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Uncertainties in quantities of work items and vagueness in unit price boundaries have mainly been disregarded in unbalanced bidding models. This article presents a fuzzy linear programming (FLP) model which treats the quantities of works and unit price limitations as fuzzy numbers. Fuzzy constraints are used to define upper and lower bounds on the unit prices proposed by the contractor. The uncertainties in quantities of works are addressed through fuzzy coefficients with asymmetric fuzziness ratio in the objective function. Therefore, the problem lends itself to an FLP model with fuzzy coefficients in the objective function and fuzzy constraints. To account for these uncertainties, two different approaches are proposed and tested. Performance of the model is demonstrated using three hypothetical case examples and the results are discussed and compared with those of a deterministic model.
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Afshar et al. (2010) studied this question.
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