Consider a process consisting of three tasks in a machine-paced (conveyor) line and a wage rate of $15 per hour. Each task is assigned to a single worker. Assume there is unlimited demand for the product.

Tasks	Processing time (minutes)
1	10
2	12
3	8

1. How much is the process capacity, in units per hour?

Task 2 having the highest cycle time is the bottleneck and its capacity = 60/12 = 5 units per hour.

1. How much is the total idle time?

Idle time in task 1 = 12 - 10 = 2 minutes Idle time in task 2 = 12 - 12 = 0 minutes Idle time in task 3 = 12 - 8 = 4 minutes

total idle time in a cycle = 2+0+4 = 6 minutes

1. Compute the average utilization of the line.

Efficiency = 1 - idle time / (no of stations x cycle time) = 1 - 6/(3*12) = 5/6 = 0.833 or 83.33%

1. What is the cost of direct labor ($/unit)?

Cost of direct labor = total wages per unit of time / the flow rate

= ($15 x 3) / 5 = $9 per unit

Now task 1 is assigned to 2 workers, and tasks 2 and 3 are combined and assigned to 4 workers, as shown below:

Tasks	Number of workers
1	2
2, 3	4

1. How much is the process capacity, in units per hour?

1. How much is the total idle time?

1. Compute the average utilization of the line.

1. What is the cost of direct labor ($/unit)?

Q2. PowerToys Inc. produces small remote-controlled toy truck on a machine-paced line with nine stations. Each station has, under the current process layout, one worker assigned to it. Stations and processing times are summarized in the following table.

Station	Task	Processing time (seconds)
1	Mount battery units	70
2	Insert remote control receiver	80
3	Insert chip	90
4	Mount front axle	30
5	Mount rear axle	70
6	Install electric motor	60
7	Connect motor to battery unit	45
8	Connect motor to rear axle	80
9	Mount plastic body	75

1. Which station is the bottleneck in this process?

1. How much is the capacity, in toy trucks per hour, of the assembly line?

1. How much is the utilization of the worker in Station 7?

1. How much is the direct labor cost for the toy truck with the current process if each worker receives $20 per hour, expressed in dollars per toy truck?

Because of a drastically reduced forecast, the plant management has decided to cut staffing from nine to just two workers per shift. Assume that (i) the nine tasks in the preceding table cannot be further subdivided; (ii) the nine tasks are assigned to the two workers in the most efficient way possible; and (iii) if one worker is in charge of two tasks, the tasks have to be adjacent (e.g. one worker cannot work on tasks 4 and 8 if he is not also assigned tasks 5, 6, and 7).

1. How would you assign the nine tasks to the two workers?

1. How much is the new capacity (in toy trucks per hour)?

1. How much is the new direct labor cost?

Management is also considering the work cell option, i.e. one worker performs all tasks. Under this alternative:

1. How much is the capacity (in toy trucks per hour)?

1. How much is the corresponding direct labor cost?