As part of its weekly production a paint company produces five batches of paints, always the same, for some big clients who have a stable demand. Every paint batch is produced in a single production process, all in the same blender that needs to be cleaned between two batches.
The durations of blending paint batches 1 to 5 are 40, 35, 45, 32 and 50 minutes respectively:
Batch 1: 40 minutes
Batch 2: 35 minutes
Batch 3: 45 minutes
Batch 4: 32 minutes
Batch 5: 50 minutes
The cleaning times depend of the colors and the paint types. For example, a long cleaning period is required if an oilbased paint is produced after a water-based paint, or to produce white paint after a dark color. The times are given in minutes in the following table CLEAN where CLEAN ( i,j ) denotes the cleaning time between batch i and batch j.
Since the company has other activities, it wishes to deal with this weekly production in the shortest possible time (blending and cleaning). What is the corresponding order of paint batches? The order will be applied every week, so the cleaning time between the last batch of one week and the first of the following week needs to be accounted for in the total duration of cleaning.
Write a GAMS model that will determine the order of the paint batches.
Hint: You will need
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