Problem 1:
The file Walmart Closing Prices, posted on Angel contains a little more than a year's worth of the daily closing values of Walmart's stock from 2003 and 2004. Use this data to develop a forecast for the day following the end of the data (October 16 2004.)
Use the following forecasting methods:
i) Moving average forecasting with a span of 3.
ii) Exponential Smoothing with a smoothing constant α=0.5.
Use a data table to give the Forecast for 10/16/2004,MAD and MSE as the smoothing constant in part ii) varies from α=0.1 to 0.6 in increments of 0.1.
Problem 2:
A contractor has found that her cost for a certain construction job is subject to random variation. She believes its actual value follows a continuous uniform distribution between $9000 and $11000 with a mean of $10,000. The cost to prepare her bid is $500. She is competing in a sealed bid competition with four other contractors. She believes that the bids submitted by the other contractors will vary triangularly with a minimum equal to her minimum cost, a most likely value equal to her 1.3 times her mean cost and a maximum equal to 2.5 times her mean cost and that their bids are independent of each other. She will win the competition if her bid is smaller than the bids of all four competitors. If she wins, her profit will be the difference between her bid and her cost minus the proposal preparation cost. If she loses her proposal preparation cost is lost and her profit is -$500.
Simulate 1000 bids in which her bid amount is $14,000 and determine the distribution of her profit. Include the histogram in your response. Also determine the probability that she wins the competition and the probability that she loses money. Compare these results for bid amounts of $13000 and $15000
Problem 3:
Consider the Special Products break even analysis spreadsheet in Figure 1.1 on page 7 of the text. You will find the spreadsheet on your CD.
The production manager has decided to order a production run of Q=35000. Use simulation to find the distribution of profit given the following random inputs:
The fixed cost varies uniformly between 9 and 11 million dollars. The marginal cost is normally distributed with a mean of $1000 and a standard deviation of $200. The Sales Forecast is triangularly distributed with a minimum of 20000, a most likely value of 30,000 and an upper limit of 40000. All variables are continuous. Don't round to integer values.
Use 1000 iterations and find the mean and the 90th percentile of the profit distribution and the probability of a loss. Include the histogram of Profit in your response.
Problem 4:
The table below gives the activity duration and precedence relationships for a small project consisting of six activities. Also shown is the cost per day of crashing each activity and the maximum number of days that each activity may be crashed.
|
Activity
|
Predecessor
|
Normal Time (days)
|
Maximum Crashing (days)
|
$/day
|
|
1
|
_
|
9
|
5
|
5000
|
|
2
|
_
|
7
|
3
|
6000
|
|
3
|
1
|
5
|
3
|
4000
|
|
4
|
1,2
|
8
|
4
|
2000
|
|
5
|
3
|
6
|
3
|
3000
|
|
6
|
4,5
|
9
|
5
|
9000
|
1) Determine which activities should be crashed, and by how much, to complete the project in 22 days.
2) Suppose there is no specific completion time but that there is a payment of $5000 for each day that the project duration is reduced below the normal completion time. Determine the optimum number of days to complete the project and which activities would be crashed and by how many days.
Problem 5:
A TV manufacturing company uses speakers at the rate of 8000/mo. When it places an order for speakers it incurs a fixed cost of $1200. The monthly interest rate for keeping a speaker in stock is assessed at 1%/mo. The cost of the speaker depends on the order size. If less than 1000 speakers are ordered the cost is $11 each. When the order size is between 1000 and 10,000 the cost is $10.50/unit. For order sizes between 10,000 and 30,000 the cost is $10 per unit. For order quantities between 30,000 and 80,000 the cost drops to $9.50. Beyond 80,000 the cost is $9.25. Determine the optimum order size and time between orders if shortages are not allowed.
Attachment:- Special Products Spreadsheet.xlsx