Sure! Let's consider a simple example of the paint shop problem:

Suppose there are three cars C1, C2, and C3. They need to be painted with the following color combinations:

1. C1: Red, Blue, Green
2. C2: Blue, Green, Red
3. C3: Green, Red, Blue

There are three paint booths B1, B2, and B3, one for each color:

1. B1: Red
2. B2: Blue
3. B3: Green

Now, let's find the optimal schedule for painting these cars.

Step 1: Identify the constraints
- Each car must be painted in the specified order of colors.
- Each car must be painted one color at a time.
- Each paint booth can only paint one car at a time.

Step 2: Create an initial solution
Let's start by painting the cars in the given order (C1, C2, C3).

1. Paint C1 with Red (B1), C2 with Blue (B2), and C3 with Green (B3) simultaneously.
2. Paint C1 with Blue (B2), C2 with Green (B3), and C3 with Red (B1) simultaneously.
3. Paint C1 with Green (B3), C2 with Red (B1), and C3 with Blue (B2) simultaneously.

Step 3: Optimize the solution
In this example, there's no need for optimization as the initial solution is already optimal. Each car gets painted with all its colors without any waiting. The total time required will be equal to the time it takes to paint each color, assuming all paint booths take the same amount of time to paint a car.

So, the optimal schedule for painting the cars is:

1. Paint C1 with Red (B1), C2 with Blue (B2), and C3 with Green (B3) simultaneously.
2. Paint C1 with Blue (B2), C2 with Green (B3), and C3 with Red (B1) simultaneously.
3. Paint C1 with Green (B3), C2 with Red (B1), and C3 with Blue (B2) simultaneously.

Please note that this is a simple example, and in more complex scenarios, optimization techniques such as dynamic programming or genetic algorithms may be necessary to find an optimal solution.
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