Would you solve this problem in the C# programming language in such a way that operations and workers are assigned to each station?

using System;

using System.Collections.Generic;

using System.Linq;

namespace AssemblyLineAlgorithm

$\{$

class Program

$\{$

$//$ Define operation durations

static readonly Dictionary operationDurations $=$ new Dictionary

$\{$

$\{1,4\},\{2,3\},\{3,2\},\{4,5\},\{5,3\},$

$\{6,4\},\{7,3\},\{8,4\},\{9,2\},\{10,2\},\{11,5\}$

$\}$;

$//$ Define premises $($dependencies$)$

static readonly Dictionary$>$ premises $=$ new Dictionary$>$

$\{$

$\{1,$ new List $\{\}\},$

$\{2,$ new List $\{\}\},$

$\{3,$ new List $\{1\}\},$

$\{4,$ new List $\{1\}\},$

$\{5,$ new List $\{2\}\},$

$\{6,$ new List $\{2\}\},$

$\{7,$ new List $\{1,2,3,4,5\}\},$

$\{8,$ new List $\{2,6\}\},$

$\{9,$ new List $\{1,2,3,4,5,7\}\},$

$\{10,$ new List $\{2,6,8\}\},$

$\{11,$ new List $\{2,6\}\}$

$\}$;

static void Main$()$

$\{$

int cycleTime $=10$;

int maxStations $=2$;

List unassignedOperations $=$ new List$($operationDurations$.$Keys$)$;

List assignedOperations $=$ new List$()$;

int$[]$ workerTimes $=$ new int$[3]$; $//$ Initialize worker times for $3$ workers at station $1$

int currentStation $=1$;

while $($currentStation maxStations && unassignedOperations.Count $>0)$

$\{$

Console.WriteLine$($$"Station $\{$currentStation$\}$ starts:"$)$;

while $($unassignedOperations$.$Count $>0)$

$\{$

$//$ Identify assignable operations

var AL $=$ unassignedOperations

$.$Where$($op $=>$ premises$[$op$].$All$($p $=>$ assignedOperations.Contains$($p$)))$

$.$ToList$()$;

if $($AL$.$Count $==0)$ break;

$//$ Select the operation with the smallest positional weight

var selectedOp $=$ AL

$.$OrderBy$($op $=>$ premises$[$op$].$Count$)$

$.$ThenBy$($op $=>$ op$)$

$.$First$()$;

$//$ Find the earliest time for assignment

int earliestTime $=$ workerTimes.Min$()$;

if $($earliestTime $+$ operationDurations$[$selectedOp$]>$ cycleTime$)$

$\{$

break; $//$ Operation doesn't fit in cycle time

$\}$

$//$ Assign the operation to a worker at the earliest time

int workerIndex $=$ Array.IndexOf$($workerTimes$,$ earliestTime$)$;

workerTimes$[$workerIndex$]+=$ operationDurations$[$selectedOp$]$;

Console.WriteLine$($$"Assigned operation $\{$selectedOp$\}$ to worker $\{$workerIndex $+1\}$ at time $\{$earliestTime$\},$ will finish at $\{$workerTimes$[$workerIndex$]\}")$;

$//$ Update lists

assignedOperations.Add$($selectedOp$)$;

unassignedOperations.Remove$($selectedOp$)$;

$\}$

Console.WriteLine$($$"Station $\{$currentStation$\}$ assignments completed."$)$;

Console.WriteLine$()$;

$//$ Move to the next station

currentStation$++$;

if $($currentStation $==2)$ workerTimes $=$ new int$[2]$; $//$ Reset worker times for station $2$

$\}$

$//$ Print final status

if $($unassignedOperations$.$Count $>0)$

$\{$

Console.WriteLine$("$All operations could not be assigned within the given constraints."$)$;

foreach $($var op in unassignedOperations$)$

$\{$

Console.WriteLine$($$"Operation $\{$op$\}$ was not assigned."$)$;

$\}$

$\}$

else

$\{$

Console.WriteLine$("$All operations assigned."$)$;

$\}$

$\}$

$\}$

$\}$

i have tried to make a code like this, but it is wrong.

We need to solve the assembly line balancing problem with this premise diagram.

The Cycle Time of this assembly line is $10$ minutes.

The maximum number of stations is $2,$ the maximum number of workers is $3.$

The algorithm is started by considering that $3$ workers will be used. Each worker is $0.$ he starts performing operations from the second. WT $=[0,0,0](3$ workers have $0.$ it means that it starts operations in seconds$)$

ALGORITHM

We start the algorithm with $3$ workers, each worker is $0.$ he starts performing operations from the second. WT$=[0,0,0]$

We are specifying an AL list,

AL$=$ is a list of unassigned, non$-$antecedent operations.

We are defining a EL list,

EL$=$ A list of AL operations that can be completed before the cycle time ends.

i$=$ The operation with the smallest Positional Weight value in the EL list, if there are alternative operations, the operation number with the smallest is selected.

t$=$ The earliest time that can be assigned to the operation.

w$=$ the worker who will give t time. If there is an alternative, the worker with the smallest index is selected.

Assign operation i$,$ worker w$\text{'}$s t time. Update the employee's assignment time i according to the completion time of the operation.

When there are no operations left on the EL list, the next station opens. WT$=$ is set to $[0,0,0].$ If there are no other stations to be opened according to the maximum number of stations, stop there.