Integer Linear Programming - Binary (0-1) Variables 1, Fixed Cost

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@joshemman, thank you for the excellent explanations of these optimization and OR concepts! Your command over the subject is clearly evident.

[@joshemman]

You're very welcome, Hayford. Thanks for dropping a note. 😊

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Awesome video! Could you make a video about how you used excel to come up with your answer?

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[@mariakudimova]

Sir, if there is any chance you could add the way you've solved these problems in excel (in this video), please, do! Your video helped me a lot to understand the concept, however, I did not understand how you did this in excel. I googled another video explaining how to solve the "fix cost" problem in excel and I solved your example. Thank you for the provided answers. But I think your video only wins if you could manage to upgrade it a little bit with the excel solver. Your channel is awesome!!!

[@joshemman]

Thanks for the feedback. I will work on it when I get back to making videos.

Good video. Is there a way to solve these problems without using optimization? That is, is there (at least for some subset of problems) a way to solve this analytically?

[@joshemman]

Irrespective of the method, is it possible to solve an optimization problem without optimizing?

@@joshemman I guess I used the wrong terminology. You are right. I didn't mean without using optimization, I guess I meant without using an iterative/approximation solver. For instance, for the least squares problem for regression of a line, you can try an iterative algorithm to get an approximate answer, but there's an analytic formulation to get the coefficients of that 1d polynomial. So rephrasing, I meant: is there a way to find such an analytical formulation for integer problems involving binary matrices? I am asking because I am currently working on a specific integer problem, and even though I've tried to find an analytical solution to it, I haven't been able to formulate one yet and I'm not sure if integer linear problems like this even allow such a formulation.

[@joshemman]

Yes, an analytical (templated) solution is possible for certain integer problems provided the problem is structured in a specific way with carefully chosen parameters and strictly defined variables and constraints. However, for general optimization problems, finding such a formulation is often not feasible due to the variability of the constraints and objectives involved.

@@joshemman Thanks for the reply! Would you be able to send me some references on these analytical templated solutions or at least examples on some problems where such solutions are feasible, by any chance? It would really, really, help me and I would really appreciate it! I've been looking for this but I couldn't find anything.

[@joshemman]

To create such template, you may need to perform some reverse engineering. Start by solving an LP, then use its optimality and feasibility ranges to set parameters that enable an analytical solution. From there, you can begin tweaking the coefficients/parameters as needed. Consider this LP where a ≤ b Max ax + by s.t. x + y ≤ c 2x + y ≤ d A quick check reveals that the optimal solution will occur at (0, min(c, d)).

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[@emcintosh8678]

Hi, Joshua, Did you happen to create a video about how you used Excel Solver to find the optimal solution for this problem? If so, please provide the link. Thank you!

[@joshemman]

I finally did, here: kzbin.info/www/bejne/Z5-1fKarisiBmpY

[@khaledqaraman]

Great lesson... Thanks a lot

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instruction very good, but lacking how we could create the spreadsheet for Solver. Just knowing the results not very helpful for my situation

[@ahmeddiab2584]

Your videos are extremely helpful! I have a question If I want to put the condition that says y1= 0 or 1 in LINDO , how that can happen ? or just by try until I find the best solution ?

[@joshemman]

In LINDO, use INT Y1

[@ahmeddiab2584]

@@joshemman Thank you

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Please explain how to find the solution for the second problem (fixed charge problem)for Msc mathematics student.I can't understand the final step please explain sir

[@joshemman]

See if this helps: kzbin.info/www/bejne/Z5-1fKarisiBmpY

[@anniebenolins1770]

@@joshemman Thank you sir

[@dianazubchenko8522]

What is the name of the next video your are referring to at the end? BTW thank you for your explantation, it is definitely going to help to pass my exam!!

[@joshemman]

kzbin.info/www/bejne/eGTFmoqpd7GYedk

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Pure gold. Thank you

[@dhgcrack3r111]

Got a question for you if you remember. 5:26 “solving this model”. I made up to that point, what does he use to plop those 6 numbers out and see that only the 2nd / 3rd machines are used?

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dear sir, gr8 explanation , Sir could u pls do problems in multi objective transportation.??

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[@madkoki96]

I have a question: If i want to minimize for example 2x1 +3x2 +3, since there is no x3 but 3 wil f be (2 3 0)?

[@joshemman]

Yes. But are you sure the x is not missing due to a typo?

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@@joshemman im sure its not missing

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[@joshemman]

You are so welcome!

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Plz upload how to solve in solver excel

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[@MarcoPeretto]

Is it possible to perform the calculation at 1:56 by hand? If so, how?

[@joshemman]

Trial and error.

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great explanation. thank you so much!

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Thanks

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Thank you!

[@joshemman]

You're welcome!

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[@aishwaryaroykvr]

how can we solve this on LINDO?

[@kunalkiran3318]

Thank you so much for the video. I had a naive doubt. We have put a condition x1=0. This means if y1 is 0, x1 must be 0. But we have not yet put a constraint where if y1=1, then x1>0 ? How do we put this constraint? We might get a solution where y1=1, but x1=0. Any help is appreciated.

[@joshemman]

Note that the constraint x1≤400y1 is still satisfied if y1=1 and x1=0 (since 0≤400). Therefore, no modification to the constraint is required.

[@gandharvasai7440]

Joshua Emmanuel how he get y1=0,y1=1,y2=1

[@HVela]

@@joshemman Thanks for the video. So going off of your explanation above, if x1 = 0 (no quantity is produced from machine 1) then Y1 has to be 0 right but since x1 = 0 and y1 = 1 is allowed by the above constraint will it not violate the rule?

[@joshemman]

@@HVela You can rent Machine 1 and decide not to produce any unit on it (y1 = 1; x1 = 0) y1 = 0 implies x1 = 0 x1 = 0 does not imply y1 = 0.

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[@banibratamanna5446]

this problem is equivalent to 0/1 knapsack problem