Cost and time are the main aspects to be considered in every project. The main objective in the construction field is to complete every project on time, within budget and quality. Time and cost are related to each other and it is very important in achieving project objectives. Cost optimization is an important issue in construction project management. Loss of time always increases cost and saving of time can provide profit to all the parties in project. We will be studying different methods of time and cost optimization with the objective of minimizing the project cost and duration an analysis is performed to identify the relationship between time and cost. the availability of expert is the main problem faced by contractor in optimizing the cost. The duration of the project and changing environment are the least problems faced by the contractor in optimizing the cost.