Answer:

The throughput rate of a set of resources will depend on the capacity of the bottleneck resource. A bottleneck is the resource having the minimum capacity. The capacity of a resource is computed by the following expression:

a.

Compute the capacity of each of the resources by using the following Excel computations.

Results

Note that the resource 2, having the lowest capacity, is the bottleneck resource. The flow rate will be equal to the capacity of the bottleneck resource i.e. 0.1667 units per minute.

Compute the total time to produce 100 units starting with an empty system as follows:

So, the total time to complete 100 units is

b.

Compute the average labour content by summing up the processing times at the three resources.

So,

The average labour content is

c.

Compute the average labour utilization using the following formula:

Compute the idle time of the workers by subtracting the processing time from the product of the system cycle time and the number of workers.

So,

The idle time of the workers at resource-1

The idle time of the workers at resource-2

The idle time of the workers at resource-3

So, the total idle time

Therefore, the average labour utilization is

d.

Compute the cost of direct labour using the following formula given the wage rate being $10 per worker-hour.

The cost of direct labour is, therefore,

Answer:

The throughput rate of a set of resources will depend on the capacity of the bottleneck resource. A bottleneck is the resource having the minimum capacity. The capacity of a resource is computed by the following expression:

a.

Compute the capacity of each of the resources by using the following Excel setup and computations.

Results

Note that the worker-3, having the lowest capacity, is the bottleneck resource. The capacity of the line will be equal to the capacity of the bottleneck resource i.e. 0.0133 units per second.

So, the capacity

b.

Use the following assignments of tasks in order to get the maximum possible capacity given the two constraints.

Worker-1: Task 1, 2

Worker-2: Task 3

Worker-3: Task 4

Worker-4: Task 5, 6

Compute the capacity of each of the resources by using the following Excel setup and computations.

Results

Note that the worker-1, having the lowest capacity, is the bottleneck resource. The capacity of the line will be equal to the capacity of the bottleneck resource i.e. 0.0182 units per second.

So, the capacity

c.

Note that there are 4 workers and 6 tasks. So, at least two combinations of tasks must be carried out to accommodate all the tasks. And none of the combinations will give rise to worker-wise processing time less than 55 minutes for the bottleneck. So, it is practically impossible to increase the capacity more than that found in part-b.

So, the capacity even after rearrangement is

_{2}Because of a drastically reduced forecast, the plant management has decided to cut staffing from nine to six workers per shift. Assume that (i) the nine tasks in the preceding table cannot be divided; (ii) the nine tasks are assigned to the six workers in the most efficient way possible; and (iii) if one worker is in charge of two tasks, the tasks have to be adjacent (i.e., one worker cannot work on tasks 1 and 3). f. How would you assign the nine tasks to the six workers g. What is the new capacity of the line (in toy trucks per hour)

Answer:

The throughput rate of a set of resources will depend on the capacity of the bottleneck resource. A bottleneck is the resource having the minimum capacity. The capacity of a resource is computed by the following expression:

a.

Compute the capacity of each of the resources by using the following Excel setup and computations.

Results

Note that the worker working at

, having the lowest capacity, is the bottleneck resource.

b.

The capacity of the line will be equal to the capacity of the bottleneck resource i.e. 0.011 units per second.

So,

The capacity is

.

c.

Given an unconstrained demand rate, the flow rate will be same as the capacity of the line i.e. 40 per hour.

Compute the cost of direct labour using the following formula given the wage rate being $15 per worker-hour.

The cost of direct labour is, therefore,

The cost of direct labour is, therefore,

d.

If a single worker performs all the tasks, then one unit will be produced in a time which is equal to the total of the processing time of all the 9 stations.

So, flow rate will be 1 unit in 665 seconds i.e.

The cost of direct labour is, therefore,

e.

Compute the utilization of a resource using the following formula:

So,

So, the utilization of workeR_{2} is

f.

There are 6 workers and 9 stations. So, at least 3 pairs of workstations must be combined. The combination pairs are as follows:

The pairs which give the least processing times in ascending order are 5+6, 7+8, and 3+4.

So, the optimal assignments will be as follows:

g.

Compute the capacity by using the following Excel setup and computations.

Results

Note that the worker working at station 3, having the lowest capacity, is the bottleneck resource.

The capacity is 0.00645 units per second or,

_{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 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 utilization of Worker 4, ignoring the production of the first and last units d. How long does it take to finish production of 100 units, starting with an empty process e. What is the average labor utilization of the workers, ignoring the production of the first and last units f. Assume the workers are paid $15 per hour. What is the cost of direct labor for the bicycle g. Based on recommendations of a consultant, Atlas Inc. decides to reallocate the tasks among the workers to achieve maximum process capacity. Assume that if a worker is in charge of two tasks, then the tasks have to be adjacent to each other. Also, assume that the sequence of steps cannot be changed. What is the maximum possible capacity, in units per hour, that can be achieved by this reallocation h. Again, assume a wage rate of $15 per hour. What would be the cost of direct labor if one single worker would perform all seven steps You can ignore benefits of specialization, set-up times, or quality problems. i. On account of a reduced demand forecast, management has decided to let go of one worker. If work is to be allocated among the four workers such that (i) the tasks can't be divided, (ii) if one worker is in charge of two tasks, the tasks have to be adjacent, (iii) the tasks are assigned in the most efficient way and (iv) each step can only be carried out by one worker, what is the new capacity of the line (in finished units/hour)