Linear Programming Problem Based on Weight System

[theperson]

Homework Statement

I've made my own problem here to solve. I'm wondering if it is even possible with linear programming.

Basically, I need to designate these parts to certain machines based on 3 different priorities and each of these priorities are weighted arbitrarily. (For example, Priority 1 is 60%, Priority 2 is 30%, Priority 3 is 10%). There are different size machines too, but I already know what parts will fit in what size machine. (Lets say there are 2 sizes of machines, Size 1 and Size 2). BUT there are multiple machines for each size. So, for example, there are 2 Size 1 machines and 3 Size 2 machines.

The main problem I am trying to solve here with a math model is what parts should go to what machines based on the weighted priorities. For example, all white parts should be on one of the Size 1 machines and black parts should be on the other Size 2 machines (if color was Priority 1)

Homework Equations

variables
max/min statement
contraints

The Attempt at a Solution

I haven't worked with linear programming in awhile, but I remember bits and parts. I can't seem to get away from remembering the profit type problems. Is my problem capable of being solved from linear programming?

Thanks!

 

[mighty2000]

Hello,

Yes, your problem is definitely capable of being solved using linear programming. Linear programming is a powerful tool for optimizing resource allocation and can be applied to a wide range of problems, including yours.

To solve your problem, you will need to define your variables, objective function, and constraints. Your variables will represent the parts and machines, and your objective function will be to maximize the weighted priorities for each part. Your constraints will include the size of the machines and the priorities for each part.

You will also need to consider any additional constraints, such as the number of machines available for each size or the maximum capacity of each machine. Once you have defined all of these components, you can use a linear programming software or algorithm to find the optimal solution.

I hope this helps. Good luck with your problem!