Good supervision on a building site will prevent mistakes and pre-empt problems and thereby save you money.  Having to rectify mistakes is always costly and time-consuming.  Supervision will also reduce the amount of  waste on a site by keeping an eye on what is happening and making sure that the builder runs a tidy site.  The flow of building materials must keep going so that the contractor is not waiting for anything.  This will reduce down time and labour costs of time extensions.  If you buy a lot of the materials yourself then you will save on the handling mark-up that the builder usually adds to the cost of materials (usually between 5-15%) plus you will be able to negotiate discounts and shop around.  Most builders will not do this as they have a fixed set of suppliers who give them good discounts.  You will also need to have a written agreement with your builder as to what materials he will supply and which are your responsibility.  If you are supplying materials then you will need a weekly program from the builder stating when the materials will be required. Bear in mind that some materials like shower doors or light fittings can  take weeks to arrive.