Product line optimization with multiples sites

We consider the problem faced by a retail chain that must select what mutual-substitute items to display in each one of its stores maximize revenues. The number cannot exceed limit space capacity store. Customers purchase product maximizes their utility, which depends on price, travel cost store, and reservation known retailer. retailer can set different price markdowns at products. considers decisions customers, solves mixed-integer bilevel optimization problem, be formulated as single-level using optimality conditions for lower level. propose Branch Cut methods include family valid inequalities solve problem. compare results with those Benders decomposition method. Our computational show proposed method obtains best performance improves current state art.