The tender process is an inseparable step of the contract award process in the public sector, and from the other point of view, it is one of the crucial elements of the core business of construction contractors. Reviewing previous research reveals a gap in the application of a project’s detailed features and historical data to support the bid/no-bid decision and to determine the cost and time contract mark-ups. In this study, a prescriptive project complexity-based model is proposed to support the bid decision in the tender strategy development phase of a contractor for the downstream sector of the petroleum industry in Iran. For this purpose, regression analysis of historical data is adopted to configure the model and to infer from previous actual trends by exploring relationships between the contractor’s bid decision and proposed mark-ups with the project’s inherent and surrounding complexity factors. Hence, using experts’ opinions and historical data from 139 previous contracts as training and test data, a model was developed to make a decision on a bid and mark-up problem. The results of the model validation show that the credibility of the model is 74.67% and 75.36% for time and cost, respectively, and the reliability of model outputs is approximately 90% overall in predicting the bid mark-ups in accordance with the project complexity index (PCI). The main contribution of this research to current knowledge has two aspects: utilizing the complexity concept for the tender problem in the form of a project complexity index (PCI) and considering both time and cost mark-ups (TMU–CMU) in the contractor’s bid simultaneously. In addition, the results show that the more complex the project is, the higher the bid rate is.