In the project scheduling and management, the time-resource tradeoff problem is to seek the objective of minimizing the project duration and the total consumed-resources cost under the requirement of the absolute due date of project, and determine an efficient project scheduling according to some precedence relationship and the renewable resource constraints. A new multi-objective optimization decision-making model with time-resource tradeoff problem is proposed, in which objective functions with conflict one another are defined as adaptive and adjustable between the project duration and the total consumed-resources cost in all period. A satisfied feasible solution can be obtained in the solution procedure by compromising and adjusting relationship between the project duration and the total consumed-resource cost. A numerical example is illustrated. In addition, some characteristics on this two-player game are given in the corresponding Lagrangian relaxation form associated with the resource constraints.