5 - Problems Finance - Operations Management

National Scan, Inc., sells radio frequency inventory tags. Monthly sales for a seven-month period were as follows:

 Month

Sales (000)Units

  Feb.

18

  Mar.

16

  Apr.

10

  May.

21

  Jun.

18

  Jul.

21

  Aug.

30

b.

Forecast September sales volume using each of the following:

(1)

A linear trend equation.(Round your intermediate calculations and final answer to 2 decimal places.)

 Yt

 thousands  

(2)

A five-month moving average. (Round your answer to 2 decimal places.)

  Moving average

 thousands  

(3)

Exponential smoothing with a smoothing constant equal to .40, assuming a March forecast of 17(000). (Round your intermediate forecast values and final answer to 2 decimal places)

  Forecast

 thousands  

(4)

The naive approach.

   Naive approach

 thousands  

(5)

A weighted average using .70 for August, .10 for July, and .20 for June. (Round your answer to 2 decimal places.)

  Weighted average

 thousands  

Freight car loadings over an 18-week period at a busy port are as follows:

Week

Number

Week

Number

Week

Number

1

240

7

305

13

455

2

255

8

345

14

460

3

270

9

385

15

490

4

255

10

370

16

505

5

270

11

410

17

520

6

275

12

450

18

535

a.

Determine a linear trend line for expected freight car loadings. (Round your intermediate calculations and final answers to 2 decimal places.)

    =  +  t

b.

Use the above trend equation to predict expected loadings for Weeks 20 & 21. (Round your final answers to 2 decimal places.)

The forecasted demand for Week 20 is  and for Week 21 is  .

c.

The manager intends to install new equipment when the volume exceeds 820 loadings per week. Assuming the current trend continues, in which week (at the earliest) should the loading volume reach that level?  (Use the rounded answers, as required, from any previous part of this problem.  Do not round any other intermediate calculations.  Round your final answer to 2 decimal places.)

  It should reach 820 loadings in Week  .

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach. The linear trend equation is Ft = 124 + 2.0t, and it was developed using data from periods 1 through 10. Based on data for periods 11 through 20 as shown in the table, which of these two methods has the greater accuracy if MAD and MSE are used? (Round your intermediate calculations and final answers to 2 decimal places.)

t

Units Sold

11

147

12

147

13

149

14

143

15

157

16

152

17

154

18

157

19

162

20

166

  MAD (Naive)

  MAD (Linear)

  MSE (Naive)

  MSE (Linear)

   provides forecasts with less average error and less average squared error.

Timely Transport provides local delivery service for a number of downtown and suburban businesses. Delivery charges are based on distance and weight involved for each delivery: 10 cents per pound and 10 cents per mile. Also, there is a $20 handling fee per parcel.

a.

Develop an expression that summarizes delivery charges. (Enter your answers as dollar amounts to 2 decimal places (x1 = weight, x2 = distance).  Omit the "$" sign in your response.)

  y = $  x1 + $  x2 + $   

b.

Determine the delivery charge for transporting a 60-pound parcel 20 miles. (Do not round your intermediate calculation. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

  y = $   

The manager of a fashionable restaurant open Wednesday through Saturday says that the restaurant does about 25 percent of its business on Friday night, 30 percent on Saturday night, and 18 percent on Thursday night. What seasonal relatives would describe this situation?(Round your answers to 2 decimal places.)

  Wednesday

  Thursday

  Friday

  Saturday