A modeling framework is proposed to study the allocation of doctors during specific time blocks to individual clinics of a major multi-branch medical practice in Hong Kong. This problem is motivated by our previous simulation work in one of the typical clinics that has identified bottlenecks in doctor's availability at various times . This paper suggests a non-linear integer multi-criteria formulation with four prioritized goals: minimum loss of demand, minimum average waiting time, minimum doctors idleness and maximum use of consultation rooms. Our computational results from such a modeling framework (or a simplified model structure) show it can generate allocation decision support predicting possible operational improvement as well as helpful insight into the existence and explanation of system bottlenecks arising from a combination of more than one factors.