Research on the part alternative resource-constrained project scheduling problem leads to achieve a optimization configuration beween the limited resources and specific tasks.It plays an important role in both manufacturing and production systems.At fast,this paper describes scheduling order on the constrained resource and alternative resource as the parallel machines with the machine eligibility restrictions by a triplet.Its ultimate goals are the minimization of makespan and the sum of tardiness.Also this paper established the corresponding mathmatical model.And then,we design the heuristic scheduling algorithm combining the dispatching rules and Genetic Algorithm to solve the problem.In the end,the project how to arrange the courses to different classrooms each term in the school is taken as an example.It does some researches on the scheduling problem that different classrooms are defined as the constrained resource and alternative resource.And this paper verifies the effectiveness and feasibility of the designed algorithm.