Hey everyone!

I’m trying to create a model that minimizes the number of periods a machine is used summed over all machines and all periods of the planning horizon.

I’m currently struggling with formulating a constraint that ensures that each machine is used only in consecutive periods or put differently that the machine running time is continuous. For example: machine 1 can’t be used in period 1, 3 and 5, but only in period 1,2 and 3.

Since I’m quite desperate, I’d really appreciate your help!

Thanks in advance and best regard,

Matze

Further information:

There are 8 periods, 5 machines and 60 products that can be produced on any of the machines

For each machine there is a specific amount of time that can be used for actual production in each period (the remaining time is needed for maintenance, etc.)

For each machine a specific minimum running time (measured in number of periods) is given

Each product has a specific production time

Each product can only be produced in a specific span of periods (for example: product 1 needs to be produced between period 1 and 5)