Math Is Fun Forum

geotrivia121

Member

Registered: 2013-12-25

Posts: 3

Any solution for optimal material allocation ? *Interesting

I have a manufacturing planning job. I have come across a problem, where in I need to allocate the available raw material, optimally between the finished goods, to maximize the production. The problem is explained as below : Say there are different types of finished goods FG1, FG2, FG3, FG4 etc., and raw materials RM1, RM2, RM3, RM4, RM5 etc,. Now raw material composition for these finished goods will be different, say
FG1 = RM1 + RM2 + RM3 FG2 = 2RM2 + 6RM4 + 2RM5 FG3 = 0.5RM1 + 3RM3 + 7RM5 FG4 = 1.5RM3 + 2RM4
Available quantity in stock for raw materials (RM) is partial, i.e. not all quantity is available for producing all the finished goods FG1, FG2, FG3 & FG4 etc. Each RM is available in some partial quantity (or some may not be totally available).
How do i optimize the use of available raw material quantity to deliver maximum amount of full Finished goods. I have to avoid a situation where in the raw material gets allocated in such a way that partial material gets available for all finished good, but very few can be completed.
This is just an example for the problem I am facing. In reality, the number of finished goods and the multiple combinations are huge (in terms of thousands).
Please suggest a solution(s) or a program (an excel program/macro) or any other program, which can be used to maximize the finished good output for such cases. Thanks in advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Any solution for optimal material allocation ? *Interesting

Hi;

Looks like a linear optimization program. Your equations are all mashed together. Are these the equations?

FG1 = RM1 + RM2 + RM3
FG2 = 2RM2 + 6RM4 + 2RM5
FG3 = 0.5RM1 + 3RM3 + 7RM5
FG4 = 1.5RM3 + 2RM4

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

geotrivia121

Member

Registered: 2013-12-25

Posts: 3

Re: Any solution for optimal material allocation ? *Interesting

You are very correct sir.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Any solution for optimal material allocation ? *Interesting

For a standard problem we will need some ranges on RM1 to Rm4 in terms of inequalities.

How much of each do you have? What is the minimum you can use for each?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

geotrivia121

Member

Registered: 2013-12-25

Posts: 3

Re: Any solution for optimal material allocation ? *Interesting

Rm1 = 2
Rm2 = 3
Rm3 = 3
Rm4 = 7
Rm5 = 8

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Any solution for optimal material allocation ? *Interesting

Now just one more thing. There must be something you want to maximize. Usually it is profit, or you want to minimze cost. Which are we doing here?

Or do want to maximize the number of items produced?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.