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I'm looking for guidance on how to reduce the following problem to a known problem or a suggestion for solving it altogether. Optimal / heuristic solutions or any other suggestions are greatly appreciated!

Consider:

  • Drop off points {t_1, t_2, ...} ∈ T

    Every drop off point has a number of required items {d_1, d_2, d_3} ∈    D_t
    
  • Transport vehicles {f_1, f_2, ...} ∈ F

    Every transport vehicle has a number of pre-determined goods {w_1, w_2, w_n} ∈ W_f
    

The specific goods loaded in a transport vehicle and required items for each drop off point are pre-fixed.

A specific good, and required item have 2 characteristics (weight and quality) that have to "at least" match for them to be compatible for delivery, i.e. the good fits the required items characteristics or better to be accepted. A certain good cannot be split to accommodate 2 required items in the case that it has sufficient weight for both.

Drop off points are geographically dispersed by a non-negative distance. Transport vehicles start dislocated from the drop off points at potentially different starting locations. No need to keep routes or roads into consideration. Just straight line distance will determine the cost.

My goal is to find a solution such that the distance traveled by transport vehicles is minimized and each drop off point has their item requirement satisfied while obeying the item vs good matching. Ideally if the entered data is impossible to solve to a 100% completion due to simply not enough goods of large enough weight or quality I would like to get a solution that maximizes the delivered goods while still minimizing the distance traveled.

Any help or suggestions are greatly appreciated! Thank you for your time.

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  • $\begingroup$ Dislocated from the drop off points at potentially different starting locations. No need to keep routes or roads into consideration. Just straight line distance will determine the cost. Thanks for looking into the problem! $\endgroup$
    – Mike
    Jun 23 at 20:06
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    $\begingroup$ I have edited the question, thank you. $\endgroup$
    – Mike
    Jun 23 at 22:05

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