Mathematics

Assignment 3 (90 pts)

1. Sunrise Baking Company markets doughnuts through a chain of food stores. It has been experiencing over- and underproduction because of forecasting errors. The following data are its demand in dozens of doughnuts for the past four weeks. Doughnuts are made for the following day; for example, Sunday’s doughnut production is for Monday’s sales, Monday’s production is for Tuesday’s sales, and so forth. The bakery is closed Saturday, so Friday’s production must satisfy demand for both Saturday and Sunday (30 pts).
　 4 WEEKS AGO 3 WEEKS AGO 2 WEEKS AGO LAST WEEK
Monday 2,200 2,400 2,300 2,400
Tuesday 2,000 2,100 2,200 2,200
Wednesday 2,300 2,400 2,300 2,500
Thursday 1,800 1,900 1,800 2,000
Friday 1,900 1,800 2,100 2,000
Saturday closed on Saturday
Sunday 2,800 2,700 3,000 2,900

Make a forecast for this week on the following basis:
a. Daily, using a simple four-week moving average.

b. Daily, using a weighted moving average with weights of 0.40, 0.30, 0.20, and 0.10 (most recent to oldest week).

c. Sunrise is also planning its purchases of ingredients for bread production. If bread demand had been forecast for last week at 22,000 loaves and only 21,000 loaves were actually demanded, what would Sunrise’s forecast be for this week using exponential smoothing with α=0.10?

d. Suppose, with the forecast made in part (c), this week’s demand actually turns out to be 22,500. What would the new forecast be for the next week?

2. A specific forecasting model was used to forecast demand for a product. The forecasts and the corresponding demand that subsequently occurred are shown as follows. Fill out the table and use the MAD, MSE, and MAPE to evaluate the accuracy of the forecasting model (15 pts).
　 Actual Forecast Absolute Deviation |At-Ft| % Deviation |At-Ft|/At |At-Ft|^2
October 700 660
November 760 840
December 780 750
January 790 835
February 850 910
March 950 890
Average Demand

 
3. Discussion question. Which type of inventory system would you use in the following situations? (10 pts)
a) Supplying your kitchen with fresh food
b) Obtaining a daily newspaper
c) Buying gas for your car
To which of these items do you impute the highest stock-out costs?

 
4. One unit of A is made of three units of B, one unit of C, and two units of D. B is composed of two units of E and one unit of D. C is made of one unit of B and two units of E. E is made of one unit of F.

Items B, C, E, and F have one-week lead times; A and D have lead times of two weeks. Assume that lot-for-lot (L4L) lot sizing is used for Items A, B, and F; lots of size 55, 55, and 200 are used for Items C, D, and E, respectively. Items C, E, and F have on-hand (beginning) inventories of 10, 50, and 160, respectively; all other items have zero beginning inventory. We are scheduled to receive 10 units of A in Week 2, 60 units of E in Week 1, and also 50 units of F in Week 1. There are no other scheduled receipts. If 32 units of A are required in Week 8, use the low-level-coded bill of materials to find the necessary planned order releases for all components (The excel template is available under the Assignments Tab). (35 pts)