The effects of the delay in construction contract execution are always negative for every party being involved. Cancelling the delays of the time schedule means the use of more production means that it was planned. It creates an additional cost. If the delays of the schedule are not cancelled, the contractor suffers from the cost increase. The penalties arisen from not keeping the milestones or the completion date are expected too. There is a trade-off: cancelling delays spending additional money now (during the contract execution) or executing a delayed contract till its end awaiting for its final settlement (showing the cost increase) and possible penalties. There is no one, correct answer how to manage a delayed construction project. There is a natural unwillingness to spend money over the budget. Nevertheless, the delayed completion date can cause much higher contractor’s expenses, than cancelling delays during the contract execution. The decisions made by the project manager depend on various factors discussed in the paper. A delay concerning the single task increases the cost of its execution at a different level. The same, the level of influence of delaying a single task, influences the completion date with varied strength. These influences depend on the location of the task in a net model – the base of a schedule. The tasks located on the critical path – defined in the Critical Path Method – should be of the special care. However, delays on not critical tasks can also break the budget and the planned completion date. The nature of delay is important as well. Lowered productivity of a workers’ brigade can make the execution of the task longer, the same as forced breaks in their efficient work. The reaction of a site manager to such causes of delay should be different, as the origin of the delays is different. The impact of the delay noticed on the single task is discussed in the paper and possible reaction (varied on the type of a delay and a task location too) are proposed. The proposed solutions aim at cost minimizing considering the total expenses spent by a contractor and possible penalties in case of the delayed completion date of a construction contract.