Sub SolveAssemblyLineBalancing$()$

$\text{'}$ Define the task times and precedence constraints

Dim taskTimes$()$ As Integer

taskTimes $=$ Array$(3,2,4,5,6,2,3,4,3,2,5)\text{'}$ Example task times

Dim predecessors$(10)$ As Collection

Set predecessors$(0)=$ New Collection $\text{'}$ Task $1$

predecessors$(0).$Add $0\text{'}$ No predecessors

Set predecessors$(1)=$ New Collection $\text{'}$ Task $2$

predecessors$(1).$Add $1\text{'}$ Task $1$ is a predecessor

Set predecessors$(2)=$ New Collection $\text{'}$ Task $3$

predecessors$(2).$Add $1$

Set predecessors$(3)=$ New Collection $\text{'}$ Task $4$

predecessors$(3).$Add $2\text{'}$ Task $2$ is a predecessor

Set predecessors$(4)=$ New Collection $\text{'}$ Task $5$

predecessors$(4).$Add $3\text{'}$ Task $3$ is a predecessor

Set predecessors$(5)=$ New Collection $\text{'}$ Task $6$

predecessors$(5).$Add $4\text{'}$ Task $4$ is a predecessor

Set predecessors$(6)=$ New Collection $\text{'}$ Task $7$

predecessors$(6).$Add $4$

Set predecessors$(7)=$ New Collection $\text{'}$ Task $8$

predecessors$(7).$Add $5$

Set predecessors$(8)=$ New Collection $\text{'}$ Task $9$

predecessors$(8).$Add $6$

Set predecessors$(9)=$ New Collection $\text{'}$ Task $10$

predecessors$(9).$Add $7$

Set predecessors$(10)=$ New Collection $\text{'}$ Task $11$

predecessors$(10).$Add $8$

$\text{'}$ Define the cycle time and maximum number of workstations

Dim cycleTime As Integer

cycleTime $=10$

Dim maxStations As Integer

maxStations $=2$

Dim maxWorkersPerStation As Integer

maxWorkersPerStation $=3$

$\text{'}$ Step $1$: Compute the positional weights

Dim positionalWeights$()$ As Integer

ReDim positionalWeights$($UBound$($taskTimes$))$

Dim i As Integer, j As Integer

For i $=$ UBound$($taskTimes$)$ To LBound$($taskTimes$)$ Step $-1$

positionalWeights$($i$)=$ taskTimes$($i$)$

For Each pred In predecessors$($i$)$

positionalWeights$($i$)=$ positionalWeights$($i$)+$ positionalWeights$($pred $-1)$

Next pred

Next i

$\text{'}$ Step $2$: Sort tasks by positional weights in descending order

Dim sortedTasks$()$ As Integer

sortedTasks $=$ SortTasksByPositionalWeight$($positionalWeights$)$

$\text{'}$ Step $3$: Assign tasks to workstations

Dim stationLoad$($maxStations$)$ As Integer

Dim stationTasks$($maxStations$)$ As Collection

For i $=0$ To maxStations $-1$

Set stationTasks$($i$)=$ New Collection

Next i

Dim taskAssigned$()$ As Boolean

ReDim taskAssigned$($UBound$($taskTimes$))$

For Each task In sortedTasks

For i $=0$ To maxStations $-1$

If stationLoad$($i$)+$ taskTimes$($task cycleTime And stationTasks$($i$).$Count $$ maxWorkersPerStation Then

stationTasks$($i$).$Add task $+1$

stationLoad$($i$)=$ stationLoad$($i$)+$ taskTimes$($task$)$

taskAssigned$($task$)=$ True

Exit For

End If

Next i

Next task

$\text{'}$ Output the assignment of tasks to workstations

For i $=0$ To maxStations $-1$

Debug.Print "Station $"$ & i $+1$ & $"$:$"$

For Each task In stationTasks$($i$)$

Debug.Print $"$ Task $"$ & task

Next task

Next i

End Sub

Function SortTasksByPositionalWeight$($weights$()$ As Integer$)$ As Integer$()$

Dim indices$()$ As Integer

Dim i As Integer, j As Integer, temp As Integer

ReDim indices$($UBound$($weights$))$

For i $=$ LBound$($weights$)$ To UBound$($weights$)$

indices$($i$)=$ i

Next i

For i $=$ LBound$($weights$)$ To UBound$($weights$)-1$

For j $=$ i $+1$ To UBound$($weights$)$

If weights$($indices$($j$))>$ weights$($indices$($i$))$ Then

temp $=$ indices$($i$)$

indices$($i$)=$ indices$($j$)$

indices$($j$)=$ temp

End If

Next j

Next i

SortTasksByPositionalWeight $=$ indices

End Function

$.$

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