In the modern day where demands are seen unlimited in comparison with sources, allocation of these sources to the right demands is of great importance. The source that should be assigned grows in proportion to the size of the demand, accordingly finding the right solution becomes more important. In this study, hospital projects selection problem under particular constraints is addressed. In the study VIKOR method is used in order to reflect the multiple criteria, which lies on the problems nature, to the solution, while AHP method is used to determine criteria weights. Subsequent to multiple criteria decision making methods, a 0-1 goal programming model is built. With the help of this mathematical model, problem specific constraints are involved in the solution. As a result of the implementation of these models, some hospital alternatives are selected. It is seen that the integrated method is efficient in solving the decision making problems under constraints.