FLEX: Using mixed integer programming to assign air cargo to flights

FLEXPORT‘s Andrew Sturges writes: 

In a previous post we outlined the basics of supply and demand in the world of air freight forwarding, and described the difficult problem of air cargo consolidation. In this post we’ll look at how Flexport uses math and data science to solve this problem and get shipments delivered on time at their lowest possible cost.

Consider a toy scenario where a freight forwarder has ten shipments, a single flight to assign any shipment to, and the only decision to make is whether to assign each shipment to the flight. (In this toy scenario, if we choose not to assign a particular shipment to the flight, assume we can move it some other way.) Each shipment has a volume and a cost, and the flight has a total available volume that cannot be exceeded. (You may recognize this as a simplified knapsack problem.) In this case there are 2¹⁰=1,024 possible solutions (actually 1,023 since we wouldn’t send the plane completely empty).

Maybe you could create a spreadsheet to list out each possible solution and choose the one with the lowest cost. But what if you had the same ten shipments but two flights to choose from? Now you have 3¹⁰=59,049 solutions to calculate. For just ten shipments!

A large freight forwarder will have many more than ten shipments and many more than two flights to choose from…

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