Multiple Objectives

While typical optimization models have a single objective function, real-world optimization problems often have multiple, competing objectives. For example, in a production planning model, you may want to both maximize profits and minimize late orders, or in a workforce scheduling application, you may want to both minimize the number of shifts that are short-staffed while also respecting worker's shift preferences.

The main challenge you face when working with multiple, competing objectives is deciding how to manage the tradeoffs between them. Gurobi provides tools that simplify the task: Gurobi allows you to blend multiple objectives, to treat them hierarchically, or to combine the two approaches. In a blended approach, you optimize a weighted combination of the individual objectives. In a hierarchical or lexicographic approach, you set a priority for each objective, and optimize in priority order. When optimizing for one objective, you only consider solutions that would not degrade the objective values of higher-priority objectives. Gurobi allows you to enter and manage your objectives, to provide weights for a blended approach, or to set priorities for a hierarchical approach.