You are correct - you cannot usually sum inventory quantities like other things although, depending on the requirements, sometimes you can average the inventory quantities.
If you have weekly inventory data and you want to sum up quantities but only for the last week week of the month you can do something like this: sum( if(Month(invdate)<>Month(invdate+7), invquantity) )
The idea works if you use the Year function instead of Month to get the last week of the year. And you could use something like this sum( if(QuarterName(invdate)<>QuarterName(invdate+7), invquantity) ) to sum inventories from the last week of the quarter.
You likely could create some sort of complex equation however in my opinion that would be the 'hard way' to achieve this. Since you have a defined hierarchy with only 3 level, I would recommend going with three charts and using buttons to show/hide the charts.
Chart 1 would be at the Year Level
Chart 2 would be at the Month Level
Chart 3 would be at the Week Level
Pushing the "Month Level" button would show Chart 2 and hide Chart 1 & 3.
This will also have the advantage of taking up less header space with the expanding pivot table. Also it will be easier for users to move between levels because they will have a button to push vs needing to hit the little expand buttons in the pivot table.
A similar technique is used on the Order and Inventory Management Demo.
You may also want to check out this video to see the general show/hide technique: