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In this case, the shop want to maximise the profit that is there $n$ products the shop can procure, but the shop only has $w$ budget. The cost of each product $x_i$ is $c_i$.

I used prediction model and predict each product $x_i$ will have total $N_i$ sales in the future 10 days. The selling price of each product $x_i$ is $s_i$.

So, I give the objective function $f$:

$$ max f=\sum_{i}^{n}(s_i - c_i)x_i \\ s.t.\\ x_i \in Z \\ \sum_{i}^{n} c_ix_i \leq w \\ x_i \leq N_i\\ i = 1,2, ..., n $$

where $n$, $w$, $s_i$, $c_i$ and $N_i$ are all constants.

I want to solve this integer programming by python. But what I find online is more about linear programming. Is there any friendly Python package solver?

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  • $\begingroup$ Hi @mmmm, are you trying to model that $x_i$ cannot exceed $N_i$? In that case you should impose $x_i\leq N_i$ directly $\endgroup$
    – Sune
    Nov 7, 2022 at 21:17
  • $\begingroup$ Your Maxf is the function that you are going to maximize. You'd need a solver either scipy/optimize or commercial ones like Gurobi/CPLEX\ I am not sure about the 2nd constraint. Assuming $x_i$ is your decision variable then is it like either $x_i$ retains its value or takes $N_i$ if $N_i$<$x_i$? $\endgroup$
    – Sutanu
    Nov 7, 2022 at 22:25
  • $\begingroup$ hi, I am editing my question, please check the latest version $\endgroup$
    – mmmm
    Nov 7, 2022 at 22:47
  • $\begingroup$ As stated by @prubin you need to use a solver like gurobipy. But one thing, your sales forecast says $N_i$. Do you really want to produce $x_i$ fewer than $N_i$? While there are more complicated cost like waste or lost sales but I guess it should be $x_i>=N_i$ while constraining the budget. Otherwise depending upon revenue & cost solver may take most of x as 0.\ Gurobi has python API or you can try scipy /optimize as problem is linear. $\endgroup$
    – Sutanu
    Nov 7, 2022 at 23:44
  • $\begingroup$ @Sutanu You cannot sell more than the demand, so $x_i \le N_i$ is correct. $\endgroup$
    – RobPratt
    Nov 8, 2022 at 0:47

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Both PuLP and Pyomo are widely used open-source Python modeling libraries with links to a variety of solver packages, both open-source and commercial.

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