Question

The Action Toy Company has decided to manufacture a new train​ set, the production of which is broken into six steps. The demand for the train is

4 comma 5004,500

units per​ 40-hour workweek:

                                                                                

Task	Performance Time ​(seconds)		Predecessors
A	2424		minus−
B	3030		A
C	1414		A
D	1515		A
E	1212		​B, C
F	3030		​D, E

This exercise only contains parts​ b, c,​ d, e, and f.

​b) Given the​ demand, the cycle time for the production of the new train set​ =

nothing

seconds ​(round your response to one decimal​ place).

c) The theoretical minimum number of workstations = (round your response up to the next whole number)

d) Using the longest operation time rule, the assignment of tasks to workstations should: (Hint: Number workstations

e) The total idle time per cycle for the process = nothing seconds (enter your response as a whole number.)

f) The efficiency of the assembly line with 5 workstations = nothing % (enter your response as a percentage rounded to one decimal place).

If one used 6 workstations instead of 5, the efficiency of the assembly line would be = nothing % (enter your response as a percentage rounded to one decimal place).

Answer 1

b)

Cycle time = 40 hours * 60 minutes * 60 seconds / 4500 units = 32 seconds per unit

c)

Sum of all task times = 24+30+14+15+12+30 = 125 seconds

Theoretical minimum number of workstations = 125 / 32 = 3.9 or 4 stations

d)

Station	Remaining time	Eligibles	Was Fit	Assigned time	Time remains	Idle time	Improved Cycle time	Idle time based on improved cycle time
I	32	A	A	24	8
	8	B, C, D	-	-	8	8	24	6
II	32	B, C, D	B	30	2
	2	C, D	-	-	2	2	30	0
III	32	C, D	D	15	17
	17	C	C	14	3
	3	E	-	-	3	3	29	1
IV	32	E	E	12	20
	20	F	-	-	20	20	12	18
V	32	F	F	30	2
	2	-	-	-	2	2	30	0
Totals				125		35		25

So, the assignment is as follows:

Station-I --> A
Station-II --> B
Station-III ---> C, D
Station-IV ---> E
Station-V ---> F

For (e) and (f), there can two sets of answers - using improved cycle time and using the required cycle time. Both are shown below.

e)

Total idle time (based on improved cycle time) = 25 seconds per cycle

Total idle time (based on required cycle time) = 35 seconds per cycle

f)

Efficiency (based on improved cycle time) = Sum of all task time / (# stations * max cycle time) = 125 / (5*30) = 83.3%

Efficiency (based on required cycle time) = Sum of all task time / (# stations * reqd. cycle time) = 125 / (5*32) = 78.1%