Keywords: bidding, unit price, factors, cost item, analytical hierarchical procedure.

Making appropriate decisions regarding the bid price of a construction project is essential for a bidder (a construction company) to win the project contract and achieve a reasonable profit. In practice, in assessing the bid price for a project, cost estimators of a bidder first conduct a quantity take-off analysis and unit-price quotation for each cost item of the project. Second, the cost of each cost item is calculated by multiplying the quantity by the unit price of the cost item. Third, the costs of cost items are summed for each cost category (e.g., foundation, structure, etc.). Fourth, the costs of all cost categories are summed to compute the total costs. Finally, a mark up is added to the total costs to obtain the bid price.

The above-mentioned estimation process is time consuming. However, the period for preparing a bid price is comparatively short. Therefore, the unit prices frequently are employed based on normal conditions of factors (such as tightness of construction duration and high project complexity) for the project. Consequently, the decision-maker, based on his experience and intuition, needs to adjust the total cost by considering the conditions of several specific factors for determining the final bid price.

This work proposes an innovative procedure to evaluate the unit price for each cost category (instead of cost item) by considering the effect of multiple factors. The unit price suggested by the procedure then can be applied to calculate the costs of each category for supporting the determination of a bid price. The proposed procedure is developed based on a multi-factor evaluation model and a unit-price-based cost mode. The multi-factor evaluation model is applied to reflect the specific conditions of factors. The unit-price-based cost model is a cumulative distribution of unit price for a cost category.

In the multi-factor evaluation model, the factors guide a bidder in deciding how to price their work above or below the estimated (or average) unit price for a cost category. For example, a long construction duration tends to increase the unit price of the cost category of temporary facilities (such as temporary utilities and office overheads). The multi-factor evaluation model is developed using an analytical hierarchical procedure (AHP) and utility theory. In the unit-price-based cost model, a normal cumulative distribution of unit prices is assumed for each cost category. The mean and standard deviation of the historical unit price data are used to develop such a normal distribution.

Then, the procedure executes the following steps: (1) evaluating the expected utility value (S_i, integrated effect) of multiple factors on a cost category i. (2) finding a suggested unit price from the cumulative distribution of the cost model, according to the value of S_i. (3) multiplying the suggested unit price by the total floor area of the project to obtain the costs of the cost category. (4) calculating the total cost according to a derived cost equation.

The research focuses on private housing projects that are made of reinforced concrete. Nine cost categories of construction costs for a housing project are identified, including foundation, structure, external finishes, internal finishes, doors and windows, elevator, mechanical / electrical / plumping, temporary facilities, and landscaping. Markup is treated as a separate cost category. The cost data of thrity-six housing projects are used for developing the cumulative distribution of the unit-price-based cost model for each cost category. The merits of the proposed procedure are demonstrated by applying the procedure to a housing project located in Taiwan.

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