1. You have been hired as Director of Conferences for the Institute for Operations Research and the Management Sciences (INFORMS). Six months before the annual INFORMS Analytics convention at the Fontainebleau Miami Beach Hotel, you must determine the number of rooms to reserve. Each attendee is guaranteed a single King Room overlooking the ocean and INFORMS can reserve King Rooms at the rate of $150.00 per room. INFORMS believes that the number of attendees will be approximately Normally distributed with a mean of 5,000 and a standard deviation of 1,000. If the number of attendees exceeds the number of rooms reserved before the deadline, extra rooms must be reserved at a cost of $180.00 per room. Explain and document well your solutions for...
a. Develop a spreadsheet model and employ simulation and @Risk software to determine the number of rooms that INFORMS should reserve to minimize total expected costs for all conference attendees. Mark Doherty, INFORMS Executive Director, wishes for you to consider all options for reserving rooms that are within two standard deviations away from the expected number of total rooms needed.
b. The Fontainebleau is considering an increase to $210.00 for extra rooms reserved after the deadline and INFORMS would be contractually obligated to that increase. How would that affect your decision for INFORMS?
2. The Ford Motor Company is entertaining the development of two new automobiles, the Racer and the Boiler, and they wish to determine which one of the two to advance for introduction into their line of cars. Each model is expected to generate sales for ten years. To determine which model should be built, information was gathered through focus groups with the Marketing department and from experts in the Engineering department and include ...
Fixed Cost of Developing - Assumed to be incurred at the beginning of Year 1 (or end of Year 0) before any sales are recorded.
Variable Production Cost - The variable cost incurred in producing one automobile.
Sales Price - Assumed to be $10,000 for each model.
Sales of Cars During Each of the Next Ten Years - For simplicity assume that all sales occur at the end of each year.
Interest Rate - It is assumed that cash flows are discounted at 10%. This means that a cash outflow of $1.00 at the beginning of Year 1 is equivalent to a cash outflow of $1.10 at the end of Year 1.
Fixed and variable costs and annual sales are not known with certainty. The views from consumers for these quantities were summarized by Marketing and include ...
Racer Boiler
Fixed Costs Probability Fixed Costs Probability
$6 Billion 0.50 $4 Billion 0.25
$8 Billion 0.50 $5 Billion 0.50
$16 Billion 0.25
Variable Cost Probability Variable Cost Probability
$4,600 0.50 $2,000 0.50
$5,400 0.50 $6,000 0.50
Year 1 Sales Probability Year 1 Sales Probability
230,000 0.25 80,000 0.25
250,000 0.50 220,000 0.50
270,000 0.25 390,000 0.25
If a model sales well during its first year, it is expected to sell well during later years and likewise if it sales are poor. Ford models this belief with the assumption that:
Actual Year t Sales for a Model = Actual Year t-1 Sales + Error Term
For the Racer it is assumed that the error term is normally distributed with a mean of zero and standard deviation of 20,000. For the Boiler, the error term is normally distributed with a mean of zero and standard deviation of 30,000. The error term models the variability of each model's sales about the expected sales for each year. Assume that variable cost for each year's production is the same and inflation is not being considered. Compare the merits of the two models for being selected as the one to further develop. For your comparison, assume that ...
a. Variable cost for the two models are uniformly distributed on the intervals [4600, 5400] and [2000, 6000], respectively.
b. It is unrealistic to assume that Year 1 Racer sales must always equal 230,000, 250,000, or 270,000 cars. A more realistic approach is to assume that any integer value between 230,000 and 270,000 may occur. Model this with a triangular distribution. Do likewise for the Year 1 Boiler sales shown in the table.
c. Rather than assuming that it is equally likely to incur $6 billion or $8 billion fixed cost for the Racer, likewise model fixed cost as a triangular distribution Do the same for the Boiler's fixed cost provided in the table.
A. Does the Racer or the Boiler result in the highest expected net present value?
B. Does the Racer or the Boiler result in the lowest standard deviation for net present value?
C. What are the chances of losing more than $1 billion in net present value terms for each?
D. What observations can you make regarding the riskiness of the two proposed automobiles? Would you choose to introduce the Racer or the Boiler?
E. Suppose that the standard deviation for sales for both the Racer and the Boiler is now assumed to be 0.2 of the previous year's sales. Modify the spreadsheet to accommodate that and reconsider your answers to A. - D.