Question

Problem for Group F (formulate the problem and find optimal solution) Allocation of Aircraft to Routes. Consider the problem of assigning aircraft to four routes according to the following data: 1 2 4 Capacity Aircraft type Number of Number of daily trips on route (passengers) aircraft 3 1 50 5 3 2 30 2 1 3 8 4 3 3 2 20 10 3 5 4 2 Daily number of customers 1000 2000 900 1200 The associated costs, including the penalties for losing customers because of space unavailability, are: Operating cost ($) per trip on route 1 2 3 4 1 1000 1100 1200 1500 2 800 900 1,000 1000 600 800 800 900 Penalty (s) per lost customer 40 50 45 70 Aircraft type Determine the optimum allocation of aircraft to routes, and determine the associated number of trips.

please excel solver and solver

Answer 1

Optimum Allocation to Aircraft as per following:

No.of Daily trips on route 2 1 3 4 Aircraft Type 1 Capacity No. of Aircrafts 50 5 2 2 30 8 3 1 3 20 10 5 5 5 5 100 23 6 12 8 10 Total Daily Passengers 1,000 2,000 900 1,200

Total Cost Structure with the Optimum Allocation as per following:

Total cost 4 Aircraft Type 1 Capacity No. of Aircrafts 50 5 No.of Daily trips on route 1 2 3 2,200 2,700 3,000 4,000 4,000 3,000 8,900 4,000 2 30 8 2,200 3,700 15,500 21,400 20 1,000 4,500 5,500 10 100 23 3 Total Cost before Penalty Penalty Total Cost 3,000 8,900 4,000 5,500 21,400

Number with The Current Scenarion as per following:

Total cost 4 Aircraft Type 1 Capacity No. of Aircrafts 50 5 No.of Daily trips on route 1 2 3 3,000 2,200 2,400 3,200 2,700 3,000 3,000 4,000 3,200 9,200 8,900 8,600 2 30 8 20 10 1,500 2,000 1,800 5,300 4,900 10,200 9,100 10,900 12,000 32,000 4,900 36,900 3 Total Cost before Penalty Penalty Total Cost 100 23 9,200 8,900 8,600

Analysis- Table for Current Scenario as per following

Aircraft Type 2 3 1 750 1 500 2 720 3 Total Daily Passengers Difference 960 1,000 2,710 1,000 1,000 2,220 2,000 500 720 800 2,020 900 4 Total 250 2,000 480 2,880 400 3,200 1,130 8,080 1,200 5,100 (70)

For Carrying 5100 Passengers we use capacity of 8080 Passengers still we loose 70 Passengers at route 4, this will result in Additional cost of Penalty of $ 4,900.

Analysis- Table for Optimum Scenario as per following

Aircraft Type 1 2 3 4 Total 1 500 500 2 240 960 3 Total Daily Passengers Difference 0 1,000 1,000 1,000 720 1,000 2,220 2,000 0 1,000 1,000 900 1,000 1,240 1,200 0 4,000 5,460 5,100 0

For Carrying 5100 Passengers we use capacity of 5460 Passengers and no loss of Passengers at any route, this will result in No Penalty

Total Saving due to Optimum Solution is $ 15,500 ($36,900-$21500).