Linear and conic reformulations for the maximum capture location problem under multinomial logit choice

This paper presents three reformulations for the well-known maximum capture location problem under multinomial logit choice. The problem can be cast as an integer fractional program and it has been the subject of several linear reformulations in the past. Here we develop two linear and a conic reformulation based on alternative treatments of fractional programs. Numerical experiments conducted on established sets of instances have shown that conic reformulation has greatly improved the solution times as well as the size of the solvable problems as compared to the most successful reformulations to date.