Calculate Total Number of Packages and Package Dimensions

[caplinq]

I have a program that calculates the shipping rate to customers. In order to do this, I need to give information to UPS to calculate a rate quote. Every one of our products has got a gross weight and "individual packaged dimensions" as if each product were already packed in its own box.

I am trying to come up with a solution/equation that will calculate how many boxes I will need as well as the dimensions of each of the boxes. I have been wracking my brain to come up with the cleanest, most logical solution.

It does not have to be 100% perfect (ie, there can be gaps in the boxes), but there are some restrictions:
a) The maximum box size of ANY package is 100 x 100 x 100cm
b) Should use the smallest possible box
c) The calculation (or program) must give the total number of boxes
d) The calculation must give dimensions of each of the packages (assuming they will not all be the same size)

I think that the logical solution will FIRST package all SAME TYPE products together and then fit these into the larger package, but I can be convinced otherwise.

Product SKU	Gross Weight	Weight Unit of Measure	Width	Height	Length	Dimension Unit Of Measure	Number of products ordered	Total Gross Weight (kg)	Number of Packages	Package Dimensions (L x W x H) in cm
Product A	0.66	kg	6	6	22	cm	12	7.92
Product B	0.05	kg	10	1	10	cm	14	0.7
Product C	0.02	kg	10	1	10	cm	30	0.6
Product D	0.08	kg	10	2	10	cm	12	0.96
Product E	0.1	kg	10	3	10	cm	2	0.2
Product F	0.01	kg	10	0	10	cm	4	0.04
Product G	0.0225	kg	6	10	6	cm	8	0.18
Product H	0.055	kg	6	10	6	cm	24	1.32
Product I	1.69	kg	10.5	10.5	25	cm	2	3.38
Product J	1.66	kg	13	13	26	cm	3	4.98
Product K	2.07	kg	15	15	30	cm	2	4.14
							Total Gross Weight	24.42
							Total Number of Packages
							Dimensions Package 1
							Dimensions Package 2
							Dimensions Package 3
							Dimensions Package 4
							Dimensions Package 5
							Dimensions Package 6
							Dimensions Package 7
							Dimensions Package 8
							Dimensions Package 9
							Dimensions Package 10
							Dimensions Package 11
							Dimensions Package 12
							Dimensions Package 13

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I would post my excel sheet if I could figure out how!