BIN PACKING Problem Given a set of M bins all of equal capac

BIN PACKING Problem

Given a set of M bins all of equal capacity B and a set of N items each of certain size Si the problem is to pack all the items into bins so that the total number of bins used is minimised without exceeding the capacity of any
bin. Consider a problem with N=12 items, M=6 bins available, each bin has capacity B=1 and the items have size given by: 0.1 , 0.3 , 0.5 , 0.4 , 0.6 , 0.4 , 0.3 , 0.25 , 0.5 , 0.15 , 0.1 , 0.2

Develop a spreadsheet optimization model in Excel to solve the problem, also type the corresponding algebraic model.

We need to solve the problem using next fit problem

void NextFit ( )

{ read item1;

while ( read item2 ) {

if ( item2 can be packed in the same bin as item1 )

place item2 in the bin;

else

create a new bin for item2;

item1 = item2;

} /* end-while */

}

Bin 1 = 0.1

Next Input Bin 1 = 0.1 + 0.3

Next Input Bin 1 = 0.1 + 0.3 + 0.5

Next Input can\'t be put in Bin1, hence it must be put in Bin2

Bin 2 = 0.4

Bin 2 = 0.4 + 0.6 = 1.0 (Bin 2 is full)

Bin 1 = 0.9

Bin 2 = full

Bin 3 = 0.4

Next input = 0.3

Bin 1 = 0.9

Bin 2 = full

Bin 3 = 0.4 + 0.3 = 0.7

Next input = 0.25

Bin 1 = 0.9

Bin 2 = full