When the user wants to formulate and solve knapsack problems — 0-1, bounded, multiple, multidimensional, or quadratic — using dynamic programming, branch-and-bound, MIP, greedy bounds, or metaheuristics. Also use when the user mentions "knapsack," "0-1 knapsack," "multidimensional knapsack," "subset selection," "capacity constraint," or when a knapsack appears as a pricing or separation subproblem inside a larger algorithm. For Bellman recursions and state design, see dynamic-programming; for pricing loops built on a knapsack solver, see column-generation.
