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We consider range minimization problems featuring exponentially manyvariables, as frequently arising in fairness-oriented or bi-objectiveoptimization. While branch and price is successful at solving cost-orientedproblems with many variables, the performance of classical branch-and-pricealgorithms for range minimization is drastically impaired by weak linearprogramming relaxations. We propose range branching, a generic branching rulethat directly tackles this issue and can be used on top of problem-specificbranching schemes. We show several desirable properties of range branching andshow its effectiveness on a series of instances of the fair capacitated vehiclerouting problem and fair generalized assignment problem. Range branchingsignificantly improves multiple classical branching schemes in terms ofcomputing time, optimality gap, and size of the branch-and-bound tree, allowingus to solve many more large instances than classical methods. Moreover, we showhow range branching can be successfully generalized to order-based objectivefunctions, such as the Gini deviation.

Efficient Branching Rules for Optimizing Range and Order-Based Objective Functions