You may want to have the 2 primitive sets: CITY e.g. CHI MNN KC_ and PERIOD or event points e.g. P0600 P0630 P0700 etc. The nodes of the network will be the 2-tuples (i,p) or (CITY, PERIOD) The arcs/decision variables will be: x(i,p,j,q) = planes flying from (i,p) to (j, q) Additionally you want the idle on ground arcs: idle( i, p) = planes idle on ground at i just after point p, The flow balance constraints will be essentially, for each (i, p): idle( i, p-1) + planes arriving at (i,p) = idle( i, p) + planes departing (i,p) The demand constraints for each (i,p,j,q) will be something like: capacity flown on (i,p,j,q) >= demand( i,p,j,q). Send me an email and I can send you runnable code for your specific data set.