Grain Silo Packing
BIN PACKING PROBLEM
Efficient silo utilization reduces storage costs by 10–20% at commercial grain elevators handling 50,000–200,000 bushels across 10–30 bins (Maier & Bakker-Arkema, 2002). Every harvest requires deciding how to assign dozens of grain lots—each a different crop type and tonnage—into a limited number of silos without mixing incompatible grains. This is the 1D Bin Packing Problem (BPP)—one of the foundational strongly NP-hard problems in combinatorial optimization.
Where This Decision Fits
Post-harvest operations chain — the highlighted step is what this page optimizes
The Problem
From grain silos to optimization theory
A grain storage facility has silos each holding 50 tons. After harvest, 12 grain lots of varying sizes must be stored. The goal is to minimize the number of silos used while fitting all lots.
This is the 1D Bin Packing Problem: pack n items into bins of capacity C using the minimum number of bins. Strongly NP-hard.
| Agriculture Domain | Bin Packing Model | |
|---|---|---|
| Grain silo (50t) | Bin (capacity C) | |
| Grain lot | Item (size si) | |
| Minimize silos rented | Minimize number of bins |
Try It Yourself
Edit grain lot weights, adjust silo capacity, and find the optimal packing
Grain Lots & Silo Configuration
12 Lots · Click any cell to edit| Lot | Crop | Weight (tons) |
|---|
The Algorithm
First Fit Decreasing (FFD) for Bin Packing
Sort Items by Size
Arrange grain lots in decreasing order of weight. Large lots are placed first.
First Fit Placement
For each lot, scan silos from first to last. Place the lot in the first silo with enough remaining capacity.
Open New Silo if Needed
If no existing silo can fit the lot, open a new silo and place it there.
Return Assignment
The resulting assignment uses at most 11/9 · OPT + 6/9 bins. Very effective in practice.
Real-World Complexity
Factors beyond the basic bin packing model
Grain Compatibility
Some grains cannot be mixed in the same silo due to contamination risk.
Temperature Control
Different grains need different storage temperatures and humidity levels.
Turnover Schedule
Silos are emptied at different times; packing changes dynamically.
Pest Control
Silo fumigation schedules create temporary unavailability.
Silo Sizes Vary
Real facilities have silos of different capacities, not just one type.
Loading/Unloading
Silo access points limit how quickly grain can be moved in and out.
References
Key literature on bin packing