2 
fij = xi - xj        if xi > xj
fij = xi - xj + 1440    if xi < xj

min sum(fij*Lij)
cons by:
0 =< xi <= 1439          #Minutes in a day

Context: xi and xj correspond to departure and arrival times. fij gives us the waiting time corresponding to ij combination. If departure happens before arrival then we add 1 day to the difference. Objective is to minimize sum product of waiting time and load corresponding to ij .

Is it possible to model this function as a linear program.

Improve this question
2
  • LP`? Probably not. MIP, sure (if Lij is constant). Look up indicator constraints. Commented Oct 18, 2017 at 14:08
  • Thanks for the tip. For simplicity, I am assuming Lij is constant for now. So I introduced a binary variable yij and modify my objective function as min sum((fij+yij*1440)*Lij) such that xi - xj +M*yij >= 0. This way yij will be forced to 1 when xi - xj < 0. Is it safe to assume that when xi - xj >= 0 the minimization function will force yij to be 0. Also M could be set at 1440. Does this look okay? Commented Oct 23, 2017 at 6:58
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