In 1972, Ishida changed the packaging industry forever by inventing computer combination weighing technology. The first machine was designed for an impossible task: automatically weighing green peppers at 50-60 bags per minute with +/-2g accuracy. That original machine is still operational today and was designated as Mechanical Engineering Heritage by the Japan Society of Mechanical Engineers in 2017.
The secret behind this 50-year success? Combinatorial mathematics. A multi-head weigher doesn’t weigh products one at a time. Instead, it evaluates thousands of possible combinations in milliseconds to find the best match for your target weight.
A multi-head weigher uses a simple but powerful formula: 2^n, where n equals the number of weighing heads. This means a 14-head machine evaluates 16,384 possible combinations every single cycle.
The process works in five steps:
The algorithm doesn’t search for a “perfect” combination. It finds the best available option within your specified tolerance. This distinction matters because it explains why multihead weigher vertical packing machines consistently outperform simpler weighing methods in real production environments.
More heads exponentially increase the probability of finding an ideal combination. The math is straightforward:
| Number of Heads | Possible Combinations |
|---|---|
| 10 heads | 1,024 |
| 12 heads | 4,096 |
| 14 heads | 16,384 |
| 24 heads | 16,777,216 |
Each additional head doubles your options. Going from 10 to 14 heads increases combinations by 16x, from 1,024 to 16,384.
This translates directly to accuracy. On a 1 kg product, a traditional rough-and-fine weigher might achieve 5% accuracy, whereas a multihead will usually be within 1% of the target weight. That 4% difference adds up fast on high-volume lines.
Here’s the counter-intuitive part: speed gains plateau after a certain point, but accuracy keeps improving. A 14-head at 120 bags per minute isn’t dramatically faster than a 12-head at similar speeds. The real benefit of additional heads is finding better combinations, not faster throughput. For most applications, I recommend prioritizing head count for accuracy rather than speed specifications.
The system uses a 99.73% confidence level threshold. If no combination of hoppers can produce a weight within this confidence level, all hoppers discharge and refill rather than package an out-of-spec weight.
This failsafe explains why proper hopper loading matters so much. Each hopper should contain approximately 20-35% of the target weight. Load them too heavy, and fewer combinations work. Load them too light, and you need more hoppers to reach target.
The machine runs what researchers call a “knapsack algorithm” – it opens or leaves shut different combinations of hoppers such that the total package weight is near its target, minimizing the amount of product given away.
This is what separates multi-head weighers from simpler alternatives. The system never compromises on accuracy. It either finds an acceptable combination or starts over. You’ll never package an out-of-tolerance product because the machine was in a hurry.
The algorithm calculates all combinations in a few milliseconds. The full weighing cycle takes approximately 0.7 seconds.
Most people confuse these two numbers. The calculation itself is nearly instantaneous. The 0.7 seconds includes feeding product into hoppers, allowing it to settle, making the selection, and releasing to the packaging station below.
Speed varies by configuration:
| Configuration | Typical Speed |
|---|---|
| 10-head weigher | 65-70 weighments/minute |
| 14-head weigher | Up to 120 bags/minute |
| 24-head weigher | Up to 160 batches/minute |
Don’t conflate algorithm speed with throughput. Vendors sometimes emphasize millisecond calculation times, but your actual throughput depends on the complete cycle. When evaluating specifications, focus on weighments per minute, not calculation speed. Understanding how multihead weighers work in their complete cycle helps you ask better questions during equipment evaluation.
Each head represents a binary choice in the combination algorithm: included or excluded. Lose one head, and you lose half your possible combinations.
The math is unforgiving. As one Yamato technical note explains: “For each additional weigh head added, the number of combinations double. Conversely, for each weigh head that becomes unavailable to use, the number of combinations cuts in half.”
On a 14-head scale, there are 16,384 possible combinations. With 13 heads, that drops to only 8,192 combinations. This directly impacts your ability to find optimal weights.
The financial impact is substantial. Consider pistachios: one industry example showed that a single non-functional head increased giveaway from 1g to 2g per package. At high production volumes, this translated to roughly $130 per hour in extra product cost, or over $10,000 per week on two-shift operations.
A single non-functional head should be treated as a critical maintenance issue, not routine. Regular calibration checks with certified weights and proper cleaning of your multihead weigher are essential to maintaining all heads operational.
Start with your accuracy requirements, then match throughput. Most buyers approach this backwards, focusing on speed first and accepting whatever accuracy comes with it.
Consider three factors:
Product Characteristics
Irregular products like snack mixes or fresh produce benefit more from additional heads. Uniform products like rice or sugar need fewer combinations to hit target weight.
Accuracy Requirements
Pharmaceutical and premium food applications often need +/-0.5g accuracy. Standard food packaging might accept +/-1.5g. Tighter tolerances require more heads.
Throughput Needs
Match your line speed requirements. A 10-head at 65 weighments per minute may be sufficient for moderate production. High-speed lines running 100+ packages per minute benefit from 14 or more heads.
Practical selection guidelines:
| Head Count | Best Applications |
|---|---|
| 10-head | Free-flowing uniform products, moderate speed requirements |
| 14-head | Mixed products, higher accuracy needs, mainstream production |
| 24-head | Maximum accuracy, high-speed lines, premium products |
Multihead weighers typically require 18-36 months to recover costs through efficiency gains. With proper maintenance, these machines remain operational for 10-15 years or more. Ishida has sold over 60,000 machines to customers worldwide, demonstrating the proven reliability of the combinatorial weighing approach.
When choosing packaging machinery, match your head count to accuracy requirements first. Speed can often be addressed through line configuration, but accuracy is built into your equipment choice from day one.
The combinatorial approach to weighing has proven its value for over 50 years. Understanding how the algorithm works helps you evaluate equipment specifications, justify investments to stakeholders, and maintain your machines for optimal performance.
Ready to discuss multi-head weigher options for your production line? Reach out to explore which configuration matches your product requirements and throughput goals.
