Your small biotech firm operatesafleet of twospecialized deliveryvans in Chicago. As a policy, yourfirm has decidedthatthe operational life ofavan is 3 years (a cycle), and both vans are purchased atthe same time to receive discounted fleetpcing.The dvingdemands placed on the vans are uncertain, as
are the maintenance costs, and each van is differentinits use, demand, and costs. In the past, the firm has been surpsed by unexpectedly high(and low)
maintenance costs associated withthe vans;thus, itis importantto analyze the potential ofcostvariation and to use this information intheannual-budgeting
process.You decidetomodel the arval of failures(breakdowns of thevan) thatlead to maintenance costs—eachfailure hasa cost.
You and you rstaff decide thatthe model should be simple, butthat itshould reflectreal y. The model should also determinethe variation in maintenance
costs for3-year cycles of vehicle use. To determinemainten ance cost, you assume the following: 1) Miles Demondforeach van is randomly selected from a
defined probabilityd istbution (Table 1)for each year of operation;thus, 3 Miles Demand (one foreach year)for each van in a cycle. 2) Oncethe Miles
Demand is known, a Yearly Failure Rate is determined (Table2). Thisisa Poisson-averageyeady arval rate and a Poisson distbution with this arrival rate is
then sampled to determineActualnumberof Failures. 3) Each failure arval is assigned a randomly selecte dcostf rom a set of normally distributed costs
(Table 3). Finally, costs are aggregated forall vans overthe 3 year cycle(an experiment) and manytrials are simulated to create a sk profilefortotal 3-year
a) Createa MonteCadosimulation that simulates the 3-yearcostof maintenance forthe fleet.A suggested structure is provided tosimplifyyourefforts.
Simulate 5000 tria ls(experiments).
b) Provide the dsk profile forthe model in (a), alongwiththe su mmary statistics—mean, standard deviation, and 5th and 95th percentile.
c) Calculate the 95% confide ncc interval forthe mean of the simulation.
d) What is the value ($ reduction ¡n cost) thatyou would deriveif you could reduce the YrlyFail-Rote by 1 for all Miles DemondforVan 1, through a
preventativemaintenance program? Forexample, in table 2the rate for 25000 would change to 1, the rate for40000 would change to 2, etc. Producethe
new Risk Profile and determine the new summary stats.
e). How much wouldyou budgetforthe 3-year maintenance cycleto meetupto9û% of the maintenance costs? (Only considerthe results priorto partd).)