set ORIG;   # origins
set DEST;   # destinations

param supply {ORIG} >= 0;   # amounts available at origins
param demand {DEST} >= 0;   # amounts required at destinations

   check: sum {i in ORIG} supply[i] = sum {j in DEST} demand[j];

param rate1 {i in ORIG, j in DEST} >= 0;
param rate2 {i in ORIG, j in DEST} >= rate1[i,j];
param rate3 {i in ORIG, j in DEST} >= rate2[i,j];

param limit1 {i in ORIG, j in DEST} > 0;
param limit2 {i in ORIG, j in DEST} > limit1[i,j];

var Trans {ORIG,DEST} >= 0;    # units to be shipped

minimize Total_Cost:
   sum {i in ORIG, j in DEST} 
      <<limit1[i,j], limit2[i,j]; 
        rate1[i,j], rate2[i,j], rate3[i,j]>> Trans[i,j];

subject to Supply {i in ORIG}:  
   sum {j in DEST} Trans[i,j] = supply[i];

subject to Demand {j in DEST}:  
   sum {i in ORIG} Trans[i,j] = demand[j];