Yes, and the mathematical reason behind this is straightforward. Capacity planning is the hardest problem in logistics[1]. You have to plan weekly capacity several months ahead of time, and you have a minimum break-even load factor to hit, but you also want enough capacity to not have to leave business on the table when demand is high.
Contractual customers commit to give you a steady weekly load, which reduces week-to-week variance in your demand and makes your forecasting more accurate. A more accurate forecast means you need less excess capacity and can run at a higher average utilization. This is very valuable, hence the discounts.
[1]Actually route optimization might be the hardest problem in logistics because the traveling salesman problem is a classic NP-complete optimization problem, but in practice it's not so hard to find a good-enough solution and the stakes are lower. Suboptimal routes won't make or break your profit margin, but poor capacity planning absolutely will.
The alternative way of thinking about it is that buying at spot rates includes an embedded option to not use the capacity. This real option has some value, so customers are willing to pay higher rates in the spot market rather than through contracts. There's necessarily some level of contract discount - otherwise, everyone would pay spot rates for the free optionality.
Contractual customers commit to give you a steady weekly load, which reduces week-to-week variance in your demand and makes your forecasting more accurate. A more accurate forecast means you need less excess capacity and can run at a higher average utilization. This is very valuable, hence the discounts.
[1]Actually route optimization might be the hardest problem in logistics because the traveling salesman problem is a classic NP-complete optimization problem, but in practice it's not so hard to find a good-enough solution and the stakes are lower. Suboptimal routes won't make or break your profit margin, but poor capacity planning absolutely will.