Robust Optimization Model for Bi-objective Emergency Medical Service Design Problem with Demand Uncertainty

Bi-objective Emergency Medical Service Design Problem is a problem to determining the location of the station Emergency Medical Service among all candidate station location, the determination of the number of emergency vehicles allocated to stations being built so as to serve medical demand. This problem is a multi-objective problem that has two objective functions that minimize cost and maximize service. In real case there is often uncertainty in the model such as the number of demand. To deal the uncertainty on the bi-objective emergency medical service problem is using Robust Optimization which gave optimal solution even in the worst case. Model Bi-objective Emergency Medical Service Design Problem is formulated using Mixed Integer Programming. In this research, Robust Optimization is formulated for Bi-objective Emergency Medical Service Design Problem through Robust Counterpart formulation by assuming uncertainty in demand is box uncertainty and ellipsoidal uncertainty set. We show that in the case of bi-objective optimization problem, the robust counterpart remains computationally tractable. The example is performed using Lexicographic Method and Branch and Bound Method to obtain optimal solution.