# Optimizing a company daily capacity

### Optimizing a company daily capacity

Hi!

I have an example question below:

A laundry service company needs to increase the laundry capacity per day. Based on the manual calculation, the capacity can be more than the current capacity. (for ex: now is 10,000 but actually it can be 15,000). Working hours per day (available time) is 21 hours (1260 minutes) with 3 shifts (8 hrs/shift and an hour break).

They have six washing machines and 11 drying machines. The materials that being washed are divided into 4 types, A, B, C, and D. Material A is needed to be washed in washing machine for 30 minutes, Material B is 45 minutes, Material C is 35 minutes, and Material D is 45 minutes.

The capacity of machines are 55 kg, 97 kg, 102 kg, 114 kg, 52 kg, and 45 kg. Normally, each day the total weight (daily) of material A is 6600 kg, material B is 1760 kg, material C is 1584, and material D is 1056. So total per day is 11,000 kg.

The question is how many cycle per washing machine in one day and which material should be washed in which machine in order to have the maximum capacity per day/to washed all of the dirty materials within 21 hours as once the dirty materials come, they have to be done in 21 hours. ( assigning the dirty materials to washing machines)

the objective function is maximizing the washing machine capacity.

And the constraints are:
1) Material A: 30 W1 + 30 W2+ 30 W3 + 30 W4 + 30 W5 + 30 W6 <= 1260 minutes per day (time needed to washed material n)
(goes the same with material, B, C, D)

2) daily capacity of the material per day
for ex: material A: W1+W2+W3+W4+W5+W6 = 6600 kg (goes the same with the material B, C, D)