Mixed-Integer Programming

MIP

An optimization method where some or all variables must take integer values, used for problems involving yes/no decisions, scheduling, and routing.

Explanation

Mixed-integer programming extends linear programming by allowing variables to be restricted to integer values. This is essential for real-world problems where you need discrete decisions: should this truck visit this location (yes/no), how many machines to assign to a job (whole numbers), which warehouse to ship from. MIP problems are NP-hard in general, solved using branch-and-bound algorithms.

How kint Uses It

MIP is kint's primary formulation for vehicle routing, production scheduling, and resource allocation. kint uses commercial solvers (Gurobi, CPLEX) and open-source alternatives (GLPK) with ML-based warm-starting to accelerate solve times.

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