Determining redistribution of items when changing carton size


New member
Mar 25, 2020

Need help on the below - apologies if wrong section

In a warehouse there are currently two carton sizes: medium and large.

However, the warehouse is transforming the medium carton (variable size) to a standardised (static size) small carton (35cm length, 30cm width, 35cm height).

Need to determine, based on current fill percentages, what percentage of the items currently contained in the medium-cartons will fit inside the new small carton, and what percentage will have to shift to the large carton (i.e. what the split between them will be).

The items inside the cartons are not fluids.

To help with the above, there is available data given to us that details every carton (medium or large), its dimensions, and its fill percentage (ie how efficiently it used the available volume in the carton). (its a big data dump)

Any steer on the most mathematically apt way to determine what the split % will be between small and large cartons upon removing the medium carton (ballpark)?

I was thinking: normally distribute the total utilised volume (volume * fill %) of each medium carton, then determine how many standard deviations from the mean the new proposed small carton size is (Z-score). This would allow me to determine what %, based on current fill rates, would fit inside the small carton. Everything else would have to go into the large cartons.

I'm sure I've made a logical error here though. Any ideas?



Elite Member
Dec 30, 2014
Why code you question so much? I would suspect that your answer depends on the size of the medium cartons. If the medium cartons are just slightly larger than the new small boxes that a very high percentage of the contents of the medium cartons will fit in the small boxes. etc etc.