Mixed Integer Linear Programming (MILP) Tutorial

Optimization with continuous and integer variables is more challenging than problems with only continuous variables. This tutorial and example problem gives details on exhaustive search and branch and bound techniques for solving Mixed Integer Linear Programming (MILP) problems.

[farisdurrani]

It's amazing how you were able to explain ILP and the methods to solve them in 10 minutes. And even more impressive when using this APMonitor tool

[Mohammad-fvzb]

Your videos and the website are amazing, very useful and practical professor. Thank you so much

[malshi]

Sir give me answer A small contractor has undertaken to supply a customer with at least 500 units in total of two products A and B during the next month. At least 30% of the total supply must be units of product A. It requires 3 labour hours to produce one unit of A and 8 labour hours to produce one unit of B. The contractor has planned to make use of 2400 labour hours for this work next month and any additional labour hours can be made available if required. The total variable cost is Rs 80 per unit of A and Rs 120 per unit of B. The contractor wishes to minimize his expenditure on this contract. questions, Formulate the linear programming model

[ElvinJones]

Thanks for the video. I have a question. Around 6:43 you add the constraints 2<=X_2<=3. You already had the solution X_2=~2.67. So how would you decide on that constraint without having already arrived at a value for one of the variables? A solution method that only works once you have part of the solution method seems incomplete but I think I must be missing something. I appreciate any feedback you can provide.

[MoGoldberger]

Can you share the link to the Linear Programming video you suggest watching before this video? I'm having trouble finding it.

[AndresGomez-pwfs]

Your videos are amazing, I want to master MILP, and the logical constrains, how to set those difficult logical constrains for them to be linear. I know that practice makes masters, but can you help me with some paper easy to read as well of some material to follow to enhance my mathematical modelling skills in MILP? Thanks God bless you!

[maddyliu]

Thank you for the video. May I ask if APMonitor can show all possible integer solutions for a problem? My problem is really simple but so far I haven't found one python package that allows a printout of all feasible solutions.

[anashasna]

great tutorial thanks to sharing it!

Actually I have a question which may be not very related to what you did in this video but stay in the same domain.
so I work on a case of the bin-packing problem, I have a modelization to this problem which has a set of binary decisions variables in some constraints not in the objective function which has just a continues variables, so my question is can we say in this case that I have a mixed integer problem ?

thank you for any feedback.

[danielgrace]

Good video, but the title is misleading. The example you gave is not a mixed-integer linear programming problem, it is an integer linear programming problem. "Mixed" implies that some (one or more) of the variables are allowed to be continuous in the (final) solution i.e. not just integers. Also I think the algorithm you use is called branch and cut.

[lizizhu]

Could the objective function be quadratic?

[georgezokaris]

I'd like to ask you...in a MILP problem for a cement industry, using Matlab, should the size of the matrix of the inequalities be the same with the matrix of equalities???

[PythonParseltongue]

Do you ever solve these kinds of problems using a programming language like Python?

[panchao]

What device did you use to write on your screen? Can it also be used on Mac?

[kaserekapatrick]

Is it possible to use MILP with Multi-objective optimization problem?

[domoto]

May I know what programming language are you using? sorry for the stupid question

[Mouna_beee]

are you able to give me your contact information if I had some questions. Going into an analyst role without analyst background and this is something I will be required to do for Supply Chain! It would be amazing.