I am working with a kind of a reconfigurable process planning, meaning that the same machine can have different configurations and perform multiple operations. Each machine has an initial configuration that can be changed according to the needs. The process plan has a given sequence, each machine $w$ can assume one position $j$ on the process plan.
My question is, how to create a constraint to ensure that if in the first occurrence of a given machine $w$ its configuration $c$ is different from its initial configuration $c_o$ there will be a cost of changing configuration?
I just need to ensure the cost of changing configuration between the first occurrence of a given machine in the process plan, because the change of configuration within the same machine between two consecutive process plan positions is stated by the binary variable presented below:
- $Y_w{_c}_{c'j-1j}=1$ if a machine $w$ changes its configuration from $c$ to $c'$ between positions $j-1$ and $j$, 0 otherwise
I am also using the following binary variable:
- $X_p{_w}_{cj}=1$ if an operation $p$ is done by a machine $w$ with a configuration $c$ at process plan position $j$, 0 otherwise
and the parameter:
- $IC_w{_c}_{O}=1$ if configuration $c$ is the initial configuration of machine $w$, 0 otherwise
Where:
$j$: process plan positions
$w$:machines
$c_w$: configuration $c$ of machine $w$
$p$: operations
Could someone help me?