Lab 7: Minnetonka Warehouse

Note!

Submit your assignment to the Dropbox located on the silver tab at the top of this page.

(See the Syllabus section “Due Dates for Assignments & Exams” for due dates.)

Scenario/Summary

Wayne Schuller managed a warehouse in Minnetonka, Minnesota. His major
concern was the number of workers to assign to his single unloading
dock. After he began contracting with motor carriers for deliveries, he
found that they were assessing him stiff penalties if their trucks had
wait time to be unloaded. Wayne started adding larger crews at the
unloading dock, but often, they seemed idle because there were no trucks
to unload. Wayne recalled from college that queuing theory might be
applicable to such a problem.

The theory of queuing is an analysis of the probabilities associated
with waiting in line, assuming that orders, customers, and so on arrive
in some pattern (often a random pattern) to stand in line. A common
situation is that on the average, a facility may have excess capacity,
but oftentimes, it is more than full, with a backlog of work to be done.
Often, this backlog has costs associated with it, including penalties
to be paid or customers who walk away rather than wait. If a firm
expands its capacity to reduce waiting times, then its costs go up and
must be paid even when the facility is idle. Queuing theory is used to
find the best level of capacity, the one that minimizes the costs of
providing a service and the costs of those waiting to use the service.

After some further research specific to his firm, Wayne determined the following facts.

1. Trucks arrive randomly at the average rate of four per hour, with a deviation of plus or minus one.
2. A team of two warehouse workers can unload trucks at the rate of five per hour, or one every 12 minutes.
3. A team of three warehouse workers can unload trucks at the rate of eight per hour, or one every 7.5 minutes.
4. A team of four warehouse workers can unload trucks at the rate of 10 per hour, or one every six minutes.
5. A team of five warehouse workers can unload trucks at the rate of 11 per hour, or one every 4.45 minutes.
6. The unloading times given in the preceding items (1-5) are average figures.
7. Each warehouse worker receives $14 per hour, must be paid for an
   entire shift, and because of union work rules, cannot be assigned to
   other tasks within the warehouse.
8. Because of its contract with the carriers, the Minnetonka
   warehouse must pay the motor carriers that own idle trucks at the rate
   of $60 per hour while the trucks stand idle, waiting to be unloaded.

Deliverables

This week’s lab consists of five questions. Please be certain that you
answer all of the questions and address all of the areas outlined in the
grading below.

Note about rounding. It is a generally accepted
practice to round numbers so the reported result has at least three more
decimals places than any of the numbers used in obtaining this result.
If an answer does not follow this procedure and is used in a subsequent
calculation(s), an incorrect final result will often occur.

LAB STEPS

Step 1: Number of Trucks in Queue

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Question 1: For each of the four work team sizes, calculate the expected number of trucks waiting in the queue to be unloaded.

Use the following to solve this problem:

Step 2: Expected Time in Queue

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Question 2: For each of the four work team sizes,
calculate the expected time in the queue; that is, the expected time
that a truck has to wait in line to be unloaded.

Use the following to solve this problem:

Step 3: Immediate Unload Probability

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Question 3: For each of the four work team sizes, what is the probability that a truck cannot be unloaded immediately?

Use the following to solve this problem:

Step 4: Lowest-Cost Team

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Question 4: Which of the four work team sizes results in the lowest cost to Wayne?

Step 5: Faster Forklift Rental

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Question 5: Wayne is also considering rental of a
forklift to use in truck unloading. A team of only two would be needed,
but the hourly cost would be $38 per hour ($28 for the workers and $10
for the forklift). The two workers could unload a truck in five minutes.
Should Wayne rent the forklift?

Step 6: Final Step

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Submit your completed assignment to the Lab Dropbox in a MS Word
document for grading. This work should adhere to the APA 6.0 guideline.

See the Syllabus section “Due Dates for Assignments & Exams” for due dates.

Grading Rubric

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• Be sure to answer all of the questions.
• It is recommended that you show all of your work. If you only
  provide the answers and any of them are incorrect, you will lose all of
  the points allocated to the incorrect answer. However, if you show your
  work, you might be able to obtain partial credit even if the answer is
  incorrect. An example would be if you set up the problem correctly, but
  you made a math error in your calculations.