Question

Roberts, an outfit manufacturer, produces a line of jackets. There are currently 3 temporary employees and 12 full-time employees to produce parkas. More temporary employees can be hired if additional production capacity is needed. Each full time employee can produce 205 jackets, whereas each temporary employee can produce 165 jackets per month. Demand for jackets for the next four months is as follows:

October 3,200

November 2,800

December 3,100

January 3,000

i. The beginning inventory in October is 403 jackets. Each jacket cost $40 to produce and the annual holding cost is 24% of the unit production cost. Develop an aggregate plan that uses the 12 full-time employees each month and a minimum number of temporary employees. Assume that all employees will produce at their full potential each month.

ii. Calculate the inventory holding cost associated with your aggregate plan based on the planned end of month inventory (i.e., ending inventory in each month).

Answer 1

Solution:-

Number of full time employees = 12

Beginning inventory in the month of October = 403

Forecast for the month of October = 3200

Production capacity for a full-time employee per month = 205

Production capacity for a temporary employee per month = 165

Cost per making jacket = $40 each

Carrying cost = 24% per annum per making jacket , i.e. 2% per month

= $ 0.80 per month per making jacket

• As all the employees produce at their full potential per month, every employee will produce to their full capacity.

Forecast for the month of October = 3200

Beginning inventory = 403

Production required = Total production for that month - beginning inventory

= 3200 - 403 = 2797

Regular workforce = 12 workers

Regular production = 12 × 205 = 2460

Temporary workers required = (2797 - 2460)/ 165 = 2.042

• Hence we require more than 2 workers. Thus temporary workers = 3

Temporary production = 165*3 = 495

Total production = Regular production + Temporary production

= 2460 + 495 = 2955

Ending inventory = Beginning inventory + Total production

= 403 + 2955 = 3358

Inventory cost = Carrying cost of beginning inventory for the month + average carrying cost for the Jackets produced during the month

= Begining inventory * Carrying cost per month + Total production * (Carrying cost per month)/2

= 403 * 0.8 + 2955 * 0.4

= 322.4 + 1182 = $ 1504.4

Forecast for the month of November = 2800

Beginning inventory for November = Ending inventory of October - Sales of October

= 3358 - 3200 = 158

Production required = Total production for that month - beginning inventory

= 2800 - 158 = 2642

Regular workforce = 12 workers

Regular production = 12 * 205 = 2460

Temporary workers required = (2642 - 2460)/ 165 = 1.10

• Hence we require more than 1 worker. Thus temporary workers = 2

Temporary production = 165*2 = 330

Total production = Regular production + Temporary production

= 2460 + 330 = 2790

Ending inventory = Beginning inventory + Total production

= 158 + 2790 = 2948

Inventory cost = Carrying cost of beginning inventory for the month + average carrying cost for the jackets produced during the month

= Begining inventory * Carrying cost per month + Total production * (Carrying cost per month)/2

= 158 * 0.8 + 2790 * 0.4

= 126.4 + 1116 = $ 1242.4

Forecast for the month of December = 3100

Beginning inventory for January = Ending inventory of November - Sales of November

= 2948 - 2800 = 148

Production required = Total production for that month - beginning inventory

= 3100 - 148 = 2952

Regular workforce = 12 workers

Regular production = 12 * 205 = 2460

Temporary workers required = (2952 - 2460)/ 165 = 2.98

• Hence we require more than 2 workers. Thus temporary workers = 3

Temp production = 165*3 = 495

Total production = Regular production + Temporary production

= 2460 + 495 = 2955

Ending inventory = Beginning inventory + Total production

= 148 + 2955 = 3103

Inventory cost = Carrying cost of beginning inventory for the month + average carrying cost for the jackets produced during the month

= Begining inventory * Carrying cost per month + Total production * (Carrying cost per month)/2

= 148 * 0.8 + 2955 * 0.4

= 118.4 + 1182 = $ 1300.4

Forecast for the month of January = 3000

Beginning inventory for January = Ending inventory of December - Sales of December

= 3103 - 3100 = 3

Production required = Total production for that month - beginning inventory

= 3000 - 3 = 2997

Regular workforce = 12 workers

Regular production = 12 * 205 = 2460

Temporary workers required = (2997 - 2460)/ 165 = 3.254

• Hence we require more than 3 workers. Thus temporary workers = 4

Temp production = 165*4 = 660

Total production = Regular production + Temporary production

= 2460 + 660 = 3120

Ending inventory = Beginning inventory + Total production

= 3 + 3120 = 3123

• Inventory cost = Carrying cost of beginning inventory for the month + average carrying cost for the jackets produced during the month

= Begining inventory * Carrying cost per month + Total production * (Carrying cost per month)/2

= 3 * 0.8 + 3120 * 0.4

= 2.4 + 1248 = $ 1250.4

Total holding cost for all months = 1504.4 + 1242.4 + 1300.4 + 1250.4

= $ 5297.6

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