On Solving a Class of 0-1 Linear Fractional Programs as Continuous Linear Fractional Programs

This work bridges the gap between the discrete and the continuous fractional programming literature by solving a class of 0-1 fractional programs as continuous fractional programs. Specifically, we consider 0-1 linear fractional programs under cardinality-type constraints and provide a continuous reformulation with integral maxima, albeit with a higher number of ratio terms. We then consider the direct relaxation and use the insights from the reformulation to show that the resultant fractional solution can be rounded off with parametric guarantees. We highlight that these guarantees improve upon existing parametric bounds for a class of assortment optimization problems. We also illustrate that the reformulation can help improve the discrete local search heuristic solution by exploiting the continuous solution space. We substantiate this further numerically and show that the reformulation is quite effective and provides significant performance gains over current approaches.