When businesses face decisions that involve discrete choices—such as how many workers to schedule or which routes delivery trucks should take—integer linear programming (ILP) provides a powerful modeling framework. In this blog, we’ll explore some of the most impactful integer linear programming examples across industries like manufacturing, finance, and more.
Integer linear programming is a form of optimization where the decision variables must take on integer values. Unlike traditional linear programming, where variables can be any real number (i.e. continuous), ILP models reflect real-world constraints—such as yes/no decisions or counts of physical items. This makes ILP indispensable for tackling problems where fractions don’t make sense. ILPs when every decision variable must take an integer value. The case when some decision variables can still be continuous while others need to be integer is called Mixed-Integer Linear Programming (MILP) which is often shortened to just MIP.
The Gurobi Optimizer is built to solve ILP problems efficiently and at scale, making it the solver of choice for many leading companies and researchers.
Workforce scheduling is another classic application of integer linear programming. The problem involves assigning workers to shifts while satisfying coverage requirements, labor laws, and individual preferences. Decision variables are binary (0 or 1), indicating whether a person is assigned to a specific shift.
With Gurobi, you can build ILP models that balance business needs with employee satisfaction. Check out our workforce scheduling model example to see how it works.
Manufacturers use ILP for production planning and scheduling, where decisions must be made about what to produce, how much, and when. Constraints include material availability, machine capacity, and delivery deadlines. Integer variables often represent product batch quantities or shift allocations.
Using Gurobi, companies can generate optimal production schedules that minimize downtime and reduce inventory costs, all while meeting customer demand.
In finance, ILP can be used for portfolio optimization—especially when there are limits on how many assets can be included in the portfolio. For example, an investor might want to choose exactly 10 assets out of 50, which introduces integer constraints on the selection variables.
These problems are hard to solve using traditional methods, but Gurobi’s solver handles them efficiently, enabling smarter, constraint-aware investment strategies.
Designing robust and cost-effective telecommunications networks often involves ILP. Decisions such as whether to install a particular link or how to route traffic through a network require binary variables. Constraints might include bandwidth limits or geographic restrictions.
ILP models help telecom companies optimize network topology and reduce infrastructure costs while maintaining high service levels.
Students and educators frequently explore ILP through well-known problems like the knapsack problem, job scheduling, and set covering. These examples illustrate the core mechanics of ILP—how to translate real-world rules into mathematical constraints.
At Gurobi, we offer extensive academic resources and example models to help learners understand and apply integer programming effectively.
Whether you’re solving a small academic problem or a large-scale enterprise optimization challenge, Gurobi delivers industry-leading performance. Our solver supports mixed-integer models, advanced presolve techniques, and parallel processing, making it ideal for complex ILP use cases.
Explore our technical documentation or get started with a free academic license to see how you can use integer linear programming to make better decisions.
From logistics to finance, integer linear programming helps solve some of the most challenging decision-making problems in business and research. These examples only scratch the surface of what’s possible with ILP—and with a solver like Gurobi, you’re empowered to tackle them with confidence.
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