Estimate production and contribution-margin losses from planned and unplanned downtime.

Minimize total blend cost while meeting batch-size and property specifications with optional min/max bounds per material. Use this for feed formulation, food blending, chemicals, alloys, fuels, and fertilizer mixes.

Minimize total production, holding, setup, and optional backlog cost across multiple periods. Use this for finite-capacity production planning and inventory balance decisions.

Assign workers to shifts at minimum labor cost with max-shift limits and optional skill matching. Optionally allow shortages with penalty to keep the problem feasible under tight staffing.

Find overtime hours that minimize total production-related cost with overtime efficiency deterioration and shortfall penalty.

Optimize product quantities to maximize monthly contribution profit subject to machine time, labor time, demand, and ramp-change constraints.