as long as it is larger than 0.5. It is generally to be noted that the method may be affected by a large proportion of false alarms. However, if multiple anomalous bids are present (even just three) the performance worsens significantly. On the other hand, the presence of courtesy bids increases both the detection probability and the false alarm probability. Since a large number of false alarms results in a cost associated to the further investigation work and may give rise to unjustified rejection of low but regular bids (which increases the price for the auctioneer), the method is recommended when the need to avoid anomalous bids is much more relevant than the costs associated to false alarms.