The three station work cell illustrated in Figure S7.7, has a product that must go through one of the two machines at station 1 (they are parallel) before proceeding to station 2.
Station 1-Machine A-Capacity: 20 units/hr
Station 2-Capacity: 5 units/
Station 3-Capacity: 12 units/hr
a). What is the process of the system?
B) What is the bottleneck time of this week cell?
c) What is the process cycle time?
D) If the firm operates 10 hours per day, 5 days per weekl, what is the weekly capacity of this work cell?
Station 1-Machine B-Capacity: 20 units/hrs
a) What is the process time of the system?
Since the product must go through one of the two machines at Station 1 before proceeding to Station 2, the process time of the system is 20 units per hour. Therefore, either Machine A or Machine B represents the process time of each assembly line.
b) What is the bottleneck time of this work cell?
The bottleneck time of this work cell is Station 2, which has a capacity of 5 units per hour. This becomes the bottleneck for the entire product because Station 1 can product 20 units per hour and if they both send to Station 2, that would be 40 units per hour. This would cause a delay or bottleneck because Station 2 is only able to produce or accommodate 5 units per hour.
c) What is the process cycle time?
The process cycle time is 20 units + 5 units + 12 units (total of 37 units per hour)
d) If the firm operates 10 hours per day, 5 days per week, what is the weekly capacity of this work cell?
10 hours per day
5 days per week
37 units per hour X 10 hours per day = 370 units per day
370 units per day X 5 days = 1,850 units per week
a) The process of the system is a three-station work cell where the product goes through one of the two machines at station 1 before proceeding to station 2.
b) The bottleneck time of this work cell is the maximum time taken in any of the three stations. In this case, the bottleneck time is at station 2 with a capacity of 5 units/hr.
c) The process cycle time is the time taken for one unit to complete the entire process. It can be calculated by adding up the processing times at each station. In this case, the process cycle time would be the bottleneck time at station 2, which is 1 hour.
d) If the firm operates 10 hours per day, 5 days per week, the weekly capacity of this work cell can be calculated by multiplying the bottleneck time with the number of hours worked in a week. Here, the weekly capacity would be 5 units/hr * 10 hours/day * 5 days/week = 250 units/week.
Station 1-Machine B has the same capacity as Machine A, which is 20 units/hr.
a) The process of the system in this three-station work cell is as follows:
1. The product enters station 1 and must go through either Machine A or Machine B (they are parallel).
2. After going through Machine A or Machine B, the product proceeds to station 2.
3. Finally, the product moves to station 3.
b) The bottleneck time of this work cell is the time taken by the slowest station or machine in the process. In this case, the capacity of station 2 is 5 units/hr, which is lower than that of other stations. Therefore, the bottleneck time is the time taken by station 2 to process a unit.
c) The process cycle time is the total time it takes for a unit to complete the entire process, including the time spent at each station. To calculate the process cycle time, we need to consider the time taken at each station.
At Station 1, the product must go through either Machine A or Machine B. Since they are parallel, we consider the higher of the two capacities, which is 20 units/hr for both machines.
At Station 2, the capacity is 5 units/hr.
At Station 3, the capacity is 12 units/hr.
To calculate the process cycle time, we add the time spent at each station:
Process cycle time = Time at Station 1 + Time at Station 2 + Time at Station 3
Time at Station 1 = 1 / (Capacity of Station 1) = 1 / (20 units/hr) = 0.05 hr/unit
Time at Station 2 = 1 / (Capacity of Station 2) = 1 / (5 units/hr) = 0.2 hr/unit
Time at Station 3 = 1 / (Capacity of Station 3) = 1 / (12 units/hr) = 0.0833 hr/unit
Process cycle time = 0.05 + 0.2 + 0.0833 = 0.3333 hr/unit
d) If the firm operates 10 hours per day, 5 days per week, the weekly capacity of this work cell can be calculated by multiplying the process cycle time by the operating hours and days:
Weekly capacity = Process cycle time * Operating hours per day * Operating days per week
Weekly capacity = 0.3333 hr/unit * 10 hrs/day * 5 days/week = 16.665 units/week
To answer these questions, let's go through the steps one by one:
a) What is the process of the system?
The process of the system is the sequence of operations that the product goes through. In this case, the product starts at Station 1 and can go through either Machine A or Machine B. After that, it proceeds to Station 2 and finally to Station 3. The process can be summarized as follows: Station 1 (Machine A or Machine B) → Station 2 → Station 3.
b) What is the bottleneck time of this work cell?
The bottleneck time is the maximum time taken at any particular station in the work cell. To determine the bottleneck time, we need to calculate the time taken at each station and compare them.
At Station 1, the maximum capacity is given as 20 units/hr for both Machine A and Machine B. Therefore, the time taken at Station 1 is the same for both machines, which is the reciprocal of the capacity:
Time at Station 1 = 1 / Capacity = 1 / 20 units/hr = 0.05 hr/unit.
At Station 2, the capacity is given as 5 units/hr.
Time at Station 2 = 1 / Capacity = 1 / 5 units/hr = 0.2 hr/unit.
At Station 3, the capacity is given as 12 units/hr.
Time at Station 3 = 1 / Capacity = 1 / 12 units/hr = 0.0833 hr/unit (rounded to 4 decimal places).
Comparing the time taken at each station, we can see that the bottleneck time is at Station 2 with a time of 0.2 hr/unit.
c) What is the process cycle time?
The process cycle time is the total time it takes for a product to go through the entire process. It can be calculated by summing up the time taken at each station. In this case:
Process cycle time = Time at Station 1 + Time at Station 2 + Time at Station 3
= 0.05 hr/unit + 0.2 hr/unit + 0.0833 hr/unit
= 0.3333 hr/unit (rounded to 4 decimal places).
d) If the firm operates 10 hours per day, 5 days per week, what is the weekly capacity of this work cell?
To calculate the weekly capacity, we need to multiply the process cycle time by the number of hours per day and the number of days per week:
Weekly capacity = Process cycle time * Hours per day * Days per week
= 0.3333 hr/unit * 10 hrs/day * 5 days/week
= 16.6665 units/week (rounded to 4 decimal places).
Therefore, the weekly capacity of this work cell is approximately 16.6665 units/week