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Exact(8)
nplusp jt = a means that a duplicates of machine type j are returned from machine depot to cells in period t.
The components of this matrix M × 1 as shown in Fig. 2 present the number of machine duplicates which is returned from machine depot to cells.
The second ingredient related to the number of machine duplicates returned from machine depot to cells in each period is named matrix NplusM,T.
If this model is allowed to remove idle machines from the formed cells, it will eliminate machines M1, M2, and M4 from cells and keep them in the machine depot to reduce the overhead cost.
Inequality (14) ensures that the number of machine type m which can be returned from the machine depot to the cells does not exceed from the number of machine type m available in the machine depot in each period.
It is worth mentioning that returning machines from the machine depot to cells can be started in the third period, because there is no any machine in the machine depot before that period.
Similar(52)
This cost is paid for several situations: (1) to install a new purchased machine or a machine returned from the machine depot; (2) to uninstall a machine removed from a cell and kept in the machine depot; and (3) to transfer a machine between two different locations.
Number of machine type m removed from machine depot and returned to cells in period t.
To define this feature, additional decision variables should be added to the mail model as follows: N mt + Open image in new window: number of machine type m removed from the machine depot and returned to cells in period t; N mt − Open image in new window: number of machine type m removed from cells and moved to the machine depot in period t.
Open image in new window Fig. 2 Returned duplicates of machines from depot to cells in period t 3.
The third ingredient related to the number of machine duplicates removed from cells and moved to machine depot in each period is named matrix NminusM,T.
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