Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assembly line at Atlas Inc. consists of seven work stations, each performing a single step. Stations and processing times are summarized below.

Step 1 (30 sec) : The plastic tube for the frame is cut to size

Step 2 (20 sec) : the tube is put together

Step 3 (35 sec) : the frame is glued together.

Step 4 (25 sec) : the frame is cleaned.

Step 5 (30 sec) : pain is sprayed onto the frame.

Step 6 (45 sec) : Wheels are assembled.

Step 7 (40 sec) : all other parts are assembled to the frame.

Complete Question:

Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assembly line at Atlas Inc. consists of seven work stations, each performing a single step. Stations and processing times are summarised here:

• Step 1 (30 sec.) : The plastic tube for the frame is cut to size.

• Step 2 (20 sec.) : The tube is put together.

• Step 3 (35 sec.) : The frame is glued together

• Step 4 (25 sec.) : The frame is cleaned.

• Step 5 (30 sec.) : Paint is sprayed onto the frame.

• Step 6 (45 sec.) : Wheels are assembled.

• Step 7 (40 sec.) : All other parts are assembled to the frame.

Under the current process layout, workers are allocated to the stations as shown here:

• Worker 1: Steps 1, 2

• Worker 2: Steps 3, 4

• Worker 3: Step 5

• Worker 4: Step 6

• Worker 5: Step 7

Assume the workers are paid $15 per hour. Each bicycle is sold for $5 and includes parts that are sourced for $0.75. The company has fixed costs of $225 per hour. Despite Lance Armstrong's doping confession, there exists substantially more demand for the bicycle than Atlas can supply.

a) What is the bottleneck in this process?

b) What is the capacity of this assembly line, in finished units/hour?

c) What is the utilisation of Worker 4, ignoring the production of the first and last units?

d) What is the average labour utilisation of the workers, ignoring the production of the first and last units?

e) Assume the workers are paid $15 per hour. What is the cost of direct labour for the bicycle?

Explanation:

a) Capacity = 1/T

Capacity W1 = 1 / (30 + 20) = 1/50

Capacity W2 = 1 / (35 + 25) = 1/60

Capacity W3 = 1 / (30) = 1/30

Capacity W4 = 1 / (45) = 1/45

Capacity W5 = 1 / (40) = 1/40

bottleneck = W2

b) Proc. Capacity = Min{Capacity}

W2 has smallest capacity = 1 unit / 60 secs

Capacity W2 = (1 unit) / (60 secs)

= 1/60 * 3600s/hr

= 3600/60

= 60 units/hr

C) U = R / C

R = 1 unit/min

Capacity W4 = (1/60) / (1/45) = 0.75

d) LU = LC / (LC + IT)

LC = 50 + 60 + 30 + 45 + 40 = 225 secs

IT = (60-50) + (60-60) + (60-30) + (60-45) + (60-40)

= 10 + 0 + 30 + 15 + 20 = 75

LU = 225 / (225 + 75)

= 0.75

e) Cost = wages/time / flow rate/time

Cost = [ ($15 * 5) / hr ] / [ 1 unit/min / 60 mins/hr]

= ($75/hr) / (1/60 unit/hr)

= $1.25 per unit