Question

... 9.13 Illinois Furniture, Inc., produces all types of office furniture. The "Executive Secretary” is a chair that has been designed using ergonomics to provide comfort during long work hours. The chair sells for $130. There are 480 minutes available during the day, and the average daily demand has been 50 chairs. There are eight tasks: TASK PERFORMANCE TIME (min) TASK MUST FOLLOW TASK LISTED BELOW A,B F, G a) Draw a precedence diagram of this operation. b) What is the cycle time for this operation? c) What is the theoretical minimum number of workstations? d) Assign tasks to workstations. e) What is the idle time per cycle? f) How much total idle time is present in an 8-hour shift? g) What is the efficiency of the assembly line, given your answer in (d)? Px

Answer 1

a) Draw a precedence diagram: A 4min. 7 min. E 6min. 6min. 6min 7min. 8min. The precedence diagram was constructed using the given task and the precedence task. • There is no precedence task were given for Task A and Task B. Thus, Task A and Task B are the initial task to start a precedence diagram. • Task A and Task B is the precedence task for Task C. Thus, Task C should follow the precedence tasks. • Task C is the precedence task for Task D. Thus, Task D must follow the Task C. The diagram continues until Task H with the same procedure.

b) Calculate the cycle time: Cycle time is total time of the process from the beginning to the end. It is calculated by dividing the production time per day with the units required per day. Production time available per day Cycle time = Units required per day 480 minutes 50 chairs = 9.6 minutes ; 10 minutes Hence, the cycle time for the process is 10 minutes

Calculate the theoretical minimum number of workstations: It is calculated by dividing the total task time given with the cycle time. Total task time Theoritical minimum number of workstations = Cycle time (4+7+6+5+6+7+8+6) minutes 9.6 minutes 49 minutes 9.6 minutes = 5.1 workstations Hence, the theoretical minimum number of workstations is 5 workstations

Assign the tasks to workstations: Workstation Termi b le Assige Idle time 10 A A (4) 6 10 IB BO CCO D D45) 10 E EO 10 F F(8) 10 G(8) 10 H(6)

Initial task should be chosen. The remaining task is the next two task of the chosen task. The task, which has the maximum task time, should be chosen. If the task comes under the same workstation, the value which is less than or equal to the previous idle time should be selected. For Task A, the idle time is calculated by subtracting the task time of Task A from the cycle time. Task B and Task C should be the remaining tasks for Task A. Task time of Task C is equal to the idle time of Task A. Thus, Task C should be selected. The idle time is calculated by subtracting the task time of Task B from cycle time. The remaining task for Task C is Task B and Task D. Task B has the maximum task time compare to Task D. Thus, Task B should be chosen The idle time for Task B is calculated by subtracting the task time of Task B from the cycle time. Hence, the process continues until Task H with the same procedure.

Calculate the idle time per 8-hours shift: Workstations Chosen task Idle time 1 A, C 0 2 BL 3 3 E 4 4 F 3 5 G 2 6 H 4 7 D 5 The sum of all idle time is the idle time per shift. Hence, the idle time per shift is 21 minutes

e) Calculate the idle time per cycle: It is given that the average demand is 50 chairs, which means 50 cycles. Idle time per 8-hours shift is 21 minutes. Idle time per cycle is calculated by dividing the number of cycles per day and idle time per shift. Idle time per shift Idle time per cycle = Number of cycles per day 21 minutes 50 cycles = 0.42 minutes = 25.2 seconds Hence, the total idle time per cycle is 25.2 seconds

Efficiency g) Calculate the efficiency of the assembly line: It is calculated by dividing the sum of task time with the value attained by multiplying the actual number of workstations and the cycle time. Total task time Actual number of workstations x Cycle time (4+7+6+5+6+7+8+6) minutes 7 workstations x 10 minutes 49 minutes 70 = 70% Hence, the overall efficiency of the assembly line is 70%