Skip to main content
SpringerLink
Log in

Generalised gamma bidding model

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

A generalised gamma bidding model is presented, which incorporates many previous models. The log likelihood equations are provided. Using a new method of testing, variants of the model are fitted to some real data for construction contract auctions to find the best fitting models for groupings of bidders. The results are examined for simplifying assumptions, including all those in the main literature. These indicate no one model to be best for all datasets. However, some models do appear to perform significantly better than others and it is suggested that future research would benefit from a closer examination of these.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. See Skitmore et al (2007).

  2. For construction contract auctions, the term ‘contract’ is equivalent to ‘item’ in the more general bidding literature.

  3. Letting σ 2 denote the second moment in f(., σ 2) we can further associate σ i =0 with Friedman (1956) and σ 1=σ 2=…=σ k with Carr (1982).

  4. The opportunities for merging cells are limited, as even with the bidder groupings described later, there is no obvious way in which contracts can be merged as well.

  5. See Ypma (1995) for example, on the background to this method, said to ‘lurk inside millions of modern computer programs’ (Thomas and Smith, 1990).

  6. Being an essentially non-parametric analysis, the term significance is used here in an observational rather than statistical sense.

References

  • Abadi A, Amanpour F, Bajdik C and Varai P (2012). Breast cancer survival analysis: Applying the generalized gamma distribution under different conditions of the proportional hazards and accelerated failure time assumptions. International Journal of Preventive Medicine 3 (9): 644–651.

    Google Scholar 

  • Alexander AB (1970). What price estimating accuracy? Paper 534, Metal Fabricating Institute, Rockford, Illinois.

  • Arps JJ (1965). A strategy for sealed bidding. Journal of Petroleum Technology 17 (9): 1033–1039.

    Article  Google Scholar 

  • Babu KS, Yarramalle S and Penumatsa SV (2012). Text-independent speaker recognition using emotional features and generalized gamma distribution. International Journal of Computer Applications 46 (2): 16–18.

    Google Scholar 

  • Brown KC (1966). A theoretical and statistical study of decision making under uncertainty—A competitive bidding for leases of offshore petroleum tracts. PhD dissertation, Southern Methodist University, Dallas.

  • Capen EC, Clapp RV and Campbell WM (1971). Competitive bidding in high risk situations. Journal of Petroleum Technology 23 (6): 641–653.

    Article  Google Scholar 

  • Carr RI (1982). General bidding model. Journal of the Construction Division. Proceedings of the American Society of Civil Engineers 108 (CO4): 639–650.

    Google Scholar 

  • Carr RI (1983). Impact of number of bidders on competition. Journal of Construction Engineering and Management, Proceedings of the American Society of Civil Engineers 109 (1): 61–73.

    Google Scholar 

  • Cauwelaert FV and Heynig E (1978). Correction of bidding errors: The Belgian solution. Journal of the Construction Division, American Society of Civil Engineers 105 (1): 13–23.

    Google Scholar 

  • Crawford PB (1970). Texas offshore bidding patterns. Journal of Petroleum Technology 22 (3): 283–289.

    Article  Google Scholar 

  • Dougherty EL and Nozaki M (1975). Determining optimum bid fraction. Journal of Petroleum Technology 27 (3): 349–356.

    Article  Google Scholar 

  • Dowe DL, Farr GE, Hurst AJ and Lentin KL (1996). Information-theoretic football tipping. Technical Report no 96/297, School of Computer Science and Software Engineering, Monash University, Clayton, Melbourne, Victoria 3168, Australia.

  • Elman HC (1982). Iterative methods for large sparse nonsymmetric systems of linear equations. PhD Thesis, Yale University, USA.

  • Emond LJ (1971). Analytical strategy for the competitive price setter. Cost and Management (Sep–Oct): 6–11.

  • Fine B and Hackemar G (1970). Estimating and bidding strategy. Building Technology and Management 8 (9): 8–9.

    Google Scholar 

  • Friedman L (1956). A competitive-bidding strategy. Operations Research 1 (4): 104–112.

    Article  Google Scholar 

  • Gates M (1967). Bidding strategies and probabilities. Journal of the Construction Division, Proceedings of the American Society of Civil Engineers 93 (1): 75–107.

    Google Scholar 

  • Grinyer PH and Whittaker JD (1973). Managerial judgement in a competitive bidding model. Operational Research Quarterly 24 (2): 181–191.

    Article  Google Scholar 

  • Hossein BR (1977). Risk analysis of tendering policies for capital projects. PhD Thesis, University of Bradford, UK.

  • Hvingel C, Kingsley MCS and Sundet JH (2012). Survey estimates of king crab (Paralithodes camtschaticus) abundance off Northern Norway using GLMs within a mixed generalized gamma-binomial model and Bayesian inference. ICES Journal of Material Science 69 (8): 1416–1426.

    Article  Google Scholar 

  • Keiding N, Hansen OKH, Sørensen DN and Slama R (2012). The current duration approach to estimating time to pregnancy. Scandinavian Journal of Statistics: Theory and Applications 39 (2): 185–204.

    Article  Google Scholar 

  • Klein JD (1976). Joint ventures and bidding for offshore oil. In: Amihud Y (ed). Bidding and Auctioning for Procurement and Allocation. New York University Press: New York.

    Google Scholar 

  • Lawless JF (1982). Statistical Models and Methods for Lifetime Data. John Wiley & Sons: New York.

    Google Scholar 

  • McCaffer R (1976). Contractor's bidding behaviour and tender price prediction. PhD Thesis, Loughborough University of Technology, UK.

  • McCaffer R and Pettitt AN (1976). Distribution of bids for buildings and roads contracts. Operational Research Quarterly 27 (4i): 835–843.

    Article  Google Scholar 

  • Mitchell MS (1977). The probability of being the lowest bidder. Applied Statistics 2 (2): 191–194.

    Article  Google Scholar 

  • Morrison N and Stevens S (1980). Construction cost database. 2nd annual report of research project by Dept of Construction Management, University of Reading, for Property Services Agency, Directorate of Quantity Surveying Services, DOE, UK.

  • Nadarajah S and Gupta AKA (2007). Generalized gamma distribution with application to drought data. Mathematics and Computer Simulation 74 (1): 1–7.

    Article  Google Scholar 

  • Oren SS and Rothkopf MH (1975). Optimal bidding in sequential auctions. Operations Research 23 (6): 1080–1090.

    Article  Google Scholar 

  • Prentice RL (1974). A log gamma model and its maximum likelihood estimation. Biometrika 61 (3): 539–544.

    Article  Google Scholar 

  • Rothkopf MH (1969). A model of rational competitive bidding. Management Science 15 (7): 362–373.

    Article  Google Scholar 

  • Shin JW, Chang JH and Kim NS (2005). Statistical modeling of speech signals based on generalized gamma distribution. IEEE Signal Processing Letters 12 (1): 258–261.

    Article  Google Scholar 

  • Skitmore RM (1991). The construction contract bidder homogeneity assumption: An empirical analysis. Construction Management and Economics 9 (5): 403–429.

    Article  Google Scholar 

  • Skitmore RM (2001). Graphical method for identifying high outliers in construction contract auctions. Journal of the Operational Research Society 52 (7): 800–809.

    Article  Google Scholar 

  • Skitmore RM (2002a). Predicting the probability of winning sealed bid auctions: A comparison of models. Journal of the Operational Research Society 53 (1): 47–56.

    Article  Google Scholar 

  • Skitmore RM (2002b). Identifying non-competitive bids in construction contract auctions. Omega: International Journal of Management Science 30 (6): 443–449.

    Article  Google Scholar 

  • Skitmore RM (2004). Predicting the probability of winning sealed bid auctions: The effects of outliers on bidding models. Construction Management and Economics 22 (1): 101–109.

    Article  Google Scholar 

  • Skitmore RM and Lo HP (2002). A method for identifying high outliers in construction contract auctions. Engineering, Construction and Architectural Management 9 (2): 90–130.

    Article  Google Scholar 

  • Skitmore RM and Pemberton J (1994). A multivariate approach to contract bidding mark-up strategies. Journal of the Operational Research Society 45 (11): 1263–1272.

    Article  Google Scholar 

  • Skitmore RM, Pettitt AN and McVinish R (2007). Gates’ bidding model. ASCE Journal of Construction Engineering and Management 133 (11): 855–863.

    Article  Google Scholar 

  • Stacey EW (1962). A generalization of the gamma distribution. The Annals of Mathematical Statistics 33 (3): 1187–1192.

    Article  Google Scholar 

  • Thomas DJ and Smith JM (1990). Joseph Raphson, FRS. Notes and Records of the Royal Society of London 44 (2): 151–167.

    Article  Google Scholar 

  • Vickrey W (1961). Counterspeculation, auctions and competitive sealed transfers. Journal of Finance 16 (March): 8–37.

    Article  Google Scholar 

  • Weverbergh M (1982). Competitive bidding: Estimating the joint distribution of bids. Working paper 82–79, Dec, Centrum voor Bedrijfseconomie en Bedrijfseconometrie Universiteit Antwerpen—USFIA.

  • Whittaker JD (1970). A study of competitive bidding with particular reference to the construction industry. PhD Thesis, City University, London, UK.

  • Ypma JT (1995). Historical development of the Newton–Raphson method. SIAM Review 37 (4): 531–551.

    Article  Google Scholar 

Download references

Acknowledgements

Thanks go to Ross McVinish for pointing out some errors in the original formulae. Also, to the QUT High Performance Computing Lab for sanctioning my continual use of their Cray Supercomputer over the last eight years.

Author information

Authors and Affiliations

  1. Queensland University of Technology, Queensland, Australia

    M Skitmore

Authors
  1. M Skitmore
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M Skitmore.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skitmore, M. Generalised gamma bidding model. J Oper Res Soc 65, 97–107 (2014). https://doi.org/10.1057/jors.2013.18

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2013.18

Keywords

Search

Navigation