Question

A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible.

Task Length
(minutes) Immediate
Predecessor
a 0.2 -
b 0.4 a
c 0.3 -
d 1.3 b, c
e 0.1 -
f 0.8 e
g 0.3 d, f
h 1.2 g

a. Do each of the following:

(2) Assign tasks to stations in order of greatest number of following tasks.

Task Following Tasks
a
b
c
d
e
f
g
h

(3)
Determine the percentage of idle time. (Round your intermediate calculations to 1 decimal place and final answer to 2 decimal places. Omit the "%" sign in your response.)

Percentage of idle time %

(4)
Compute the rate of output in printers per day that could be expected for this line assuming a 470-minute working day. (Round your answer to the nearest whole number.)

Rate of output units per day

b.
Answer these questions:

(1)
What is the shortest cycle time that will permit use of only two workstations? (Round your answer to 1 decimal place.)

Shortest cycle time minutes

(2)
Determine the percentage of idle time that would result if two stations were used. (Leave no cells blank - be certain to enter "0" wherever required. Omit the "%" sign in your response.)

Percentage of idle time %

(3)
What is the daily output under this arrangement? (Round your answer to 1 decimal place.)

Daily output units per day

(4)
Determine the output rate that would be associated with the maximum cycle time. (Round your answer to 2 decimal places.)

Rate of output units per day

Answer 1

The precedence diagram will be as below: 0.2 0.4 lis 0.3 1.3 0.3 1.2 0.1 0.8 Maximum cycle time -Sum of tasks time 0.2+0.4+0.3+1.3+0.1+0.8+0.3+12-4.6 minutes. Minimum cycle time length of longest task 1.3 minutes. Number of work stations required-(sum of total task times)/(cycle time) -3.53 rounded off to 4 Therefore four workstations are required.

2) Assign tasks to stations in order of greatest number of following tasks Tasks Following tasks 4 (b.d,g.h) 3 (d,g.h) 3 (d,g.h) 2 (g,h) 3 (f.g.h) 2 (g,h) 1 (h) Work StationEligible Assign Task time Time Remainin Idle Time 0.2 0.4 0.3 0.7(1.3-0.6) 0.4(1.3-0.9) 0.3(1.3-1.0 0.3 (1.3-1.0) 0.0(1.3-1.3) 0.5(1.3-0.8) b,c,e, (tie) 1.3 0.8 0.3 1.2 0.0 IV Total idle time-0.6

2sum of idle time No.of workstation X Cycletime =-0.6-= 0.1153=11.53% 3) Percentage of idle time - 4x1.3 4) Rate of output in printers per day that could be expected for this line assuming a 470- minute working day is as below: 470 OUTPUT-Qperating time =361.53 units Cycle time 1.3 min/cycle b) 1) The shortest cycle time that will permit use of only two workstations is Number of work stations required = (sum oftotal task times) / (cycle time) 2 4.6/cvcle time Cycle time 4.6/2 2.3 minutes 2) WorkEligibl AssignTask time Time Statione Idle Time Remainin a.b.c.d.e2.3 0.0 0.0 f,g,h 2.3 0.0 0.0 If two workstations are used then idle time vill be zero.

3) Rate of output in printers per day that could be expected for this line assuming a 470- minute working day is as below: OUTPUT-Operating time 470204.34 units Cycle time2.3 min/cycle Determine the output rate that would be associated with the maximum cycle time: Maximum cycle time -Sum of tasks time 0.2+0.4+0.3+1.3+0.1+0.8+0.3+12-4.6 minutes. Operating time_102.17 units Maximum Cycle time 4.6 min/cycle 470