Mathematical Optimization - The best answer, not the best guess
Most business planning works the same way. Someone builds a spreadsheet, tries a few scenarios, and the team picks the one that looks best. Push the high-margin product. Cut the one losing money. Run the plant flat out. Staff for the peak.
These rules of thumb aren’t stupid. They’re often right, and they’re easy to explain in a meeting. But they share one blind spot: they can only find the best answer among the options someone thought of trying.
Mathematical optimization works the other way round. You don’t give it a plan. You describe the problem in three parts:
- What you can control. How much of each product to make, how many people to put on each shift etc.
- What you want. The highest EBITDA, the lowest cost, the most customers served.
- What limits you. Machine hours, raw material supply, cash, contracts you have to honour, rules you can’t break.
A solver then searches every plan that fits within those limits and hands you the best one. For a large class of business problems, it can also prove that nothing better exists.
Traditional planning answers “what happens if we do this?” An optimization model answers “what should we do?”
Why the rule of thumb falls short
Rules of thumb look at one thing at a time: margin, or volume, or utilization. Real businesses have several limits pulling against each other, and the one that actually holds you back is often not the one you’re watching.
A product with a great margin per kg can be a terrible use of your scarcest machine. A shift pattern that covers every hour can still have people sitting idle for half the day. And when you fix one bottleneck, the problem usually just moves somewhere else. A person juggling three or four limits at once will rarely land on the best plan. A solver does it in seconds.
The useful by-product
An optimization model also tells you what each limit is costing you. It can work out what one more hour on the bottleneck machine is worth, or one more tonne of a scarce raw material, or one more person on the evening shift. It also tells you which limits don’t matter at all right now.
That’s very handy the next time someone asks for capex. You stop debating whether a new dryer is a good idea and start comparing what it would earn against what it costs.
None of this is new
The maths has been around since the late 1940s. Oil refineries were using it to decide what to blend by the 1950s, and airlines, shipping lines and logistics companies run on it today. Excel has had a solver built in for more than thirty years.
What surprises me is how rarely it’s used anywhere else. I don’t think the tool is the reason. Most people simply don’t know that this kind of question can be answered exactly, so they never ask it.
What this series will cover
Each post takes one business problem, shows where the rule of thumb and the optimal answer split apart, and comes with a model you can download and play with:
- What should a multi-product plant make?
- How many people do you actually need on each shift?
- Where should the next rupee of marketing go?
- Which projects make the cut when capital is tight?
- Where should the warehouse be?
First up: what product mix should a pharma API plant produce to maximize EBITDA [a rule thumb based approach leads to ₹3.9 crore EBITDA and the optimal one earns ₹7.3 crore, from the same equipment.]