ework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30 pieces…

ework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30 pieces and (b) a shift output of 24 pieces. assume an 6 - hour shift, and use the rule: choose the assignable task with the longest processing time. compute the line efficiency for each case.\na. fill in the table below for a shift output of 30 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation tasks total time idle time\n1 a, b, d 12 0\n2 e, g, c, h 12 0\n3 f, i, j 11 1\n4 k 2 10\ntotal 37 11\nwhat is the assembly - line efficiency? round your answer to one decimal place.\n77.1 %\nb. fill in the table below for a shift output of 24 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation tasks total time idle time\n1 - select -\n2 a, b, e, c\na, b, c, d\nb, c, f, e\n3

ework: facility and work design\nbalance the assembly line shown below for (a) a shift output of 30 pieces and (b) a shift output of 24 pieces. assume an 6 - hour shift, and use the rule: choose the assignable task with the longest processing time. compute the line efficiency for each case.\na. fill in the table below for a shift output of 30 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation tasks total time idle time\n1 a, b, d 12 0\n2 e, g, c, h 12 0\n3 f, i, j 11 1\n4 k 2 10\ntotal 37 11\nwhat is the assembly - line efficiency? round your answer to one decimal place.\n77.1 %\nb. fill in the table below for a shift output of 24 pieces. break ties by choosing the lowest task number. if your answer is zero, enter \0\. round your answers to the nearest whole number.\nworkstation tasks total time idle time\n1 - select -\n2 a, b, e, c\na, b, c, d\nb, c, f, e\n3

Answer

Explanation:

Step1: Calculate cycle time for 30 - piece output

The shift is 6 hours long. 6 hours = 6×60 = 360 minutes. For a shift - output of 30 pieces, the cycle time (C_1=\frac{360}{30}=12) minutes.

Step2: Calculate cycle time for 24 - piece output

For a shift - output of 24 pieces, the cycle time (C_2=\frac{360}{24}=15) minutes.

Step3: Calculate total task time

Sum the times of all tasks: (5 + 4+2 + 3+4 + 5+4 + 2+3 + 3+2=37) minutes.

Step4: Calculate efficiency for 30 - piece output

The formula for assembly - line efficiency (E=\frac{\sum t_i}{n\times C}), where (\sum t_i) is the total task time, (n) is the number of workstations, and (C) is the cycle time. Here, (\sum t_i = 37), (n = 4), and (C = 12). (E_1=\frac{37}{4\times12}\times100%\approx77.1%) (already given and verified).

Step5: Balance the line for 24 - piece output

We will assign tasks to workstations using the longest - task - time rule and break ties by choosing the lowest task number. Workstation 1: Tasks (a,b,c) with total time (5 + 4+2=11) minutes, idle time (15 - 11 = 4) minutes. Workstation 2: Tasks (d,e,g) with total time (3 + 4+4 = 11) minutes, idle time (15 - 11 = 4) minutes. Workstation 3: Tasks (f,h,i,j) with total time (5+2 + 3+3=13) minutes, idle time (15 - 13 = 2) minutes. Workstation 4: Task (k) with total time (2) minutes, idle time (15 - 2 = 13) minutes. Total idle time (=4 + 4+2 + 13=23) minutes.

Step6: Calculate efficiency for 24 - piece output

(E_2=\frac{37}{4\times15}\times100%=\frac{37}{60}\times100%\approx61.7%)

Answer:

For part (b): Workstation 1: Tasks (a,b,c), Total Time 11, Idle Time 4 Workstation 2: Tasks (d,e,g), Total Time 11, Idle Time 4 Workstation 3: Tasks (f,h,i,j), Total Time 13, Idle Time 2 Workstation 4: Task (k), Total Time 2, Idle Time 13 Assembly - line efficiency: (61.7%)