Each week, you will be asked to respond to the prompt or prompts in the discussion forum. Your initial post should be a minimum of 300 words in length, and is due on Sunday. By Tuesday, you should respond to two additional posts from your peers. 
Distribution and Network Models
We know that most problems which have resources to be allocated from many sources to multiple destinations can be solved using the maximum flow method. Examples may include airline scheduling or fairness in car sharing, etc. Can you explain why for them or find other example(s) to explain it so we can better understand how maximum flow method works in real world scenarios? (If you prefer, you may also choose other examples to illustrate other methods covered in this Distribution and Network Models Module.)

John Pfeffer 
The maximum flow method is used for airline scheduling because there is a lot of air traffic and when they are scheduling flights they want to ensure they are getting the shortest flight times or the most convenient flight path. This makes it fair to everyone and it allows people to know when and where they will be headed if they have a layover on the way to their final destination. I’m sure at some point all of us have looked for plan tickets and chosen the one with a layover because it is the cheaper option. It is always more convenient to take a non-stop flight but financially you may want the cheaper option and the longer route works best.
Another example that is similar to this process is a flow chart that technicians may use for troubleshooting. There could be multiple different steps you can take but it ultimately comes down to if and then statements. I have used this method before in real life when I was in the Navy and I knew I was going to get in trouble. I could either go the long route or the short route that ended quickly.
I think we all use the maximum flow method in our everyday lives we just have not realized it until we learned about this method. If we need to figure out the best way to get some where or the best flow of something and have multiple different stopping points it is the best method. It provides you with the ability to find the shortest, maximum, and best route for your situation.
David R. Anderson; Dennis J. Sweeney; Thomas A. Williams; Jeffrey D. Camm; James J. Cochran; Michael J. Fry; Jeffrey W. Ohlmann (2018) An Introduction to Management Science: Quantitative Approach, (15th Edition) Cengage Learning

Robert Martinez 
Hello all,
After thinking about this question for the past few days I decided that the best answer I could provide would be based upon personal experience.  When I started to search for some reference material, I was rather surprised to find an article in EBSCO that dealt with what I did in the Army. It is a good read and give much better insight as to what we in Army Aviation faced when developing a maintenance program.  As a former Aviation Maintenance Officer one of the many hats I had to wear involved the scheduling of aircraft made available for various missions.  It may seem to be a simple matter of assigning any aircraft requested by supported units in order for them to accomplish assigned missions, and trust-you-me I wish that it was.  The easiest situation I had come across was when we received aircraft from the factory or overhaul.  Knowing that all aircraft were required to have scheduled maintenance at 250 flight hours and then heavy maintenance at 500 flight hours we started out by aligning said aircraft to owning units.  Once this was accomplished the next task was to create a “phase flow” whereby airframes were chosen to fly x amount of hours before the next one was scheduled to fly and so forth until all 21 aircraft were set to fly missions spaced a staggered amount of hours.  By doing this we insured that scheduled maintenance task did not get stacked up thus not giving maintenance crews the time they needed to complete all necessary task within an “acceptable” time frame.  Each scheduled maintenance tasks had established hours needed to complete listed in the associated maintenance manual, allowing us a baseline or target date as to when the entire process should be completed. 
By spacing out the phase flow hours we also gave ourselves a little bit of time for unscheduled maintenance tasks which, unfortunately happened more often than not.  Throw into the mix the availability of repair and or replacement parts and now what started out as a neatly organized maintenance flow chart starts getting muddy.  Then you have critical components that have a certain life in the form of flight hours that have to be replaced when their expected life span expires.  As much as possible these components are identified and scheduled to be replaced when the aircraft is brought into phase.  On paper this always looks nice but more often than not these components fail before their end date and have to be replaced which means that the scheduled dates have to be adjusted. 
Long story short all of these various tabulations have been created and put into Excel Spreadsheet form.  At the end of each flying day Production Control personnel take all of the days hours flown and enters the information into the spreadsheet that give all those needing to know a snapshot as to how the unit is in the form of readiness rates.  What I have just described is extremely simplified as there are many more components involved in all of this, but I believe I have given enough information so that one can relate as to how I see this being a good example of utilizing the maximum flow method.  Our goal was to meet all missions requested of us while also maintaining high levels of mission readiness.  I could have gone into Fully Mission Capable and Partially Mission Capable, night/day operations, weapons systems status’, Avionics and so forth but I leave that for another day.
Safaei, N., Banjevic, D., & Jardine, A. K. S. (2011). Workforce-constrained maintenance scheduling for military aircraft fleet: a case study. Annals of Operations Research, 186(1), 295–316. https://doi.org/10.1007/s10479-011-0885-4

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