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Loading Dock Queuing

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Deliveries clogging the loading dock area
The specific details regarding the delivery process at the receiving dock.

1-Receiving dock open from 7am to 3pm, 8 hours, or 480 minutes.
2-The average number of arrivals on any given day is 28, which is 3.5 arrivals per hour, average.
3-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.

References/ material to use/help
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.
Queuing Theory. (n.d.). Encyclopedia of Business, 2nd Ed.; Reference for Business, retrieved from: http://www.referenceforbusiness.com/encyclopedia/Pro-Res/Queuing-Theory.html
Attached in the PowerPoint file named Queuing theory provides lecture notes on queuing and queuing equations. It also has Exercises for you if you need them
Also attached is the Excel file QueueCalc. 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 if need be!
Once you have mastered the examples and exercises; need your help in writing a report tackling the company's problem. And please use the QueueCalc for the problem when writing the report.
Use the above information and the Analyze this situation and determine what we need to know and give me a 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.
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.

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The solution discusses loading dock queing

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Load Docking Queuing
In the current single server situation that is used in unloading trucks in this system, given that average number of arrivals on any given day is 28, which is 3.5 arrivals per hour on average, and the number of truck that are unloaded per hour are 4.2 trucks, then using the excel Queue calculator, the queuing system state data is noted to be there is an average of 5 trucks in the system with an average of 4 trucks waiting on line to be unloaded. It is also noted that it is only 0.833 or four fifth of the time that trucks are usually unloaded in this system. The average time that a truck spends in the system from arrival to being serviced is 85.7 minutes with the average time that it spends in line before being unloaded being 71.4 minutes and ...

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