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(K_{o,p,m}) A binary datum which equals 1 if operation (o) of product (p) can be processed on machine (m); 0 otherwise.
Outsourcing cost per unit part type p. Inventory holding cost per unit part type p during each period. 1 if operation k of part type p can be processed on machine type m; 0 otherwise.
Constraint 4 defines that if machine (j) is assigned to cell (k), each operation of part (i) can be processed on machine (j) by tool (t) in route (r) in cell (k).
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Scheduling models in manufacturing usually include determining the optimal order/schedule according to which jobs should be processed on machines.
Each job has a different release date and consists of ordered operations that have to be processed on machines from different machine centers in the same order.
Jobs that are processed on machine k at stage t.
For instance, operation k of part type p is processed on machine type m assigned to location l in cell c at time t.
For instance, assume that operation k of part type p is processed on machine type m in cell c at time t.
(Z_{jk}): 1 if machine (j) is assigned to cell (k); 0 otherwise (X_{sirjkt}) : 1 if operation (s) of part (i) in route (r) is processed on machine (j) in cell (k) by tool (t); 0 otherwise (R_{ir}) : 1 if route (r) is selected for part (i); 0 otherwise.
The value of the variable (d_{o,n,p,t}) is equal to the product (widetilde{E}_{l,l'} cdot b_{n,p,t}) if operations (o) and (o+1) of (n th sublot of product (p) are processed on machines (m) at location (l) and (m') at location (l'), respectively, in period (t).
We have m independent parallel machines at the first stage and every part of a job should be processed on just one machine at the first stage and each machine can process only one part.
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