Please help me build a mathematical models (Linear Programming Problem)


I have an example case about job shop scheduling in a home laundry service.

It has 6 washing machines and 11 dryers. Here are the each capacities of the machines.
Washing machine: 1) 10 kg, 2) 14 kg, 3) 20 kg, 4) 7 kg, 5) 22 kg, 6) 10 kg
Dryer: 1, 2 and 3 =12 kg
4, 5,7,8,9,10 and 11= 18 kg
6= 11 kg

Due to the preventive maintenance, after finished the washing process, they split the clothes from a washing machine into two dryer. (ex: I wash 10 kg clothes in washer no 1 (10 kg capacity) and I split them into dryer 1 and 2).

Therefore, 1 washing machine needs two dryer. However, it still allowed to 1 dryer for 1 washing machine.

Every machines work in the same process time despite of their capacities. 30 minutes for washing machines and 45 minutes for washer.

They placed side by side, except for 3 dryers (number 9, 10, 11). They placed in front of dryer number 6, 7, 8.
I have to optimize the workers movement from washing machines to dryers. I also have confusion to determine the objective function (OF). Should I determine the OF with the walking time from washing machine to dryers OR the capacity OR the distance?

Please help me! Thanks for your help!

Charlotte :slight_smile:

I will help you … by telling you to do your own school assignments.

1 Like


This is not related to school things or any assignments anyway :smile:

Thanks for your advice! :wink:

Even if not a school assignment, it is still out of scope for this forum.

I suggest you read “Model Building in Mathematical Programming”, H. Paul Williams which does a good job at addressing formulation of Mixed-Integer Linear Programming (MILP) problems.

I’ve just realised that I went to wrong forum… :blush: :smile:

Sorry and thank you, again! :slight_smile: