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Distribution and Network ModelsAnswer intial Post word and then Respond to two peers dicussion listed belowDistribution and Network ModelsWe 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.)Peer1Maximal flow is used to determine the maximum amount of flow that can efficiently enter a network, go through all its arcs, and exit a network system during a timeframe (Anderson, 2019). As mentioned, airlines must use this method for real-world scheduling, and car-sharing companies use the Maximum Flow Method for fairness. For airlines, getting it wrong can be detrimental. To design an efficient revenue management system for airlines, it is necessary to have a representative probability distribution of demand by period, fare class, and order of arrival (Bilegan et al., 2007). Without these calculations, airlines would be more prone to experience delays, over/under booking, and crowded terminals. Air traffic control could even be affected.Therefore, airline revenue management systems aim to maximize airlines’ revenues from selling the available seats on their scheduled flights. Bilegan (2007) explained that advanced revenue management systems present four main components: forecasting, overbooking, seat inventory control, and pricing. He further explained that a revenue management system works online, gathering the most recent updates provided by the demand forecasting functions and the current state of reservations. Forecasts must be updated with the latest information available. The Maximum Flow Method is highly beneficial in solving problems for airlines and other industries where resources are allocated from many sources to multiple destinations.seressaAnderson, D. R. (2019). An introduction to management science: Quantitative approaches to decision making (Fifteenth edition). Cengage.Bilegan, I. C., Cosenza, C. A. N., González-Rojo, S., & Mora-Camino, F. (2007). A maximum entropy approach to update airlines’ demand distributions. Inverse Problems in Science & Engineering, 15(1), 19–29. https://doi.org/10.1080/17415970600573825Peer 2Planes save money both while in the air and while waiting at the airport. Every flight is a multi-thousand-dollar bet on whether people will buy tickets. Aside from the price, the total flight length is a big deal for people who need to get on a plane. So, airlines spend a lot of time putting together their puzzle flights so that the time between connections is as short as possible. Most routes must connect, so it makes sense that airlines need connecting passengers to stay in business (Bazargan, 2016). Because there is so much air traffic, airlines use the maximum flow method to schedule flights. They want to ensure they get the shortest flight times or the most convenient flight paths. This makes it fair for everyone and lets people know when and where they will be going if they have a layover on the way to their destination. Most people look for plane tickets and pick the cheaper one with a layover. It’s easier to take a flight that doesn’t stop, but the longer route is the best choice if you want to save money.Water distribution networks are another place where the maximum flow method can be used. Many critical infrastructure networks are connected to water resource networks (Kyi & Naing, 2018). When people talk about water transportation problems, they talk about how water moves through pipes or other ways. Getting the water to where it needs to go can be challenging, especially if it isn’t distributed well and must go further than required. A water distribution network comprises many parts that work together to get water to customers. These parts include pumps, reservoirs, pipes, and valves. Most of the capital cost consists of the pipes that connect. The best way to design this system is to figure out the best way to set up the pipe sizes so that the design of the network costs as little as possible while still meeting the restrictions on water amounts and pressures at the customers’ nodes.Have a great week!-Michele-ReferencesBazargan, M. (2016). Airline operations and scheduling. https://doi.org/10.4324/9781315566474Kyi, M. T., & Naing, L. L. (2018). Application of Ford-Fulkerson algorithm to maximum flow in Water Distribution Pipeline Network. International Journal of Scientific and Research Publications (IJSRP), 8(12). https://doi.org/10.29322/ijsrp.8.12.2018.p8441
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