# Matching Supply with Demand

## Quiz 3 :Estimating and Reducing Labor Costs

(Empty System, Labor Utilization) Consider a process consisting of three resources in a worker-paced line and a wage rate of $10 per hour. Assume there is unlimited demand for the product. a. How long does it take the process to produce 100 units starting with an empty system b. What is the average labor content c. What is the average labor utilization d. What is the cost of direct labor Free Essay Answer: 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,

Free
Essay

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.
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

(PowerToys) PowerToys Inc. produces a small remote-controlled toy truck on a conveyor belt 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: a. What is the bottleneck in this process b. What is the capacity, in toy trucks per hour, of the assembly line c. What is the direct labor cost for the toy truck with the current process if each worker receives $15/hour, expressed in dollars per toy truck d. What would be the direct labor cost for the toy truck if work would be organized in a work cell, that is, one worker performs all tasks Assume that the processing times would remain unchanged (i.e., there are no specialization gains). e. What is the utilization of the worker in statioN2 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) Free Essay Answer: 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 workeR2 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,

Essay
(Geneva Watch) The Geneva Watch Corporation manufactures watches on a conveyor belt with six stations. One worker stands at each station and performs the following tasks: These six workers begin their workday at 8:00 a.m. and work steadily until 4:00 p.m. At 4:00, no new watch parts are introduced into station A and the conveyor belt continues until all of the work-in-process inventory has been processed and leaves station F. Thus, each morning the workers begin with an empty system. a. What is the bottleneck in this process b. What is the capacity, in watches per hour, of the assembly line (ignore the time it takes for the first watch to come off the line) c. What is the direct labor content for the processes on this conveyor belt d. What is the utilization of the worker in station B (ignore the time it takes for the first watch to come off the line) e. How many minutes of idle time will the worker in station C have in one hour (ignore the time it takes for the first watch to come off the line) f. What time will it be (within one minute) when the assembly line has processed 193 watches on any given day
Essay
(Atlas Inc.) 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 here: • Step 1 (30 sec.): The plastic tube for the frame is cut to size. • SteP2 (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)