I need to model the following problem:

For a planning horizon of $P$ equal periods, one has $N$ harvesting locations and $K$ contractors who can harvest at those locations ($K < N$). Each harvesting site has a given volume to be harvested before a period $t_i$, with $i \in \{1,\ldots,N\}$. Each of the $K$ contractors has one or more machines to do that job. The idea is to assign contractors to do the harvesting at each of the sites, such that travel between harvesting sites is kept to a minimum. I must also decide when a contractor starts harvesting at each location and in what period $ p \in \{1,\ldots,P\}$ he will be harvesting. I know in advance the harvesting productivity of each of the $N$ sites (how much volume a machine can harvest at that site during a period).

In each period, a certain harvesting demand must be met. The periods can be months of the year.

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    $\begingroup$ This looks to be quiet possible to do with MILP. Is the cost traveling between any two harvesting location the same or does that differ? Is the number of contractors fixed or just upper bounded. Are they hired per period or are they hired for some sequential periods (1,3,7,9) vs (1,2,3,4,5,6)? Are all machines identical? $\endgroup$ Commented Sep 10, 2021 at 8:59
  • $\begingroup$ Can machines be freely moved between periods at no cost? $\endgroup$ Commented Sep 10, 2021 at 9:11
  • $\begingroup$ The cost of travel between the different sites is different (and symmetrical). The idea is that the contractor (there is a fixed number of them) work sequentially at each site (e.g. in periods 1,2,3,4,5,6). The machines are all identical. $\endgroup$ Commented Sep 10, 2021 at 10:27
  • $\begingroup$ Is the number of machines per contractor fixed, choose-able per contractor but constant for all time, or chooseable per time and contractor point? $\endgroup$ Commented Sep 11, 2021 at 13:05
  • $\begingroup$ Each contractor has a fixed number of machines throughout the planning horizon (they may have different number of machines between them) $\endgroup$ Commented Sep 12, 2021 at 14:59


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