This is a cost minimization problem, where I have to plan the development of a field and the installation of some machines there.

Rectangles A,B,C,D represent production areas, that can overlap. I show 4, but I have almost 100.

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I was given the projected production of those areas day by day, month over month:

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Each production area, need production recovery units that need to be installed.

I have some options... in the example from my figure, I offer 5 optional places: O1, ..., O5. Where O5 seems suboptimal, because it can only recover from B, where O1 to O4 could recover from 2 areas at the same time.

Now with that info, I know how much I should recover each day, and so I need to plan those units installation knowing that a small unit can recover up to 20 and cost USD 10k, and that a big one can recover more than 20 but cost USD 20k.

So I can install a small/big recovery unit in each location: O1,...,O4

With that in mind, I'd say in order to minimize cost by day 1 I'd install one small in O1 and one small in O2, which would cost me USD 20k. So that's my option a for day 1 ("1a"). when I reach day 2, I see my best option for the day is 2a. If I accumulate the cost, my acc. cost is now 65 BUT if I choose option 1d on day 1, my acc. cost by day 2 would be 58 (taking into account the interest penalization - present value cost), so I don't know how to get to that option if not going back and forth for every day. At the end of the day, my final goal is to get the minimum present value cost for the project installations. The real data has about 100 producing units and 2 years of production detailed day by day.

This is something really challenging for me and I need to provide an output soon, so I'd appreciate any hint or advice.

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  • $\begingroup$ Is this problem static (given the data for the whole planning horizon, find an optimal solution) or dynamic (you have to take decision on a daily basis)? $\endgroup$ – Marcus Ritt May 25 at 17:24

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