Problem 5 (20 pts) Three types of aircraft, A, B, and C, need to be assigned to

Question

Problem 5 (20 pts) Three types of aircraft, A, B, and C, need to be assigned to four routes, 1,2, 3, and 4. The first table below describes the capacity for each aircraft, the number of aircraft for each type, and the number of trips an aircraft makes if it is assigned to a route. The numbers of passengers for routes 1, are 1000, 2000, 900, and 1200, respectively. The second table below describes the operating cost of an aircraft if it is assigned to a route. If a passenger cannot take a flight due to aircraft capacity limit on a route, there is a revenue loss. The revenue loss per passenger for routes 1, 2, 3, and 4 are $40, $50, $50, and $70, respectively. Please formulate an LP and assign aircraft to routes so that th cost, including operating cost of aircraft and revenue loss, is minimized. Please use G optimal solution and optimal value. 2, 3, and 4 AMS to find the ypeasences) Amcrarts Capacity Number of Number of Trips on a Route (passengers) Aircraft 50 30 20 Operating Cost (S) per trip on a Route 1 2 34 1000 1100 1200 1600 800 900 1000 1000 600 800 800 900 Aircraft Type

Explanation / Answer

1. Let variables be defined as the number of aircrafts assigned to a particular route. Let it be Xij where i=A,B and C while j = 1, 2, 3, 4. These variables are to be integers.

2. Calculate number of trips each plane takes in each route Tij = Xij*tij where tij is the trip each plane can take in each route

3. Calculate toral operating cost, Cij = Tij *cij where cij is the operational cost per trip for each i, j combination

4. Total Number of passengers Pij = Tij*Cap(i) where Cap (i) is capacity of plane i

5. Total Passengers not serviced P(ns) j= Passengers per route i - Summ (Pij) for each j

6. Total Cost of non-service for route j C(ns)j = P(ns)j * c(ns)j where c(ns)j is the revenue loss per passenger

7. Total Cost TC = Summ (Cij) for each i, j + C(ns)j for each j

Objective Function - Minimize Total Cost

Therefore, Min (TC)

Constraints:

1. All variables are integers

2. Total number of passengers being travelled for each route should be less than the passengers per route

3. Summation of each aircraft in all routes = given number of aircraft

Detailed solution provided below:

Aircraft Type Capacity (Passengers) Number of Aircraft Number of Trips on a route Aircraft Type Actual Aircraft Assignment Aircraft Type Total Number of Trips 1 2 3 4 1 2 3 4 Sum 1 2 3 4 A 50 5 3 2 2 1 A 5 0 0 0 5 A 15 0 0 0 B 30 8 4 3 3 2 B 0 0 0 8 8 B 0 0 0 16 C 20 10 5 5 4 2 C 0 10 0 0 10 C 0 50 0 0 Number of Passengers 1000 2000 900 1200 Revenue Loss per passenger 40 50 45 70 Aircraft Type Aircraft Operating Cost per trip Aircraft Type Total Number of passengers Aircraft Type Total Operating Cost 1 2 3 4 1 2 3 4 1 2 3 4 A 1000 1100 1200 1500 A 750 0 0 0 A 15000 0 0 0 B 800 900 1000 1000 B 0 0 0 480 B 0 0 0 16000 C 600 800 800 900 C 0 1000 0 0 C 0 40000 0 0 Total 750 1000 0 480 Total 15000 40000 0 16000 Aircraft Type Total Revenue Loss 1 2 3 4 Total 10000 50000 40500 50400 Total Cost Grand Total 25000 90000 40500 66400 221900

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