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LOG 501:Queuing Analysis/Logistics Challenges

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EBBD EMAIL - for Internal Use Only
To: You
From: Danny Wilco <dwilco@ebbd.com>
You asked for the specific details regarding the delivery process at the receiving dock. Since you've been busy at your other jobs, I had this information determined for you.
• Receiving dock open from 7am to 3pm, 8 hours, or 480 minutes.
• The average number of arrivals on any given day is 28, which is 3.5 arrivals per hour, average.
• The data we have collected indicate that we can unload 4.2 trucks per hour.
This should help you get started to think about how to approach this problem. I will get back to you with your specific assignment shortly.
~DW, VP LogOps.
Learning Wizard
Case 4 Resources
Queuing systems are "stochastic", which means based on random variables. The arrival rate of the customers is random but is theorized to follow a specific probability function. The key to analyzing queues is using the theory and equations that allow you to determine the probabilities
This website provides a good general overview of Queuing and waiting lines in business.
Download this PowerPoint file [Waiting Lines Queues] (Attached) which provides lecture notes on queuing and queuing equations. It also has Exercises for you work on.
****WATCH THESE TWO VIDEOS THAT EXPLAINS THE POWERPOINT - IN YOUTUBE:
PART 1: http://youtu.be/xxlixF0deqE
PART 2: http://youtu.be/NQdt2ldymaM
Download the Excel file [Excel QueueCalc] (Attached). There are two Tabs - the first is for Single Server models, and the second is for Multi-Server models. You enter the relevant information of a queuing problem and it will calculate the pertinent results. The values shown in this worksheet when you open it are the Phlebotomy Examples in the PowerPoint.
You can use the QueueCalc spreadsheet to try all of the examples and exercises in the PowerPoint.
Once you have mastered the examples and exercises you should be ready to tackle the EBBD problem. You can use the QueueCalc for the EBBD problem in the Case.

EBBD EMAIL - for Internal Use Only
To: You
From: Danny Wilco <dwilco@ebbd.com>
OK, here's what I want to know: how often do we have more than 5 trucks, more than 6 trucks, and more than 7 trucks. What is the highest number of trucks we may have in the system with a 95% probability? And then, assuming the arrival rate of the deliveries does not change, what does the unload rate need to be so that we can service up to five trucks 95% of the time? In other words if we want a 95% probability of 5 or fewer trucks in the system at any one time, what does the unloading (service) rate need to be? Then, consider that we have two unloading teams, each able to unload trucks at the same rate. What does the unloading rate need to be for each team in order to ensure (100%) 5 or fewer trucks in the system at any time? I know we don't have room for two unloading teams at this time, but there is a possibility we might make room in the future.
Analyze this situation and determine what we need to know and give me report. At this point in time, I am looking only for the problem to be quantified and the unload rate determined for the current situation (single server) and possible two servers.
Let me know if you have any questions.
~DW, VP LogOps.
Learning Wizard
If you have mastered the examples and exercises provided in the Background from the Queuing PowerPoint, you are ready to tackle the EBBD problem.
The current situation is a Single Server situation. Enter the arrival rate and service rate to calculate the pertinent queuing system state data. Find out the probabilities of 5 or more trucks in the system, then 6, then 7. Then use trial and error to find the greatest number of trucks or less that can be in the system with 95% (or as close to 95%).
For the Multi-server problem you will need to use a similar process.
Record the results of your calculations and save the Excel file.
Assignment Expectations of the written report - write the report to your boss, Danny Wilco.
• Problem situation: clearly elucidate the problem situation at EBBD
• Assumptions: what are the assumptions that need to be made and your critical evaluation
• Solution: discuss how you developed the Solver solution. Keep in mind that your audience is not too technical and do not need a lot of detail on this.
o Make sure you attach the Excel file.
o You should refer to the Excel file when necessary.
• Explanation: clear articulation of the results that you obtain, based on what Mr. Wilco is asking for.
• Conclusion: Even though Mr. Wilco is not asking for a conclusion, you should determine if there is a conclusion to this situation and elucidate what it is.
• Writing style & Organization: well-formed sentences and paragraphs, well organized with flow of reason, and good use of language that pertain to concepts and terminology
• Use of references & citations: If you use references, be sure to include appropriate use of citations in the paper and reference list (APA is required).

Solution Preview

Report

To: Danny Wilco

From: Me

Problem situation

The receiving dock receives trucks throughout the day. The arrival rate of the trucks is random, but is assumed to follow an identifiable probability function. We would like to analyze the current delivery situation at the docks. In addition, We would like to determine whether having 2 unloading teams would significantly help alleviate any perceived congestion.

Assumptions

The following data were collected:
• The receiving dock receives truck arrivals from 7am to 3pm, for a total of 8 hours/day.
• On average, there are 3.5 arrivals/hour.

The above values were assumed for problem. Note that the Powerpoint presentation slide 12 incorrectly states that μ is the average service time for a customer. In actuality, μ is the average customer service rate.

Solution

The solutions to your specific questions below were computed using the Excel file attached. By using formulas from Queuing theory, the probability of each occurrence was computed.

How often do we have more than 5 trucks, more than 6 trucks, and more than 7 trucks.

A summary of the solutions from the Excel worksheet is provided below.

Number of trucks Probability
> ...

Solution Summary

The Word file attached contains the solution in 1109 words. An Excel file with formulas and computations is provided.

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