A Multiobjective Optimization Algorithm to Solve the Part Feeding Problem in Mixed-Model Assembly Lines

Algorithm 2

Second stage: minimizing the inventory level.

Identify the AT and NA according to (viii) and (ix), respectively.
𝑡∈AT⟺∑^𝑛𝑖AB𝑖𝑡≠0∀𝑡=1,…,NT		(viii)
NA=∑𝑡∈AT𝑡		(ix)
While AT is not empty
Select the first possible tour (which is in the AT) and find the number of removed consecutive tour(s)
after the selected tour (NR𝑡) according to (x).
𝑡∈RT(𝑡)⟺∑^𝑛𝑖AB𝑖𝑡=0∀𝑡=𝑡+1,…,NT		(x)
Keep as many bins as necessary to satisfy (xi) and transfer the extra bins to the
next available tour. Update all the information related to the current tour and the tour that received
the extra bins. Remove the selected tour from AT.
IL𝑖𝑡+AB𝑖𝑡≥(NR𝑡+1)×𝑑𝑖𝑡		(xi)
End while
For 𝑡=NA to 2
If (xii) is not satisfied
^𝑛∑𝑖=1NA𝑖𝑡≤𝐴		(xii)
While (xii) is not satisfied
Identify the nearest available tour before the current tour (ℎ) that satisfies (iv) and (xiii).
∑^𝑛𝑖AB𝑖𝑡≠0		(xiii)
Create the FICL according to (xiv).
𝑖∈FICL(𝑡)⟺AB𝑖𝑡+IL𝑖𝑡^−>𝑑𝑖𝑡∩AB𝑖ℎ+IL𝑖ℎ^+<𝐶𝑖		(xiv)
Use the solution string and select a reference that is in the FICL
and transfer one bin of the selected reference to tour ℎ.
Update the information related to the current tour and the tour that received the selected reference
End while
End if
End for