Question

1. This exercise is based on one in Hartman (2007). A pharmaceutical company needs to use a supercomputer to run simulation models as part of its research on cures for AIDS, cancer, and other diseases. The firm expects to perform thousands of simulation runs per year for the next 3 years. The firm can purchase a supercomputer for $2.5 million; the annual operating and maintenance costs are $200,000 per year, and the supercomputer can perform 15,000 runs per year. For every simulation run above 15,000 in a year, the operating costs rise $1,000 per year to cover the needed overtime. A second alternative is to outsource the simulation runs to an IT firm that offers supercomputing services on demand. They will charge the pharmaceutical company $400 per simulation run. Consider a 3-year time horizon, and assume that the number of runs per year is the same every year. The firm is not sure how many simulation runs they will need to perform each year. What is the range of total cost if the number of simulation runs varies from 10,000 to 20,000 runs per year? For what range of activity (number of simulation runs per year) is purchasing a supercomputer the lowest cost alternative?

2. Consider the supercomputer example from Exercise 1 above. The firm is not sure about some of the relevant costs. The following probability distributions reflect their beliefs about the uncertain costs: the annual operating and maintenance costs are uniformly distributed on the range [$150,000, $250,000]; the additional operating costs for simulation runs above 15,000 per year are uniformly distributed on the range [$500, $1500] (per run per year). Use the method of moments to estimate the mean and variance of the costs if the firm purchases the supercomputer and they perform 20,000 runs per year. Use Monte Carlo sampling to estimate the distribution of costs if the firm purchases the supercomputer and they perform 20,000 runs per year.

Answer 1

SOLUTION:

Given that data This exercise is based on one in Hartman (2007). A pharmaceutical company needs to use a supercomputer to run simulation models as part of its research on cures for AIDS, cancer, and other diseases. The firm expects to perform thousands of simulation runs per year for the next 3 years. The firm can purchase a supercomputer for $2.5 million; the annual operating and maintenance costs are $200,000 per year, and the supercomputer can perform 15,000 runs per year. For every simulation run above 15,000 in a year, the operating costs rise $1,000 per year to cover the needed overtime. A second alternative is to outsource the simulation runs to an IT firm that offers supercomputing services on demand. They will charge the pharmaceutical company $400 per simulation run

So

==>Total cost= Fixed cost + fixed O&M costs + Overtime costs

Fixed cost for 3 years= 2.5 million+0.2 million of O&M cost per year*3 years= 3.1 million USD ; this cost is upto 15000 simulations/year for next 3 years

1)   

   Thus, the range of cost is as follows:

No overtime cost till 15000 runs and 1000 USD/run of overtime cost beyond 1000 Runs

No. of Runs	System pruchase cost	fixed O&M cost for 3 years	Over time cost for 3 years	Total cost for 3 years	Cost/Runs
10000	25,00,000	6,00,000	0	31,00,000	103.33
11000	25,00,000	6,00,000	0	31,00,000	93.94
12000	25,00,000	6,00,000	0	31,00,000	86.11
13000	25,00,000	6,00,000	0	31,00,000	79.49
14000	25,00,000	6,00,000	0	31,00,000	73.81
15000	25,00,000	6,00,000	0	31,00,000	68.89
16000	25,00,000	6,00,000	30,00,000	61,00,000	127.08
17000	25,00,000	6,00,000	60,00,000	91,00,000	178.43
18000	25,00,000	6,00,000	90,00,000	1,21,00,000	224.07
19000	25,00,000	6,00,000	1,20,00,000	1,51,00,000	264.91
20000	25,00,000	6,00,000	1,50,00,000	1,81,00,000	301.67

               

2)    

  Assume Y to be the number of per year simulations over which outsourcing cost will be equal to the in-house cost. Then,

3*400*Y=2.5 million + 0.2 million of fixed yearly O&M cost*3 years+ 1000 USD /run of overtime cost *(Y-15000)*3 years

Thus, Y=23277 simulations/year

Hence, till 23277 simulations/year- it will be cheaper to do it in-house than outsource.

Also, between 14000-15000 simulations/year- the cost of in-house setup will be cheapest.