set ITEMS:=1..13;
set BINS:=1..10;

param bin_size:=100;
param size{i in ITEMS};

var open{j in BINS} >=0, <=1;
var x{i in ITEMS, j in BINS} >=0, <=1;

minimize number_of_bins: sum{j in BINS}open[j];

subject to must_pack{i in ITEMS}: sum{j in BINS}x[i,j]=1;

subject to Bin_size{j in BINS}: sum{i in ITEMS} x[i,j]*size[i]<=bin_size;
subject to Open_bins_only {i in ITEMS, j in BINS}: x[i,j]<=open[j];

#subject to Bin_size_impr{j in BINS}: sum{i in ITEMS} x[i,j]*size[i]<=bin_size*open[j];

data;

param size:=
1	20
2	20
3	20
4	20
5	20
6	81
7	81
8	81
9	81
10	82
11	91
12	49
13	51
;