A min-max regret approach to unbalanced bidding in construction

Unbalanced bidding is a method to benefit from uneven markup distribution among different items of project. As bidding process is applied for a project which is going to be done in future, most of parameters cannot be estimated accurately. Therefore, there are some uncertainties in bidding phase. Uncertainties in quantities of works play an important role for unit price determination in an unbalanced bidding model. Therefore, in this paper these uncertainties are considered, applying Minimize Maximum Regret (MMR) and Minimize Total Regret (MTR) approach in a discrete area where each scenario represents a set of possible quantities of works. Allocating interval scenario case for quantities of works seems to be more appropriate than discrete one. Thus, the unbalanced bidding model with interval quantities of works using MMR is proposed. To define manageable number of scenarios resulting from possible combinations of different unit prices in formulating the Min Max Regret (MMR) model as interval scenario case, a relaxation procedure is employed. In this approach, instead of considering all possible objective functions, a model which is called "Candidate Maximum Regret (CMR)" is applied to determine worst case scenarios. Models are applied to a hypothetical case example and the results are compared.