Problems

1. The Snow Mountain Ski Company produces pairs of skis. Its business is highly seasonal, and for the next fiscal year it has the following forecasts of the demand for pairs of its skis for each month. The fiscal year runs from July 1 to June 30.

The company has a beginning inventory on July 1 of 50 pairs of skis. The company has a capacity of 16 pairs of skis per eight-hour shift, and it works one shift per day, for 48 five-day weeks per year. Here are financial data on producing, storing, and selling skis.
Variable cost during the day shift (8 AM to 5 PM): $60.00 per pair
Variable cost during the night shift (5 PM to 2 AM): $70.00 per pair
Cost of storing skis for one month: $2.00 per pair in the average inventory
Cost of acquiring skis from a supplier: $64.00 per pair
The selling price of skis: $150.00 per pair

Skis may not be backordered, since they must be available during the skiing season. In case of shortages, the company does have options, however. It may schedule half of a night shift (four hours, with a capacity of 8 pairs of skis); or it may schedule a full night shift (8 hours with a capacity of 16 pairs of skis); or it may purchase from an outside supplier. In the event of surplus production, the company may reduce the day shift to half-time (4 hours per day, with a capacity of 8 pairs of skis). It will not close the plant entirely.

1. Construct an aggregate planning schedule for the fiscal year in the style of Example 1 of Chapter 12 of your textbook. Assume that the company schedules one 8-hour shift per working day with no outside purchases. Unsold pairs of skis will be kept in inventory.
2. How many sales will be lost under the plan in a above?
3. How much gross margin will be made per month under the plan in a? For the entire year? (Gross margin = Revenue - Cost of goods sold - Storage costs.)
4. It is proposed to schedule half of the night shift beginning in the month in which a shortage appears in the schedule in a (for four weeks) and continuing until the month in which the shortage disappears (for two weeks). Prepare the aggregate planning schedule in the style of Example 1 in your textbook.
5. How many sales will be lost under the plan in part d?
6. How much gross margin will be made under the plan in d per month? For the entire year? Compare this amount to the gross margin in part c.
7. What is one obvious improvement that could be made in the plan in part d.
8. What other options might be explored?

2. Use the data in Problem 1 to .draw a cumulative graph of demand and the inventory, by months, in the style of Figure 12-3 in your textbook, for the plan in la.

3. Use the data in Problem 1 to answer this question. Formulate the production problem in the style of the transportation model, as shown in Table 12-4 of your textbook. Construct the table for the months of October, November, December, and January. In each period the alternatives are to produce skis during the day shift, or during the night shift, or both. Backorders are not allowed. You may ignore the beginning and ending inventory. Do not solve.

4. As large as the matrix is in Problem #3, EXCEL can solve it.

1. How do you enter the problem in an EXCEL spreadsheet?
2. How do you enter the objective function?
3. How do you enter the constraints?
4. What is the solution?
5. What is the cost of the solution?

5. Here is information on the Caribou Beer Company regarding sales of its six-packs for the period of May and June. It is now April 30, and the inventory contains 60 six-packs. The forecasts for each week of the period are given below, along with the firm orders.

Six-packs are produced in lots of 1,200, once a week, if needed.

1. Construct the Master Production Schedule for May and June.
2. When should the Production Manager plan on producing more six-packs?

Solutions

g. The day shift might be reduced to half-time during the spring months, to reduce the inventory build-up. h. Peak demand might be met by obtaining skis from a supplier. Or the night shift might be scheduled to begin earlier, say in December, to anticipate the winter demand for skis.

2. X = Calendar Time; Y = The cumulative demand or production from July 1 up to date.

The month's initial refers to the last day of the month. Graph the following points:

3. Place the months in the columns; the column totals will be the monthly demand. A dummy column will be needed. Place the day shifts and the night shifts in the rows; the row totals will be the monthly capacities of each shift. A different row will be needed for each shift for each month. The costs will be the variable cost per pair of skis plus the cost of storage. Thus, skis produced by the day shift in July and stored until September will cost $60 + $2 + $2= $64. Because it is not possible to produce skis in November for sale in October, enter a large cost ($100) in the October column and November row, in order to exclude those cells from the solution.

4. a.

c. In cell I3: =SUM(C3:G3) etc. Hint: use the copy and paste facilities of EXCEL. In cell C12: =SUM(C3:C10)

etc. Hint: use the copy and paste facilities.

e. $116,700.

5. a.

b. Six-packs will produced in the weeks of May 6, May 20, May 27, and June 17