Gurobi MIP Example: Practical Mixed-Integer Models in Business

In practice, a Gurobi MIP example is a decision model where some choices are discrete: yes or no selections, integer counts, or assignment decisions. You combine those with continuous quantities like flows, hours, or inventory. Common objectives include minimizing total cost, lateness, or emissions, or maximizing service level or margin, subject to capacity, policy, and timing constraints. Gurobi is the optimization solver that takes this deterministic MIP model and, when solved to completion, provides a proven optimal solution or proves infeasibility or unboundedness.

Use linear programming (LP) when all decisions can be fractional and that is acceptable. Use mixed-integer linear programming (MILP) when fractionality is not allowed or meaningful, such as opening a facility (open or not), assigning each order to exactly one line, or selecting a fixed number of shifts. If your operations require discrete commitments, MIP is usually the right abstraction.

Realistic models are not defined by size alone, but by the structure of decisions and constraints. A typical pattern is: 

• Choose discrete actions (assign, open, schedule, select) 

• Decide quantities (produce, ship, stock, allocate time) 

• Enforce operational rules (capacities, coverage, precedence, budgets) 

• Optimize a KPI (cost, profit, on-time performance, utilization) 

The “example” becomes realistic when the constraints reflect policy and physics, and the objective matches how performance is judged. 

Consider a multi-product plant planning weekly production and inventory. Integer decisions often represent changeovers, minimum batch requirements, or limited parallel lines. Continuous decisions represent production quantities and inventory levels. Constraints can include line capacity, labor limits, storage bounds, and service requirements. The objective might minimize total cost: production, setup, overtime, and holding costs. This is a classic MILP where integrality captures the real cost and feasibility implications of switching and batching.

Routing problems add discrete structure quickly: each stop is either visited by a vehicle or not, and sequencing choices are combinatorial. MIP can model decisions like assigning jobs to technicians, respecting skill compatibility, limiting route duration, and meeting time windows. The objective could minimize travel time and overtime, or maximize completed high-priority jobs.

Shift scheduling and job-shop style scheduling are common. Discrete decisions assign people to shifts or jobs to machines, while constraints enforce coverage, rest rules, and precedence. Objectives include minimizing understaffing penalties, overtime, and late completion. These models often expose tradeoffs clearly: for example, how much overtime is needed to reach a target service level, or which constraints are driving infeasibility. 

Gurobi solves deterministic models, so uncertainty is handled by how you model it. Common approaches include scenario sets (multiple demand or travel-time realizations), parameter sweeps (solve for several assumptions), or robust or stochastic formulations at a high level. The key is to define what must hold in all cases (hard constraints) versus what can be penalized when it occurs (soft constraints), then test stability of decisions across scenarios.

The most important issues are usually consistency and unit alignment: calendars, capacities, lead times, costs, and eligibility rules. Also watch for missing business rules that planners apply informally. If the model output surprises stakeholders, it is often because a constraint is absent, costs are mis-scaled, or the objective is missing a service penalty that is implicitly important. 

Start with a baseline process and define measurable KPIs: cost-to-serve, overtime hours, fill rate, late orders, miles driven, or asset utilization. Then compare the optimized plan against the baseline under the same assumptions and constraints. Many teams find the biggest value is consistency and speed of re-planning when conditions change, not just a single-point cost reduction.