For many construction projects, It is common for the customer to pay an incentive to the contractor for finishing the project in a shorter length of time. In contrast, the contractor pays delay penalties if the project is delayed. Goldratt 1997 suggested critical chain project management method (CCPM) as an attempt for minimizing project duration. Goldratt approach and related buffer sizing approaches result in different values of project buffer and feeding buffer which do not satisfy construction projects circumstances. The proposed model uses multiple shifts and discrete relationship between activity time and cost to be solved by integer programming to express real- life construction projects, optimize project duration with minimum cost and overcome Student's Syndrome and Parkinson's Law. A simplified representation of a small example project is formulated to represent this model. Final solution shows that this method is simple and generates a shorter time at low cost.