Developing an optimal bidding strategy in two-envelope fee bidding

Two-envelope fee bidding is used frequently in allocating commissions to willing consultants such as architects, engineers and surveyors. Consultant fees and technical scores are normally aggregated to form a total score. The consultant obtaining the highest total score is usually awarded the commission. The consultant's objective is to get the highest total score possible because this maximizes the chance of winning. Consultants can submit to the procurer any of a number of different technical proposals which is then converted to a technical score. Only one technical score+fee combination will result in the highest total score, i.e. the optimum technical score+fee combination. This paper offers consultants an approach to better identify their optimum technical score+fee combination. In using this approach consultants need to develop a total score continuum based on (1) the consultant's original technical proposal and fee, (2) the absolute lowest fee and corresponding technical score, and (3) the absolute highest technical score and corresponding fee. The total score becomes the dependent variable and the fee the independent variable. Since the total score continuum is regressed on three points it will almost certainly be curvilinear in shape. Given that the optimum total score is at the highest point of the continuum, the optimum fee can be determined through differentiation. The corresponding technical score can then be found. After adjusting the original technical proposal to reflect the corresponding technical score, the optimum fee and adjusted technical proposal can then be submitted to the procurer.