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Solver with multiple variables (56)

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    Solver with multiple variables (56)

    Hey there,

    I'm new to this forum and looking for help from experienced people.

    I'm trying to solve the problem using 56 variables.
    I have 56 different molds/shapes which are making the final products of different size (50,75,100,150,200,250). Every mold is 600 mm in size, it can be 250-250-50-50, 50-100-200-250 and so on.
    I have SUM of their manufactured products by size.
    I have cost, selling price and profit for each final product.
    I need to know which mold should I work with and how many days to get maximum profit with given constraints.
    Constraints: Each size of product should be produced with given % range. e.g. 50 mm size product should be approx. 10% of whole manufactured product amount (min - 0.05 %, max - 0.02 %) and so on.
    I have 30 working days, 56 different molds, with different ratio of final products, so I need to calculate which molds should I use and for how many days to get maximum profit with given constraints.

    I've written all the constraints and model but solver can't find the result for given constraints.
    P.S. Test version of this model works with 3-6 variables (molds).

    Thank you very much in advance

    Below is the Excel File with solver model.
    Attached Files Attached Files
    Last edited by ambokadze; 05-17-2021 at 08:46 AM.

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    Re: Solver with multiple variables (56)

    Looks like a stock-cutting issue.
    I don't quite understand your meaning of "days".
    Is there any connection between days and molds?
    Why do you put days as decision variables?

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    Re: Solver with multiple variables (56)

    Hey,

    Yes there is a connection, if you choose to use for example "mold 1" to work for "1 day" (A25), then you can see that in "mold 1 table" (A2:D9) you will get the 40+30 monthly manufactured product. Because "mold 1" is "75-75-75-75-100-100-100" in size, total of 600mm. We have 4 lines of "75 mm" (C4) and 3 lines of "100 mm" (C5) sized final product, we can "produce" 10 molds per day (L14) so we have 10*4*1=40 (D4) where 10 is molds per day, 4 is lines per mold, 1 is 1 day. If we will work for 2 days, with the same "mold 1" it will be 10*4*2=80 and so on.
    After that, this amount of final products (by sizes) are summed up in B14:B19, (every 4-th row, D-H-L-P-T....) they are taking part to build constraints also and in final "Total profit" cell, which we want to maximize.
    So we want to know which "mold" we should work with and for how many days to get the best result with given constraints. Maybe we can choose 5 different molds and work for 6 days per mold in total of 30 days, or we can choose 4 different molds and work for 10-5-4-11 days.
    "To choose a mold" means you work it for 1 day at least, if you don't want to choose/use a mold you can write 0, in "days" row (25).

    Hope I explained that understandably?

    I really hope to find some help here

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    Re: Solver with multiple variables (56)

    This should be a typical stock-cutting problem, if I get your meaning correctly.

    The problem can be modeled as :
    Stock size: 600mm
    Number of stock: 30
    demand size: 50mm, 75mm...250mm.
    There is a mininum & maximum requirement for each demand size.
    each demand size has a profit.
    How to cut(choose which cut patterns, and cut how many stock for each pattern), to maximize profit?
    Attached Files Attached Files
    Last edited by astupig; 05-23-2021 at 11:11 PM.

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    Re: Solver with multiple variables (56)

    Hey,

    Thanks for your response. I have seen your file, yes I want to maximize profit with given min & max requirements.
    Your solution seems perfect, model is great, you had some "mechanical errors" in data, you have entered data (min, max, profit) for 50 mm in 250 mm mold cells and etc. But it's nothing. I have corrected all small issues and now waiting for solver to solve the problem, 5 mins have passed

    I will update you for the outcome, hope it will work.

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    Re: Solver with multiple variables (56)

    Please try Open Solver. https://opensolver.org/
    It is compatible with the Excel built-in solver, but it is much faster.
    Excel built-in solver is always too slow.
    Open Solver can get this model solved in seconds.

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    Re: Solver with multiple variables (56)

    Thanks man,

    It works!!!

    I had Open Solver but it was not working on my model, but now it's 100 times faster than Excel built-in and it works.
    I think main problem was that my type of model was too complex and I had to solve it using GRG, but now after refreshing the model it can be solved as Simplex (Linear).

    Thank you very much for your time and help, I really do appreciate it a lot.

    Cheers!

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    Re: Solver with multiple variables (56)

    Hey,

    I tried to change your model, by changing min & max constraint ranges, with the same 0.1 - 0.4 range for all or some other, but the open solver is running for ages without result. How can that be so, it works fine with our first type of constraints but it can't with any other. Or maybe it just want more time (hours)?
    Attached Files Attached Files

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    Re: Solver with multiple variables (56)

    Quote Originally Posted by ambokadze View Post
    Or maybe it just want more time (hours)?
    I think you are asking too much to Jimmy's model (which is as good as it could get using Excel tools).

    This kind of combinatorial problems can easily become unsolvable, if you are asking for the best solution, and not only a reasonable good one. Setting a wider range for max and min constraint forces OpenSolver to check a much greater number of solutions.

    My advice is to open the Options menu under Model, and set Branch & Bound tolerance value to 0.5. You can also add a max solution time, if you prefer.

    HTH,

    Francesco
    Aim high or don't even try.
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    If your question has been answered, don't forget to mark the thread as SOLVED.
    If you find an answer helpful, click on the star icon at the bottom of the post.

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    Re: Solver with multiple variables (56)

    Thanks for your response Francesco, changing Branch & Bound tolerance helped a lot.

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