Your small biotech firm operates a fleet of two specialized delivery vans in Chicago. As a policy, your firm has decided th (a cycle), and both vans are purchased at the same time to receive discounted fleet pricing. The driving demands placed maintenance costs, and each van is different in its use, demand, and costs. In the past, the firm has been surprised by un costs associated with the vans; thus, it is important to analyze the potential of cost variation and to use this information decide to model the arrival of failures (breakdowns of the van) that lead to maintenance costseach failure has a cost. You and your staff decide that the model should be simple, but that it should reflect reality. The model should also dete for 3-year cycles of vehicle use. To determine maintenance cost, you assume the following: 1) Miles Demand for each v probability distribution (Table 1) for each year of operation; thus, 3 Miles Demand (one for each year) for each van in a c known, a Yearly Failure Rate is determined (Table 2). This is a Poisson-average yearly arrival rate and a Poisson distributi to determine Actual number of Failures. 3) Each failure arrival is assigned a randomly selected cost from a set of norma costs are aggregated for all vans over the 3 year cycle (an experiment) and many trials are simulated to create a risk pro a) Create a Monte Carlo simulation that simulates the 3-year cost of maintenance for the fleet. A suggested structure is Simulate 5000 trials (experiments). b) Provide the risk profile for the model in (a), along with the summary statisticsmean, standard deviation, and 5th an c) Calculate the 95% confidence interval for the mean of the simulation. d) What is the value ($ reduction in cost) that you would derive if you could reduce the Yrly Fail-Rate by 1 for all Miles D maintenance program? For example, in table 2 the rate for 25000 would change to 1, the rate for 40000 would change t determine the new summary stats. e). How much would you budget for the 3-year maintenance cycle to meet up to 90% of the maintenance costs? Risk Profile and Summary Stats here b). c). d). Place New Risk Profile here Explain Difference in stats here e). Place Answer here y, your firm has decided that the operational life of a van is 3 years e driving demands placed on the vans are uncertain, as are the m has been surprised by unexpectedly high (and low) maintenance nd to use this information in the annual-budgeting process. You each failure has a cost. he model should also determine the variation in maintenance costs Miles Demand for each van is randomly selected from a defined ch year) for each van in a cycle. 2) Once the Miles Demand is te and a Poisson distribution with this arrival rate is then sampled d cost from a set of normally distributed costs (Table 3). Finally, ulated to create a risk profile for total 3-year maintenance cost. . A suggested structure is provided to simplify your efforts. dard deviation, and 5th and 95th percentile. il-Rate by 1 for all Miles Demand for Van 1, through a preventative for 40000 would change to 2, etc. Produce the new Risk Profile and aintenance costs? a). Van 1 Demand (miles) Miles Demand 25000 40000 65000 80000 Van 2 Demand (miles) Probability 0.5 0.25 0.15 0.1 1.00 Column with many possible failure arrivals to be used by adjacent column to determine the "actual" # of failures Van 1/Yr1 Actual # Failures=> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr1= BRAIN TABLE 1 TABLE 2 Van 2 Demand (miles) Miles Demand 16000 24000 32000 38000 mn with many possible e arrivals to be used by ent column to determine actual" # of failures Van 1 Demand vs Fail-Rate Probability 0.25 0.25 0.25 0.25 1.00 Miles Demand 25000 40000 65000 80000 Column for "actual" failures; sampling of a Poisson distribution and selecting a quantity equal to the "# of Failures" Yrly Fail-Rate 2 3 3 4 Actual # Failures=> # Failure Rate Miles Demand 16000 24000 32000 38000 The Average Arrival Rate per Year of failures for a Poisson process. Used to sample a Poisson distribution Van 1/Yr2 Miles Demand Van 2 Demand vs Fail-Rate Van 1/Yr3 Miles Demand Actual # Failures=> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr2 3 Year Cycle Total= # of Failures Actual # Failures=> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr2 Demand vs Fail-Rate TABLE 3 Yrly Fail-Rate 1 2 2 3 Cost of Failure mean 3800 stdev 1000 ge Arrival Rate per ures for a Poisson sed to sample a tribution Van 2/Yr1 Miles Demand # of Failures Van 2/Yr2 Miles Demand # of Failures Actual # Failures=> Actual # Failures=> 0 1 2 3 4 5 6 7 8 Cost of Failures=> 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr1= Grand Total Van 1-2/Yr. 1-3= Van 2/Yr2 Van 2/Yr3 Miles Demand Actual # Failures=> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr2 3 Year Cycle Total= # of Failures Miles Demand Actual # Failures=> 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Total Yr2 # of Failures