Cascading Knapsack Inequalities: Hidden Structure in some Inventory-Production-Distribution problems

In the last decade Mixed-Integer Programming solvers have evolved enormously contributing to the widespread application of optimization in real world problems in industry. Nonetheless, it is paramount for practitioners to have basic knowledge on how these solvers work and to be able to identify model structures, so one can take full advantage of the machinery at hand. In this paper we present a reformulation to a simple problem that appears as sub-problem in many supply chain models, and we show the advantage of using suitable mathematical structures in the form of cascading knapsack inequalities to solve it. Moreover, we introduce new reformulations to some special cases, producing tighter linear relaxation and faster solution times.