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This model is used to balance workloads on an assembly line. Five heuristic rules can be used for performing the balance. The cycle time can be given explicitly or the production rate can be given and the program will compute the cycle time. This model will not split tasks. Task splitting is discussed in more detail in a later section.

The general framework for assembly line balancing is dictated by the number of tasks which are to be balanced. These tasks are partially ordered as shown for example in the precedence diagram below.

*Method.* The five heuristic rules which can be chosen are:

longest operation time

most following tasks

ranked positional weight

shortest operation time and

least number of following tasks.

**NOTE:** Ties are broken in an arbitrary fashion if two tasks have the same priority based on the
rule given.

The remaining parameters are:

*Cycle time*. The cycle time can be given in one of two ways. One way is when the cycle time is
given directly as shown above. While this is the easiest method, it is more common to determine
the cycle time from the demand rate. The cycle time is converted into the same units as the times
for the tasks. (See example 2).

*Time unit*. The time unit for the tasks is given by this dropdown box. You must choose either
seconds, hours or minutes. Notice that the column heading for the task times will change as you
select different time units.

*Task times*. The task times are given.

*Precedences*. Enter the precedences, one per cell. If there are two precedences they must be
entered in two cells. Do not enter 'a,b'. In fact, a comma will not be accepted

Notice that in the precedence list we have typed both 'a' and 'A'. As mentioned previously, the case of the letters is irrelevant.

Example 1

In this example we have 6 tasks named *a* through *f*. The precedence diagram for this problem
appears above. The time to perform each task is above the task. Also, note that the tasks which are
ready at the beginning of the balance are tasks *a* and *b.* Finally, in this first example we use a cycle
time of 10.

The screen above contains the solution to our first example. The solution screen will always have the same appearance and contain the same information regardless of the rule which is chosen for the balance. The information is as follows.

*The cycle time.* The cycle time which was used appears below the balance. This cycle time was
either given directly or was computed. In this example the cycle time was given directly as 10
seconds.

*Station numbers*. The station numbers appear in the far left column. They are printed only for the
first task which is loaded into each station. In this example three stations are required.

*Task names*. The tasks which are loaded into the station are listed in the second column. In this
example tasks *b, e *and *a* are in station 1, tasks *d* and *c* are in station 2 and task* f *is in station 3.

*Task times*. The length of time for each task appears in this column.

*Time left.* The length of time which remains at the station is listed in this column. The last number
at each station is of course the idle time at that station. For example, there is 1 second of idle time
at station 1, 1 second at station 2, and 2 seconds at station 3 for a total of 4 seconds of idle time
per cycle.

*Ready tasks*. The tasks which are ready appear here. A ready task is any task which has had its
precedences met. We emphasize this because some books do not list a task as ready if its time
exceeds the time remaining at the station. Also, if the number of characters in the ready task list is
very long you might want to widen that column.

*Time allocated*. The total time allocated for making each unit is printed. This time is the product of
the number of stations and the cycle time at each station. In this example we have 3 stations each
with a cycle time of 10 seconds for a total work time of 30 station-seconds.

*The time needed to make one unit.* This is simply the sum of the task times. In the example we
have 1 + 5 + 2 + 7 + 3 + 8 = 26 seconds.

*Idle time.* This is the time needed subtracted from the time allocated. This example has 30 - 26= 4
which matches the 4 seconds found in the column of time left.

*The efficiency*. Efficiency is defined as the time needed divided by the time allocated. In this
example the efficiency is computed as 26/30 which is .8667

*The balance delay*. The balance delay is the percentage of wasted time or 100% - the efficiency.
In this example it is 4 (the idle time)/30 or .1333 which is also determined by 1-.8667.

*Minimum theoretical number of stations*. This is the total time to make one unit divided by the
cycle time and rounded *up* to the nearest integer. In this example we have 26 seconds required to
make one unit divided by a 10 second cycle time for an answer of 2.6. which we round *up* to 3
stations.

The precedence graph can be displayed as well as a bar graph indicating how much time was used at each station. These are shown at the end of this section. In addition, if there is idle time at every station then a note will appear at the top indicating that the balance can be improved (by reducing the cycle time).

Suppose that for the same data we require a production of 2250 units in 7.5 hours.

We assume full minutes and hours and compute the cycle time as

(7.5 hrs/2,250units)*60 min/hr*60 sec/min = 27,000/2,250 = 12 seconds

as illustrated in the balance in the screen below.

A common way to choose tasks is by using the task with the most tasks following. Notice from the
diagram that* a *has three tasks following it and *b* has 2 tasks following it. Therefore the first task
scheduled is task *a* when using this rule.

The ranked positional weight computes the sum of the task and all tasks which follow. For
example, for task *a* the ranked positional weight is 1 + 2 + 7 + 8 = 18 while for task *b* the weight is
5 + 3 + 8 =16. The task with the largest weight is scheduled first (if it will fit in the remaining
time). Notice that *e *has a higher ranked positional weight than *c*.

Another rule that is used sometimes is to give priority to the task which takes the least amount of time.

The last rule which is available is the least number of followers.

Some books and some software do not apply the longest operation time rule properly. If the task with the longest time will not fit into the station then the task with the second longest time should be placed in the station if it will fit.

In the screen below we present data for 8 tasks. Notice that tasks *b* and *c* follow task* a*.

The balance appears above for a cycle time of 5 seconds. After task *a *is completed tasks *b* and *c
*are ready. Task *b* is longer but will not fit in the 4 seconds which remain at station 1. Therefore,
task *c* is inserted into the balance. We caution you that if the answer in your book differs from the
program to check if the book has neglected to put in the task with the longest operation time that
will fit.

If the cycle time is less than the amount of time to perform a specific task then there is a problem. We perform what is termed task splitting but in reality is actually duplication. For example, suppose that the cycle time is 2 minutes and a task takes 5 minutes. Then we have the task performed three times (by three people at three machines independent of one another). The effect is that three units will be done every 5 minutes which is equivalent to one unit every 1.33 minutes which fits into the 2 minute cycle.

Now, the actual way that the three people work may vary. While other programs will split tasks the assumptions vary from program to program. Rather than making assumptions we leave it to you to split the tasks by dividing the task time appropriately.

Suppose that in Example 1 we wanted to use a cycle time of 6 seconds. Then it is necessary to replicate both tasks d and f since they will not fit in the cycle time. The approach to use is to solve the problem by dividing the task times by two since this replication is needed. We present the results below

Two different graphs are available. The first is a precedence graph as shown below. Please note
that there may be several different ways to draw a precedence graph.

The second graph is of time used at each station. In a perfect world these would all be the same (a perfect balance)

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