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Develop a production plan and calculate the annual cost for a firm whose demand

ID: 366649 • Letter: D

Question

Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $110 for each temp; layoff, $220 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)

Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000; winter, 8,000; spring, 7,000; summer, 12,000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $110 for each temp; layoff, $220 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. In each quarter, produce to the full output of your regular workforce, even if that results in excess production. In Winter and Spring, use overtime only if needed to meet the production required in that quarter. Do not use overtime to build excess inventory in prior seasons expressly for the purpose of reducing the number of temp workers in Summer. (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round up "Number of temp workers, Workers hired and Workers laid off" to the next whole number and all other answers to the nearest whole number.)

Explanation / Answer

The aggregate plan is as follows:

Fall

Winter

Spring

Summer

A

  Forecast

10000

8000

7000

12000

B

  Beginning inventory

500

-2300

0

200

C = A - B

  Production required

9500

10300

7000

11800

D = C/2

  Production hours required

19000

20600

14000

23600

E = 30*60*8

  Production hours available­­1

14400

14400

14400

14400

F

  Overtime hours

0

6200

0

0

G

  Temp workers2

0

0

0

20

H = G*8*60

  Temp worker hours available

0

0

0

9600

I = E+F+H

  Total hours available

14400

20600

14400

24000

J = I/2

  Actual production

7200

10300

7200

12000

K = J -A

  Ending inventory

-2300

0

200

200

L

  Workers hired

0

0

0

20

M

  Workers laid off

0

0

0

20

Rate

Fall

Winter

Spring

Summer

5

  Straight time (5*(E+H))

$     72,000

$      72,000

$     72,000

$     120,000

8

  Overtime (8*F)

$           -  

$      49,600

$           -  

$             -  

5

  Inventory (5*K),

$           -  

$             -  

$      1,000

$        1,000

10

  Backorder (10*K)

$     23,000

$             -  

$           -  

$             -  

110

  Hiring  (110*L)

$           -  

$             -  

$           -  

$        2,200

220

  Layoff (220*M)

$           -  

$             -  

$           -  

$        4,400

  Total

$     95,000

$     121,600

$     73,000

$     127,600

  Annual cost

$     417,200

Total cost pf plan = $417,200

Fall

Winter

Spring

Summer

A

  Forecast

10000

8000

7000

12000

B

  Beginning inventory

500

-2300

0

200

C = A - B

  Production required

9500

10300

7000

11800

D = C/2

  Production hours required

19000

20600

14000

23600

E = 30*60*8

  Production hours available­­1

14400

14400

14400

14400

F

  Overtime hours

0

6200

0

0

G

  Temp workers2

0

0

0

20

H = G*8*60

  Temp worker hours available

0

0

0

9600

I = E+F+H

  Total hours available

14400

20600

14400

24000

J = I/2

  Actual production

7200

10300

7200

12000

K = J -A

  Ending inventory

-2300

0

200

200

L

  Workers hired

0

0

0

20

M

  Workers laid off

0

0

0

20

Rate

Fall

Winter

Spring

Summer

5

  Straight time (5*(E+H))

$     72,000

$      72,000

$     72,000

$     120,000

8

  Overtime (8*F)

$           -  

$      49,600

$           -  

$             -  

5

  Inventory (5*K),

$           -  

$             -  

$      1,000

$        1,000

10

  Backorder (10*K)

$     23,000

$             -  

$           -  

$             -  

110

  Hiring  (110*L)

$           -  

$             -  

$           -  

$        2,200

220

  Layoff (220*M)

$           -  

$             -  

$           -  

$        4,400

  Total

$     95,000

$     121,600

$     73,000

$     127,600

  Annual cost

$     417,200