ISDS 576

Syllabus

Final thesis paper requirements

Bidding

You bid on a project that costs you $10 million dollars. You expect four competitors to bid on the project uniformly in the range [10,30]. What should be your bid to maximize your expected profit?

Project Management 

What is the expected duration of the project?

What is the probability the project will be completed in 40 days?

Simulation Files

Store

Call Options

Additional Problems

Ordering Calendars

 You need to order calendars for next year. A calendar costs $7.50 and before Feb. 1 is sold for $10. After Feb.1 you can sell all remaining calendars for $2.50. The expected demand is distributed as follows:

You consider ordering 150, 200, or 250 calendars. What is the expected profit for each?

Developing a New Car

Plan for the next 10 years.

• Fixed cost of developing the car at the beginning of year 1 is normal with a mean of $2.3 billion and a standard deviation of $0.5 billion.
• Inflation factor has a mean of 5% with a standard deviation of 1.5%
• Variable production cost is normal with a mean of $7,800 and standard deviation of $600 and increases by inflation.
• Selling price is $11,800 and increases by inflation.
• Demand at year 1 is normal with a mean of 100,000 with a standard deviation of 10,000. In consecutive years the mean demand is normally distributed with the mean being the actual sales of the previous year and the standard deviation of 10,000.
• Production for next year must be done before the actual demand is known. The company will produce the mean +k S.D. where k needs to be determined.
• If cars are left at the end of the model year, the remaining cars are sold at a 30% discount.
• Use a 5% interest rate discount for future years cash flow.
• Try various values of k (0.5, 1, 1.5 ,2) and see which one is the best.

Cash Balance

Monthly sales from November 2005 to July 2006 are normally distributed with the following means and standard deviations.

Each month there is a fixed cost of $250,000. Taxes are due $150,000 in March and $50,000 in June. Dividends of $50,000 must also be paid in June. Receipts from sales are 20% of sales in the present month plus 60% of sales of last month and 20% of sales of two months ago. Materials are 80% of sales and must be paid a month earlier.

At the beginning of January there is $250,000 in cash. Cash balance for each month should not go below $250,000 and a loan to bring the balance to $250,000, if necessary, must be taken at 1% interest per month and paid back a month later. The company earns 0.5% on its cash balance.

You wish to know the maximum loan amount and total interest on loans. Repeat the simulation for mean sales being 20% below the numbers in the table, and 20% above the numbers in the table.

Machine Replacemment

A machine can be in one of 4 states: Excellent, Good, Average Bad. If a machine is excellent or good there is a 30% chance it deteriorates to the next state after a week. If it is average, there is a 40% chance it becomes bad, and if it is bad, it stays bad. The weekly revenues are $100, $90, $50, and $10 for the four states, respectively. It costs the company $200 to replace a machine with an excellent one.

Determine which of the following policies is best (simulate 50 weeks):

1. never replace a machine,

2. replace bad machines

3.Replace average or bad machines,

4. not replace only excellent machines.

Daisy must build a plant to produce Wozac by the beginning of 1995. Once the plant is built, the plant’s capacity cannot be changed. Each unit sold brings in $10 in revenue. Assume an increase of 8% in demand per year from 1994 levels (it is better to estimate the increase in demand by a regression model).

The fixed cost (in dollars) of building a plant that can produce x units per year of the drug is

Fixed Cost of Building Plant = 5,000,000 + l0x.

This cost is assumed to be incurred at the end of 1995. We assume that all cost and sales cash flows are incurred at the end of each year.

If a plant of capacity x is built, the variable cost of producing a unit of Wozac will be

Variable Cost per unit = 6 - .1 * (x - 1,000,000)/100,000.

Thus a plant capacity of 1,100,000 units will result in a variable cost of $5.90.

Each year a plant operating cost of $1 per unit of capacity is also incurred.

If demand for a year exceeds production capacity, all sales in excess of plant capacity are assumed lost. Determine a capacity level that will maximize expected discounted (at an interest rate of 10%) profits for the time period 1995-2004.