Question 3: (5 points) Service Management Bulb Replacement Problem: Lighting on exit ramp 167 on 1-55 consists of a cluster of 3 bulbs. Safety regulations require that whenever a bulb fails, it must be immediately replaced. Cost of the bulb is $450 per unit. Cost of making the trip to replace one or more bulbs is $900 (independent of the number of bulbs replaced). Based on past experience, a bulbs life is described by the following probability distribution. Use only the random numbers provided. Duration (life of bulb) in Probability Cumulative Probability months 2 0.2 3 0.3 0.3 4 5 0.2 Highway department wants to investigate two possible alternative policies- i) replace a bulb when it fails, or ii) replace all bulbs whenever one or more bulbs fail no matter when that bulb was installed. Simulate the system (alternative-1 for 25 months and alternative-2 for 25 months). A) Which policy the department should use. B) What is the optimum monthly average cost of operating the system? C) Can you suggest yet third alternative policy which may be worthwhile investigating? 2 Q3. Engine Replacement 3 Objectiv Minimize Average cost per year 4 5 Alternatives: 6 1 Replace only engine that fails Life in je Prob. Rando 7 2 Replace all three engines when one fails 3 0.3 0.1.2 4 0.4 3,4,5,6 9 5 0.3 7,8,9 10 Note: After pulling down the formula -- clean as needed (only keep the lowest F-Time) 11 Alternative 1: Replace only engine that fails 12 Engine 1 Engine 2 ne (gea Cost Engine 3 13 RE Life F-Time RE Life F-Time RE Life F-Time Plan gine Cd Total 14 5 6 3 1100 15 2 8 3 0 1100 16 3 8 3 5 1100 17 4 7 9 0 1100 18 5 3 2 9 1100 19 6 9 9 5 1100 20 7 4 1 0 1100 21 8 7 7 1100 22 9 6 3 2 1100 23 10 6 8 8 1100 24 11 8 6 3 1100 25 12 8 2 2 1100 26 13 0 0 9 1100 27 14 1 7 7 1100 28 15 3 6 2 1100 29 16 4 3 4 1100 30 17 5 6 3 1100 31 18 8 3 0 1100 32 19 8 3 5 1100 33 20 7 9 0 1100 34 21 3 2 9 1100 35 22 9 9 5 1100 36 23 4 1 0 1100 37 24 7 2 6 1100 38 25 9 2 7 1100 39 26 6 7 7 1100 40 27 1 8 3 41 28 8 1 11 42 29 9 2 1100 43 30 3 3 9 44 31 2 4 6 1100 45 32 4 7 5 1100 46 47 48 49 Total Cost 0.00 50 Average Cost per year 0 51 Alternative 2: Replace all three engines when one fails 52 Engine 1 ne (gea Engine 2 Engine 3 Cost Total 53 RE Life F-Time RI Life F-Time R! Life F-Time Plan gine Cd Cost 54 55 56 57 58 59 60 al Cost 0.00 61 er gear #DIV/0! 62 63 a) FAA should use alternative-2 that when one fails replace all three engines 64 #DIV/0! 65 1100 1100 1100