You're staring at three purchase orders. So three products. Same machines. And same factory. Same people. And somehow, every time you try to schedule the week, the numbers fight each other Worth keeping that in mind..
Sound familiar?
This isn't just a textbook problem. It's Tuesday morning at Ace Manufacturing — or whatever you call your shop — and the scheduler just quit, or the ERP system coughed up a plan that ignores the fact that Machine 4 has been making a sound like a dying goose for three weeks.
Let's talk about what actually happens when you have orders for three similar products competing for the same constrained resources. And more importantly, how to stop guessing Nothing fancy..
What Is the Three-Product Product Mix Problem
At its core, this is a resource allocation puzzle. Plus, you have Product A, Product B, and Product C. They're "similar" — meaning they share production steps, maybe even the same bill of materials for the first few operations. But each one eats up machine hours, labor hours, and raw material at different rates. And each one carries a different margin Simple, but easy to overlook..
The goal: fulfill the orders (or maximize profit if you can't fulfill all of them) without blowing past your constraints.
Constraints are the boring part that actually matters. In practice, machine capacity. Because of that, labor shifts. Raw material on hand. Tooling changeover time. That one operator who knows how to run the CNC lathe and is on vacation next week.
The Classic Formulation (Without the Math Speak)
Every operations textbook uses a version of this. Consider this: three products. This leads to two machines. In real terms, ace Manufacturing. Still, limited hours. Maximize profit.
Product A: $50 contribution margin, 2 hours on Machine 1, 1 hour on Machine 2
Product B: $40 contribution margin, 1 hour on Machine 1, 3 hours on Machine 2
Product C: $45 contribution margin, 2 hours on Machine 1, 2 hours on Machine 2
Machine 1: 100 hours available
Machine 2: 90 hours available
Orders: 20 units of A, 30 of B, 15 of C
Looks clean on a whiteboard. Machine hours aren't fixed — they shrink when maintenance runs long. Contribution margin changes when you factor in expedited freight for late raw materials. In real life, the data is messier. And "similar products" often means they share a bottleneck operation that nobody mapped properly.
Why This Keeps People Up at Night
Most shops don't ignore this problem because they don't know it exists. They ignore it because the answer keeps changing.
Monday's optimal mix is Tuesday's disaster when:
- A key supplier shorts you 20% on a shared raw material
- The night shift calls out sick
- A rush order from your biggest customer drops in at 3 PM
- You realize Product C's routing was never updated after the engineering change last quarter
The cost of getting it wrong isn't academic. Overtime you didn't budget. It's late shipments. Practically speaking, expedite fees. The customer who stops calling because you missed two delivery dates in a row Easy to understand, harder to ignore..
And here's what most people miss: the optimal product mix isn't a number. It's a decision process. You need a way to re-optimize fast when reality shifts — not a static spreadsheet that was right for three hours last January.
How to Actually Solve It (Without a PhD)
You don't need to solve the simplex method by hand. But you do need a framework that holds up when the data gets ugly.
Step 1: Map the Real Constraints — Not the Theoretical Ones
Start with a constraint audit. Walk the floor. Talk to the supervisors.
What actually limits you this week?
- Machine 3 is down for bearing replacement until Thursday
- Only two operators certified on the welding cell
- Steel allocation from the mill is 15% short
- Changeover between Product A and B takes 45 minutes, not the 15 in the router
Write these down. Quantify them in hours or units. This is your real constraint set. Everything else is noise.
Step 2: Calculate True Contribution Margin Per Constraint Unit
This is where most people stop at "margin per unit." Wrong metric.
If Machine 3 is your bottleneck, you need margin per Machine 3 hour Most people skip this — try not to. Surprisingly effective..
Product A: $50 margin / 2 Machine 3 hours = $25/hr
Product B: $40 margin / 1 Machine 3 hour = $40/hr
Product C: $45 margin / 3 Machine 3 hours = $15/hr
Suddenly Product B looks like the winner — even though its per-unit margin is lowest. Because it burns the least of your scarcest resource And it works..
Do this for every binding constraint. Worth adding: labor hours. That's why pallet spots. Paint booth time. The product that wins on the tightest constraint usually wins overall.
Step 3: Build a Living Model — Not a Monument
Excel works. So does Google Sheets. So does a whiteboard if your mix is simple enough Most people skip this — try not to..
What matters:
- Inputs are visible and editable in one place
- Constraints are labeled with source ("Machine 3 hours — per maintenance schedule 3/12")
- The objective cell shows total contribution margin
- You can change one number and see the ripple in 10 seconds
And yeah — that's actually more nuanced than it sounds Simple as that..
If your model takes 20 minutes to update, you won't update it. You'll guess. And guessing is how you end up with 500 units of Product C sitting in WIP while the Product A order ships late.
Step 4: Run Scenarios Before You Commit
Don't just solve once. Ask:
- What if Machine 3 stays down two extra days? On the flip side, - What if the steel shipment arrives Monday instead of Wednesday? - What if we subcontract Product B's welding step?
Scenario planning turns a schedule into a strategy. You'll know which constraint breaking hurts most — and you'll have a Plan B ready when it does.
Step 5: Communicate the Plan in Operations Language
"Optimal product mix: 18A, 24B, 12C" means nothing to the floor.
Translate:
- "Run Product B first on Machine 3 — it's our highest margin per bottleneck hour"
- "Machine 1 has 14 hours slack — use it for changeover prep or preventive maintenance"
- "If steel doesn't land by noon Tuesday, we drop Product C and shift those hours to A"
Post it at the scheduling board. Review it in the 7 AM huddle. Make it visible, not filed.
Common Mistakes / What Most People Get Wrong
Treating All Constraints as Equal
They're not. And the rest have slack. Think about it: one constraint is binding. Optimizing for a non-binding constraint wastes time and distorts the mix. Find the real bottleneck — the one that would increase total margin if you relaxed it by one unit. That's your drum. Everything else marches to it But it adds up..
Using Standard Cost Margins
Standard cost includes allocated overhead. Allocated overhead doesn't change with this week's product mix. Use contribution margin — revenue minus truly variable costs. Direct material Simple, but easy to overlook..
labor. Variable machine costs (power, tooling wear, per-unit consumables). So that’s it. Practically speaking, no absorbed rent, no depreciation allocations, no “corporate burden” rates. If the cost doesn’t walk out the door with the unit, it doesn’t belong in the decision.
Ignoring Setup and Changeover Time
Your model says Machine 3 has 120 hours. Batch sizing and sequencing are the scheduling problem. Reality says 15 of those vanish into changeovers between Product A and B. If you don’t model setup time — and sequence-dependent setup time at that — your “optimal” mix is a fantasy. Solve them together or don’t bother Not complicated — just consistent..
Optimizing for Utilization Instead of Throughput
Running Machine 1 at 95% utilization feels good. But if Machine 1 feeds Machine 3 (the bottleneck), and Machine 3 is starved because Machine 1 made the wrong parts, you’ve just built expensive WIP. So naturally, **Utilization of non-bottlenecks is irrelevant. Now, throughput at the bottleneck is everything. ** Let non-bottlenecks idle if it protects the constraint’s flow Practical, not theoretical..
Forgetting the Human Constraint
The model balances perfectly. The crew? A schedule that ignores skill matrices, shift handoffs, and fatigue isn’t a schedule — it’s a wish list. Build in 15–20% buffer for “life happens.Worth adding: they’re exhausted, cross-trained on only two of three machines, and the lead mechanic is on vacation. ” Protect the bottleneck and the people running it Not complicated — just consistent..
Conclusion: The Schedule Is a Hypothesis — Test It Daily
You don’t build a product mix model to get the “right answer.So when Monday morning breaks the plan — and it will — you don’t scramble. Because of that, ” You build it to make your assumptions visible, your trade-offs explicit, and your bottlenecks undeniable. You adjust.
You know exactly which constraint snapped. You know which product drops margin fastest per lost hour. You know where the slack lives to absorb the hit. And you’ve already told the floor, in their language, what “Plan B” looks like.
That’s not scheduling. That’s control.
Next week, the constraints shift. A new order lands. A machine gets PM’d. A supplier ghosts you. Because of that, pull the model up. Change the numbers. Day to day, watch the ripple. Post the new plan at 7 AM Which is the point..
The optimal mix isn’t a number. It’s a discipline.
