Solution
First, determine the batch production time (tb) and then the average production time (tp). From the average production time, calculate production rate (Rp) in parts/hr. The governing equations are
tb = tsu + Qtc
tp = tb/Q
Rp = 1/tp,
where the values are
| t c | = | 6.75 min/part (calculated in Example 2.3) |
| t su | = | 4 hr |
| Q | = | 3000 parts. |
It is important to keep consistent units: convert operational cycle time to units of hr/ part. Thus,
tc = (6.75 min/part)(1 hr/60 min) = 0.1125 hr/part.
The batch production time is then
tb = 4 hr + (3000 parts)(0.1125 hr/part) = 4 hr + 337.5 hr = 341.5 hr.
The average production time is
tp = 341.5 hr/3000 parts = 0.1138 hr/part.
Therefore the production rate is
Rp = 1/tp = 1/0.1138 hr/part = 8.78 parts/hr.
The last example highlights how to determine production rate of any type of manufacturing process in which parts are run in batches and setup time is a significant portion of batch production time. As setup time decreases and quantities processed increases, operational cycle time approaches the same value as average production time. This is the case in quantity type manufacturing systems. Thus, the production rate can be determined directly from the operational cycle time:
tp = tb/Q = (tsu + Qtc)/Q.
Since setup time becomes small relative to the product of quantity and operational cycle time tc, then clearly
tp ~ tc.
Then
Rpq = 1/tc,
where
Rpq = average production rate for a quantity manufacturing systems (parts/min)
tc = operational cycle time (min/part).
Example 2.6
Calculate the average production rate (Rpq) of the injection molding process in Example 2.4, in units of parts/hr.
Solution
The injection molding process is a quantity type manufacturing process. Therefore, the governing equation is
Rpq = 1/tc.
Taking the operational cycle time from Example 2.3 and converting the units to hr/ part yields
tc = (0.334 min/part)(1 hr/60 min) = 0.00567 hr/part.
Therefore
Rpq = 1/(0.00567 hr/part) = 179.64 parts/hr.
Consider the flow-line type manufacturing system shown in Figure 2.1. In it the product is traveling to each workstation via a conveyor belt. At each workstation the product is processed accordingly. Upon completion of the processing, the product is moved to the next station. The transporting of the part is coordinated with the time it takes to complete the processing at each workstation. Some workstations finish processing sooner than others. However, the conveyor cannot move the parts until the slowest process (i.e., the process that takes the most time) is completed. This workstation is called the bottleneck station.
Figure 2-1 Flow-line manufacturing system
When all the stations have processed the product, it exits the conveyor belt. Thus, at specific time intervals a finished product is produced. The time interval may be expressed in minutes, hours, days, weeks, months, or even years. The production rate has been defined as the number of parts produced per hour, which corresponds to number of parts that drop off the conveyor line in an hour in this example. Therefore, to calculate the production rate it is necessary one determine how often a part falls from the conveyor. This operational cycle time of the flow line (tc) is the sum of the time to move the product between the workstations and the actual processing time at the bottleneck station. In equation form:
tcf = tr + max to
where
tcf = operational cycle time of flow line system (min/part)
tr = time to transfer parts between stations (min/part)
max to = actual processing time of bottleneck workstation (parts/min).
The production rate or cycle rate of the flow line then becomes
Rc = 1/tcf,
where Rc = cycle rate of a flow-line manufacturing system (parts/min).
Example 2.7
Calculate the cycle rate (Rc) of the flow-line manufacturing system shown in Figure 2-1; assume the transfer rate is 3 sec per part and the processing time for each work station is as shown in the table.
| Workstation | Processing time (m in/pc) |
| 1 | 1. 5 |
| 2 | 0. 7 5 |
| 3 | 1. 2 5 |
| 4 | 1. 5 |
| 5 | 0. 5 |
Solution
The governing equations are
tcf = tr + max to
Rc = 1/tcf.
The transfer rate was given as
tr = 3 sec/part or 0.05 min/part.
The actual process