Paint Production-Distribution Planning Problem

Question 1

What is the context ?

Answer 1

A paint company produces 3 types of paints in 5 colours. There are five possible production sites. Each site would have one production line running 8 hours per day, each day of the week. There are 10 distribution centers that can be supplied by any production site.

Question 2

What is the goal ?

Answer 2

Your main goal is to decide which production site(s) should be built.

A production site would have one production line that can only produce one type of paint of one colour at any point in time. The production rate is the same regardless of the type product being produced and is equal to 200 liters (250kg) per minute.

Question 3

There is a penalty when switching from one product type to another, because of the change of material and the change of colour, there is production loss, expressed in minutes.

Each time there is a change in colour, there is loss of 20 minutes, while when there is a change of material, there is a loss of 12 minutes. When both are changed simultaneously, the loss is the maximum of the two, 20 minutes.

How to handle the switching ?

Answer 3

We count the number of paint that we produced on a given line at a given time, this can be done with a binary variable. To activate the binary variable we can use this constraint:

color_used_{c, t} * 1 000 000 >= paint_{i, c, b, t}

This is for all i, c and t and we sum the paint variable for type because we want to know if the paint is produced.

Then we sum the binary variable (minus 1, the first color doesn’t need change) on a given day and we obtain the number of color change.

To compute the type switchings we just substract the previous number from all the color, type paint used. Those will be type switching !