Solve a linear programming problem by selecting an objective, defining decision variables, and applying linear constraints.

Solve a nonlinear optimization problem by selecting an objective, defining decision variables, and applying nonlinear constraints.

Assign tasks to agents at minimum total cost under capacity constraints. Use this for worker-task assignment, machine-job assignment, and ticket routing problems.

Allocate limited capacity to required demand while minimizing cost and shortage penalties. Use this for capacity planning, staffing plans, and shortfall-penalty balancing problems.

Maximize value under a capacity limit with binary or integer item decisions. Use this for budget selection, portfolio picking, and constrained mix-selection problems.

Assign entities to locations with a blended score and cost objective under location capacity limits. Use this for slotting, host-placement, and entity-to-site assignment problems.

Select backup pairings with minimum extra cost while meeting optional average coverage targets. Use this for backup design, failover planning, and resilience-cost optimization problems.

Find minimum-cost flow from a source node to a target node over constrained edges. Use this for network pathing, lane selection, and constrained transfer-flow problems.