What it means
Every optimisation problem has three parts. There is an objective, which is the thing to be maximised or minimised, such as profit or cost.
There are decisions, such as how many units of each product to make, and there are constraints, such as limited machine hours, cash or demand. The idea is old, but computers have made it practical for large problems.
A spreadsheet add-in can solve a production mix with a handful of products, and specialist software can handle thousands of variables for airlines, logistics firms and banks. The same logic sits behind portfolio construction, where an investor seeks the highest expected return for a chosen level of risk.
A key lesson is that the best answer depends on what is scarce. When machine hours are the limit, the product with the highest contribution per hour wins, not the one with the highest contribution per unit.
Finance teams use this reasoning when allocating a fixed capital budget across projects, ranking them by return per dollar of scarce capital. There are important cautions.
An optimiser gives the best answer to the question it was asked, so a model with wrong inputs or missing constraints produces a confident but wrong result. Forecasts, costs and demand estimates all carry uncertainty, so sensible teams test how the answer changes when assumptions move, which is called sensitivity analysis.
Optimisation can also be pushed too far. A plan that squeezes out every bit of slack may be fragile, leaving no room for late deliveries, price shocks or equipment breakdowns.
Many businesses deliberately accept a slightly lower theoretical result in return for resilience.
In practice
Real-world examples.
Example
A manufacturer with limited factory hours chooses the product mix that gives the highest total contribution. The finance team builds the model in a spreadsheet and reruns it each month as demand and costs change.
Example
A delivery company plans its routes so that vans cover all stops with the fewest kilometres driven. Lower mileage reduces fuel and wage costs, and the saving is reported as a reduction in operating expenses.
Example
An investment manager builds a portfolio that aims for the highest expected return for a set level of risk. She reviews the mix each quarter because the inputs to the model, such as expected returns, change over time.
Formula
Calculation
Maximise total contribution = (contribution per unit of A x units of A) + (contribution per unit of B x units of B), subject to hours used not exceeding hours available
A workshop has 1,000 machine hours. Product A earns a contribution of $30 per unit, uses 2 hours and has demand of at most 400 units. Product B earns $50 per unit and uses 4 hours. Contribution per hour is 30 / 2 = $15 for A and 50 / 4 = $12.50 for B, so A is made first. Making 400 units of A uses 400 x 2 = 800 hours and earns 400 x 30 = $12,000. The remaining 200 hours make 200 / 4 = 50 units of B, earning 50 x 50 = $2,500. The best total contribution = 12,000 + 2,500 = $14,500, which beats making only B (250 units x 50 = $12,500).Case study
Seen in the real world.
Riverbend Furniture is a fictional company that made tables and chairs on the same production line. For years the owner simply made as many tables as customers ordered, because tables had the higher profit per item.
The finance manager worked out the contribution per hour of line time and found that chairs earned $22 an hour against $18 for tables. Since line time was the real limit, she recommended shifting capacity toward chairs wherever demand allowed.
In this illustrative story the change raised monthly contribution by about $6,000 with no new equipment. She noted that the result depended on chair demand holding up, so she set up a monthly review of the assumptions.
Watch out
Common mistakes.
- Optimising the wrong objective, such as maximising revenue when profit or cash is what matters.
- Trusting the result without testing the inputs, when small changes in costs or demand can change the best answer.
- Removing all slack from a plan, which makes it fragile when something goes wrong.
Questions
People also ask.
Is optimisation the same as maximising profit?
Not always, because the objective can also be minimising cost, risk or time, and the right one depends on the decision.
Do I need special software to optimise?
Simple problems can be solved with a spreadsheet solver, but large ones with many variables and constraints need specialist tools.
What is a constraint?
It is a limit on the choices available, such as a budget, a number of machine hours or a legal requirement.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related