Tetris vs Palletising
The mathematics behind “just stack the boxes” – and why your pallet configuration actually matters
You’ve played Tetris. Your warehouse staff probably call palletising “playing Tetris.” We do too – we tell customers we’re the best at Tetris in Gauteng.
Here’s what we don’t usually mention: Tetris has been mathematically proven impossible to play optimally. In 2002, MIT researchers demonstrated that Tetris belongs to a problem class called “NP-hard” – meaning no computer algorithm can guarantee the best solution in reasonable time.
The game you think is “just spatial reasoning” defeats supercomputers.
And palletising is harder than Tetris.
Tetris vs Palletising: Why Your Pallet Is the Harder Problem
| Factor | Tetris | Palletising |
|---|---|---|
| Dimensions | 2D (flat grid) | 3D (length × width × height) |
| Shapes | 7 fixed shapes | Dozens of box sizes |
| Placement | Gravity drops pieces | You fight gravity |
| Rotation | 4 orientations | 6 orientations per box |
| Failure mode | Game over | Crushed product, rejected shipment |
| Physics | None | Weight, stability, crush resistance |
Tetris gives you seven shapes on a flat grid with gravity doing the work. Palletising gives you mixed box sizes in three dimensions where you’re responsible for weight distribution, structural stability, and ensuring nothing gets crushed over 1,200 kilometres of road.
If the “easy” version stumps supercomputers, what chance does “quickly stack these 47 different boxes before the truck leaves” have?
What You’re Actually Optimising
Most people think palletising means “fill the pallet, minimise gaps.”
That’s one constraint. You’re actually solving for five or more competing objectives simultaneously.
- Space efficiency: Maximise product per pallet to reduce shipping cost per unit. More product, fewer pallets, lower freight bill.
- Stability: The pallet must survive forklift handling at both ends, loading/unloading forces, and 1,200km of road vibration. A space-efficient arrangement that collapses in transit is worthless.
- Weight distribution: Heavy items at the bottom, centre of gravity low and centred. Top-heavy pallets tip. Uneven weight distribution causes load shift during braking.
- Crush resistance: Frozen meat cases can bear significant weight. Ice cream tubs cannot. The arrangement that maximises space might put 80kg on top of products rated for 20kg.
- Weight limits: 840-940kg maximum depending on route. You cannot simply “add more product” once you hit the limit, regardless of remaining space.
These constraints conflict with each other. The space-optimal arrangement often compromises stability. The most stable arrangement wastes space. Heavy-at-bottom conflicts with customer order groupings. Every pallet is a compromise.
The Combinatorial Explosion: Real Numbers
Let’s calculate what “just figure it out” actually means.
A customer sends us 30 boxes for palletisation – a small assignment. The mix:
- 8× Stock 3 (250 × 150 × 250mm)
- 10× Stock 5 (450 × 300 × 300mm)
- 6× Stock 6 (600 × 450 × 300mm)
- 6× Butcher’s boxes (577 × 369 × 145mm)
Orientation combinations:
Each box can be placed in 6 different orientations (which face points up, which points forward). For 30 boxes:
6^30 = 2.2 × 10^23 possible orientation combinations
That’s 220 sextillion combinations – just for deciding which way each box faces.
Placement sequences:
The order you place boxes affects what fits where. For 30 boxes:
30! = 2.65 × 10^32 possible placement sequences
Combined possibilities:
Orientation × Sequence = approximately 10^55 possible configurations
For perspective: There are roughly 10^50 atoms in Earth. Your 30-box pallet has more possible configurations than atoms on the planet.
And the vast majority of those configurations:
- Won’t physically fit on a 1m × 1.2m pallet
- Will be unstable
- Will exceed weight limits
- Will crush product
Finding the good configurations among 10^55 possibilities is the actual problem.
Why Computers Struggle
“NP-hard” means no shortcut exists. The computer cannot be clever about this – it essentially tries configurations until it finds acceptable ones.
What this means practically:
- Optimal solution for 30 boxes: computation time exceeds the age of the universe
- “Good enough” solution: seconds to minutes using approximation methods
- But “good enough” might be 15-20% worse than optimal
Logistics software uses heuristics – rules of thumb that usually work. They find acceptable solutions, not best solutions. The gap between acceptable and optimal is money. Your money.
The human advantage: Experienced palletisers develop pattern recognition that sometimes beats algorithms for specific product mixes. The algorithm doesn’t know that butcher’s boxes from Supplier X are always slightly oversized. Your trained staff do.
The Real Box Problem: Nothing Tiles Perfectly
Here’s where theory meets your actual shipment.
The Pallet Grid
Standard Euro pallet: 1,000mm × 1,200mm footprint. We have 1.2 square metres to fill.
Stock 6 Boxes (600 × 450 × 300mm)
The largest standard box. How does it tile?
Option A – Length along 1200mm edge:
- 1200 ÷ 600 = 2 boxes
- 1000 ÷ 450 = 2.22 boxes → only 2 fit
- Result: 2 × 2 = 4 boxes per layer
- Coverage: (1200 × 900) ÷ (1200 × 1000) = 90%
- Dead space: 100mm strip along one edge
Option B – Rotated 90°:
- 1200 ÷ 450 = 2.67 → only 2 fit
- 1000 ÷ 600 = 1.67 → only 1 fits
- Result: 2 × 1 = 2 boxes per layer
- This is worse. Option A wins.
The 10mm problem:
Some suppliers list Stock 6 as 610mm × 450mm × 300mm. That extra 10mm matters:
- 1200 ÷ 610 = 1.97 → only 1 fits along that edge
- Your entire arrangement changes for 10mm of cardboard
This is exactly the “assumptions” problem. We plan for 600mm boxes, receive 610mm boxes, and the arrangement we’d mentally prepared no longer works.
Mixed Load: Stock 5 + Stock 6
Now it gets interesting.
Stock 5: 450 × 300 × 300mm Stock 6: 600 × 450 × 300mm
Both are 300mm tall – good, we can build flat layers. But the footprints don’t share common factors that tile nicely together.
One approach:
- 4× Stock 6 in a 2×2 block (1200mm × 900mm)
- Remaining strip: 1200mm × 100mm
- Stock 5 is 450mm wide – doesn’t fit in the 100mm gap
Result: You either waste the strip or fill it with smaller boxes. No clean mixed arrangement exists.
The Butcher’s Box Nightmare
Butcher’s boxes: approximately 577 × 369 × 145mm
Neither dimension divides cleanly into 1000 or 1200.
- 1200 ÷ 577 = 2.08 → 2 boxes, leaving 46mm
- 1000 ÷ 369 = 2.71 → 2 boxes, leaving 262mm
Layer calculation:
- 2 × 2 = 4 butcher’s boxes per layer
- Uses: 1154mm × 738mm
- Wastes: 46mm + 262mm strips = significant dead space
Height mismatch:
Butcher’s boxes are 145mm tall. Stock boxes are 250-300mm tall.
- 2 × butcher’s (290mm) ≈ 1 × Stock 3 (250mm) – but not exactly
- You cannot build flat layers mixing these heights
- Uneven layers create instability and wasted vertical space
The Worked Example
Assignment: Mixed load for Johannesburg to Cape Town
| Box Type | Quantity | Dimensions (mm) | Volume Each | Total Volume |
|---|---|---|---|---|
| Stock 3 | 8 | 250 × 150 × 250 | 9.4 L | 75 L |
| Stock 5 | 10 | 450 × 300 × 300 | 40.5 L | 405 L |
| Stock 6 | 6 | 600 × 450 × 300 | 81 L | 486 L |
| Butcher’s | 6 | 577 × 369 × 145 | 30.9 L | 185 L |
| Total | 30 | 1,151 L |
Theoretical pallet capacity:
1.0m × 1.2m × 1.65m (usable height) = 1,980 litres
Theoretical fill rate:
1,151 ÷ 1,980 = 58% if perfectly packed
Reality check:
These boxes don’t tile perfectly. Mixed heights prevent clean layers. Actual achievable fill rate: 45-52%.
Three approaches compared:
| Approach | Fill Rate | Stable? | Time | Risk |
|---|---|---|---|---|
| “Just stack it” | 55% | ❌ Collapses | 10 min | High – product damage |
| Software default | 42% | ✓ | Instant | Low – but wastes space |
| Trained professional | 50% | ✓ | 20 min | Low – balanced solution |
“Just stack it” achieves higher fill but creates an unstable pile that fails in transit. Software plays it safe and wastes space. The professional balances constraints.
Cost difference:
- Wasted 8% space = might need second pallet on larger orders
- Second pallet JHB→CPT = R800-1,200 additional freight
- Unstable pallet rejected at depot = R2,500+ delay costs
- Crush damage from poor weight distribution = R5,000-15,000 product loss
How Professionals Actually Solve This
We don’t run algorithms in our heads. We use heuristics – rules of thumb developed through experience.
Heuristic 1: Normalise the problem
Odd-sized boxes create chaos. We repack unusual items into standard stock boxes. This costs a few minutes upfront but dramatically simplifies the arrangement problem. Fewer unique dimensions = fewer combinations = faster, better solutions.
This is why we educate customers on using Stock 3, 4, 5, 6 boxes. Not because they tile perfectly – they don’t – but because they tile consistently. We know how they behave.
Heuristic 2: Build layers by height
Group boxes by height. Build complete horizontal layers. Stock 5 and Stock 6 are both 300mm tall – they can share a layer even though footprints differ.
Butcher’s boxes (145mm) get their own layers or pair up to approximately match taller boxes.
Heuristic 3: Heavy and strong at the bottom
Frozen meat cases go at the bottom. Ice cream, pastries, anything crushable goes on top. This isn’t just weight distribution – it’s structural. Strong boxes become the foundation.
Heuristic 4: Interlock layers
Each layer rotates 90° from the one below. This creates a brick-like pattern where vertical seams don’t align. Interlocked layers resist horizontal forces during transport – crucial for surviving emergency braking.
Heuristic 5: Fill gaps strategically
Dead space is inevitable. Position gaps toward the centre of the pallet, not the edges. Centre gaps get compressed by surrounding boxes. Edge gaps allow movement and collapse.
Heuristic 6: When in doubt, test it
Push the completed pallet. If boxes shift, it’s not ready for transport. Better to discover instability in your facility than on the N1.
The Assumptions Problem
Here’s our confession: even professionals make mistakes when working blind.
A customer says “I’m sending 30 boxes.” We plan for Stock 5 and Stock 6 – the common sizes. The boxes arrive and include:
- 10 boxes we expected
- 12 boxes in dimensions we’ve never seen
- 8 butcher’s boxes from a new supplier (different dimensions than usual)
The arrangement we’d mentally prepared is useless. We’re solving the problem from scratch under time pressure with a truck waiting.
Common assumptions that burn us:
| Assumption | Reality | Impact |
|---|---|---|
| “Stock 6 boxes” | Some are 600mm, some are 610mm | Arrangement doesn’t fit |
| “30 boxes” | 30 boxes of vastly different sizes | Estimated pallet count wrong |
| “Frozen meat” | Mix of meat, ice cream, pastries | Different crush resistance, can’t stack freely |
| “Light load” | Concentrated heavy items | Hits weight limit before space limit |
Every wrong assumption costs time, money, or both.
The Solution: Tell Us Before You Send
This is why we’re building a tool.
The concept:
Before your shipment arrives, you input:
- Box dimensions (or select from standard sizes)
- Quantities
- Product type (affects weight estimates and crush resistance)
- Any special handling requirements
The tool outputs:
- Estimated pallet count
- Suggested arrangement diagrams
- Weight distribution preview
- Potential problems flagged in advance
Why this helps both of us:
You get accurate quotes before committing. No surprises on pallet count.
We get advance warning of complex loads. Time to plan rather than improvise.
The truck doesn’t wait while we solve a 10^55-configuration problem from scratch.
What This Means For Your Shipment
When you send us mixed boxes and say “palletise this,” you’re asking us to:
- Solve a mathematically impossible optimisation problem
- Balance five competing constraints simultaneously
- Work with physical dimensions that don’t tile cleanly
- Account for product-specific crush resistance
- Do it under time pressure
- Take responsibility for the result surviving 1,200km
This is not “stacking boxes.” This is applied logistics engineering with your product value at stake.
Your options:
- DIY with guidance: Follow our Palletising Frozen Goods guide – works well for uniform products in standard boxes
- Use the planning tool: [Coming soon] Input your box dimensions, get arrangement recommendations before shipping
- Use our palletisation service: We receive loose goods, palletise to specification, photograph the result, and coordinate handover to your long-haul carrier
Quick Reference: Standard Box Dimensions
For customers using our recommended stock boxes:
| Box | Dimensions (L × W × H) | Volume | Boxes per Layer* | Layers to 1.65m |
|---|---|---|---|---|
| Stock 3 | 250 × 150 × 250mm | 9.4 L | 32 (theoretical) | 6 |
| Stock 4 | 300 × 230 × 300mm | 20.7 L | 17 | 5 |
| Stock 5 | 450 × 300 × 300mm | 40.5 L | 8 | 5 |
| Stock 6 | 600 × 450 × 300mm | 81 L | 4 | 5 |
*Theoretical maximum on 1000 × 1200mm pallet; actual results vary with mixed loads.
Butcher’s boxes vary by supplier. Confirm dimensions before planning.
Summary
Palletising looks simple. The mathematics prove otherwise.
- Tetris is NP-hard – no algorithm guarantees optimal play
- Palletising is harder – 3D, mixed sizes, physics constraints
- Standard boxes don’t tile perfectly – gaps are inevitable, management is the skill
- Competing constraints require trade-offs – space vs stability vs weight vs crush resistance
- Assumptions kill efficiency – unknown box dimensions force improvised solutions
- The solution is information – tell us what you’re sending before you send it
We’re the best at Tetris in Gauteng. But even Tetris champions can’t solve problems they can’t see coming.
Related resources:
- Palletising Frozen Goods for Long-Haul Transport
- Technical Formulas Reference (see Palletisation Mathematics section)
- Our Terms and Conditions – Section 3.7
