Solving Complex Business Problems with Mixed-Integer Linear Programming

Author(s): Shenggang Li

Originally published on Towards AI.

A Practical Exploration of MILP Applications: From Workforce Optimization to Financial Planning and Beyond

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If you’re a hedge fund manager managing an investment portfolio, your goal is to maximize returns by year-end. However, you have limits on how much or when you can invest in certain assets. This is where Mixed-Integer Linear Programming (MILP) comes in.

I use a practical example — optimizing shift schedules for customer service agents — to show its application. After reading this paper, you may discover many other valuable uses of MILP in your field.

Additionally, this paper will show you how to set up an optimization model, translating real-world problems into mathematical terms when balancing goals and constraints.

Imagine you’re managing a call center with five agents.

Every day, you assign them to one of the shifts: early (E) or late (F). The challenge is to balance the workload while ensuring the agents don’t work too many consecutive days. Shifts should be distributed fairly among the agents to prevent any one person from being overloaded.

You have a 30-day month with two shifts per day and five agents. One key rule is that no agent should work more than five consecutive days. In addition, each agent… Read the full blog for free on Medium.

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Published via Towards AI