True,
for the task shown. That for me is the rub. As an engineering problem I'm looking at it like "The robot cost $x, operating it costs $y, and setting it up to operate costs $z." So I want to make sure that the costs add up to (ideally) less than an operator or two.
Optimization is about what can you assume is "fixed" about the environment (and so not engineer a solution around it) and what must you consider "variable". Clearly fixed constraints are easier to engineer around, and if all of your pallets and racks were arranged similarly, then a robot you could move somewhere, have it extend its "base" to provide stability, and then run all day would be a win.
The other variable then is how often do I do this task from this space. Assuming setup and tear down of the robot takes some number of minutes/hours, those add as a cost to change tasks. If the robot is mobile and can move itself from task to task, that changes its economics as well.
So lets assume as an example, that there are six bays (loading docks) at the warehouse and each bay of the warehouse receives one truck a day which offloads up to 6 pallets that need to be transported on to the conveyor.
If all trucks arrive at the same time:
Six robots will efficiently unload them as soon as they arrive. (optimizing for truck parking time) At the expense of six robots.
One robot that can be packed up, moved, and unpacked, can work all bays at the cost of loading bays that cannot be reused until all previous bays have been unloaded. How long does that take? And how does it affect how many goods can be moved through the warehouse? (which is how money comes in)
Then there are trucks that arrive at different times. Same options but now you have idle robots (if you have six robots) which are waiting for a truck. Although you might be able to overlap robot movement with truck arrival to keep your bays reasonably busy.
At the outermost level of the problem (where the business people look at it), a warehouse is essentially a "switch" that moves goods from bulk carriers to more specific carriers. Each good moved through earns its percentage of the transport cost. Each good incurs a storage cost while sitting in the warehouse. Lots of metrics around how many times you can completely fill and empty the warehouse of goods vs the money you can get for transporting goods.
Bottom line is that reality (and logistics in particular) are pretty complicated and I expect there are times when a stationary arm would make more sense than a moving arm. However I consider the 'moving arm' to be the super class of 'arm' (to me it seems easier to turn an arm that can move on its own to one that is stationary, and much harder to give a stationary arm the ability to move.)