Linear Programming: Cash Flow with Excel Solver

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Given a planning horizon, an initial amount of money, a set of investments and intermediate inflows and outflows of cash, how to invest (and re-invest) the money over the years in order to maximize the amount you'll have at the end of the horizon or reach a certain target amount?

[@SardsSards-p7j]

Great Video, you deserve more subs. Keep it up!!

[@SardsSards-p7j]

I meant great playlist, not just this video. Doing a marathon of the playlist now :)

[@vuduy9763]

this is a difficult problem, if the time is large, the number of variables generated will be extremely large, but this is a useful video, thanks

[@TallysYunes]

The issue you describe is true of all models with variables indexed by time. But modern solvers are able to handle very large models.

[@SardsSards-p7j]

Note that the you will get 74,908.9 as initial amount for target 100K if the inflows/outflows are baked in. Without inflows/outflows, you should get 71,179.44 as the initial amount needed.

[@maps_zim]

Great video. I have a similar question I have been working on but I keep on hitting dead ends with it.

[@Sherlock_Ohms]

Hi Tallys, I was wondering if you could tell me why when you increase the initial amount to say, $100,000, the solver then says that the problem is no longer linear?

[@TallysYunes]

Assuming it was solving before (with 50,000) as the initial amount and not complaining of non-linearity, simply changing the initial 50K to 100K should not be generating this issue. Therefore, it's some sort of bug. I've seen these before with Solver. Sometimes, clicking (or un-clicking) the box that says "Automatic scaling" in the Solver options takes care of this.

[@Sherlock_Ohms]

@@TallysYunes Thanks! I suppose another way around it would be to convert the initial amount to thousands of dollars, so 100 in my case. This solves fine.

[@TallysYunes]

Yes, indeed. Sometimes if you scale the numbers yourself so that the difference between the smallest and the largest number in the data is reduced, this kind of bug goes away. Good thinking!

[@fadi9165]

I did the same exact thing but the solver keeps giving an error message saying that the linear conditions are not satisfied !!!!

[@TallysYunes]

There must be a little something in your sheet that is different from how I did it. Just go back and double check every formula carefully.

[@drougfree]

hello do you know the book you did this exercise?

[@TallysYunes]

It's not from a book.