Individual Homework Assignment # 1
Note: This is an individual homework assignment. You need turn in a hard copy of your own work in the beginning of the session in Week 3.
- (Process Analysis with One Product) Consider a process consisting of three stations (Station 1 comes first, followed by Station 2 and then Station 3):
Station | Processing Time [Min./Unit] | Number of Machines |
1 | 5 | 3 |
2 | 3 | 2 |
3 | 8 | 4 |
Assuming 100% machine availability and 100% yield, answer the following questions:
- Which station(s) is the bottleneck of the system? What is the process capacity (measured in # units/hour)? [Partial solution: capacity of station 1 = 36 units/hr; capacity of station 2 = 40 units/hr.]
Capacity:
Station 1: (60*3)/5=36 units/hr
Station 2: (60*2)/3=40 units/hr
Station 3: (60*4)/8=30 units/hr
The bottleneck of the system is station 3, because station 3 can only produce 30 units per hour. Station 1 and 2 can produce more than 30 units per hours.
- If demand is 16 units per hour, what is the output rate of the process, and what is the utilization of each station? [Partial solution: Output rate of the process=16 units/hr.]
Output rate of the process is 16 units per hour.
Utilization
Station 1: 16/36=44.44%
Station 2: 16/40 = 40%
Station 3: 16/30 =53.3%
- (Process Analysis with Multiple Products and Multiple Stages) A small toy manufacturer produces toy castles to go with their popular line of “Action Masters” action figures. At final assembly, each castle is made by fitting 2 “bottom” pieces together and then topping that with 3 “top” pieces. Their production process is diagrammed below. Each Step (A, B, C, and D) consists of a single machine, and the average production rates are included when the machine is 100% available and in use. Note that the machine at Step A is used to make both the “top” and “bottom” pieces (with the production rates for making each type given), and assume that no setup time is incurred when switched between making the “bottom” and “top” pieces. Note also that the machine can work on one piece at one time.
[pic 1]
Question: Calculate the overall capacity of this system (in terms of the number of castles per hour) and identify the bottleneck. Hint: First calculate the capacity of each step and then determines the bottleneck and the capacity of the entire process. [Partial solution: Overall system capacity=85.37 castles/hr.]
Step A:
Set in one hour step A produce number of Top = XT; produce number of Bottom = XB