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CARGO LOADING PROBLEM:

Cargo loading problem is an optimization problem in which a logistic company has to take a decision regarding the loading of items subjects to its weight or volume, so that, the return to the company will be maximum.

EXAMPLE:

Alpha logistic company has to load a cargo out of four items whose details are shown in the table below. The maximum weight of the cargo is 7 tons. Find the optimal cargo loading using dynamic programming method such that the total return is maximized.

Items	1	2	3	4
Weight(in tons)	2	1	4	3
Return(in rupees)	1000	400	2100	1400

Stage 1 1 4 State Variable x Alternative mi 2 3 Allocated Weight 2 4 F*1 M1 0 6 0 0 0 1 1 0 0 1 2 0 1000 1000 2 3 0 1000 1000 2 4 0 1000 2000 2000 wwN 3 5 0 1000 2000 2000 3 6 0 1000 2000 3000 3000 4 7 0 1000 2000 3000 3000 4 Stage 3 State Variable X3 Alternative m3 1 2 Allocated Weight 0 4 F3 M*3 0 0+0=0 0 1 1 0+400=400 400 1 2 0+1000=1000 1000 1 3 0+1400=1400 1400 1 4 0+2000=2000 2100+0=2100 2100 2 5 0+2400=2400 2100+400=2500 2500 2 6 0+3000=3000 2100+1000=3100 3100 2 7 0+3400=3400 2100+1400=3500 3500 2 Stage 4 1 3 State Variable x4 Alternative me 2 Allocated Weight 3 F4 M*4 0 6 0 0 0+0=0 0 1 1 0+400=400 400 1 2 0+1000=1000 1000 1 3 0+1400=1400 0+1400=1400 1400 1,2 4 0+2100=2100 1400+400=1800 2100 1 5 0+2500=2500 1400+1000=2400 2500 1 6 0+3100=3100 1400+1400=2800 2800+0=2800 3100 1 7 0+3500=3500 1400+2100=3500 2800+400=3200 3500 1,2