Good question! There are several ways to address the version of this problem with thousands of "pieces of equipment" that need replacement. If they're all completely different from one another, you can create one network for each (with their individual variables, arcs, etc.) but place them all into a single (large) optimization model and run it once to solve all shortest paths at once. If you can somehow aggregate similar equipment into classes, you just need to solve one shortest path per class and apply the same answer to all pieces of equipment in that class. Finally, besides linear programming, shortest paths can be solved via dynamic programming (another kind of optimization technique) and via Dijkstra's or Bellman-Ford's shortest path algorithms, which you could simply code in your favorite programming language. If you're not familiar with the latter, they're not difficult algorithms to code; just google them. Dijkstra's algorithm requires that all arc weights be positive (like in my example), i.e. they all represent costs.

I am afraid the solver is not sufficient. I tried to reproduce your example, but with a 75 year time span. The solver is not able to do it. I was hoping that there would be a less computational demanding method. But thank you anyway.

Indeed, the free student version of Solver is limited to 200 variables and isn't very robust. When optimization problems grow large, Excel isn't the ideal environment anymore. There exists, though, a Solver add-in for Excel that does not have a size limit. You can get it for free from OpenSolver dot org. Other than that, you have the programming route (as I described above, which will just run a shortest path algorithm) or commercial solver packages like Gurobi, CPLEX, or Xpress, where you can interface with the solver engine (load the model, solve, read solution etc.) through a programming API in Python or C++.