The current aggregate demand requirements for a firm are shown below for the nex

Question

The current aggregate demand requirements for a firm are shown below for the next six months:

The firm always plans to meet all demand. The firm currently has 270 workers capable of producing 270 units in a month (1 unit/worker). The workforce can be increased (at a cost of $700 per worker) or decreased (at a cost of $1,400 per worker). Inventory holding cost is $175 per unit per month. The firm currently has 30 units of inventory on hand, and it would like to have 30 units available at the end of each month. Regular production cost is $3,750 per unit. Assume hiring and layoff/firing, if necessary, occur at the beginning of the month.

a.

What should the aggregate plan be if the inventory holding cost is to be minimized? (Leave no cells blank - be certain to enter "0" wherever required.)

b. What is the cost of this plan?

Month May June July Aug Sept Oct Demand 270 250 250 250 280 300

Explanation / Answer

Given:

Productivity of worker = 1 unit/worker/month (Each worker produces one unit per month)

Cost of hiring a worker = $700

Cost of firing a worker = $1400

Inventory holding cost = $175/unit/month

Production cost per unit = $3750

a.

The opening inventory (inventory in hand) is given as 30 units and 30 units are to be available at the end of each month (which means the ending inventory in each month should be 30).

As the aim is to minimize holding cost, it must be ensured that the demand for each month is met at that month itself and no excess must be produced.

Note: The 30 units in opening inventory are the same as 30 units which must be kept as ending inventory each month. So, we need not bother about these 30 units but ensure that each month production must equal demand in that month.

Steps to fill the table:

1. Ending inventory is 30 for every month (as 30 units are to be maintained at the end of each month)

2. Productivity of worker is 1 unit per month, so number of workers should equal the demand of that month.

3. Fill the hire and fire by comparing the number oif workers in the previous month, with the present month.

Present month- previous month = Hire/Fire ( Hire if value positive and fire if value negative)

b. The Total cost is made up of teh following 4 components:

1. Production cost = 1600 units * $3750/unit = $6000000

2. Cost of hiring = 50 * $700 = $35000

3. Cost of firing = 20 * $1400 = $28000

4. Holding cost = 150 * $175 = $ 26250

Note: 150 units are taken instead of 180 as we are calculating the cost upto month October.The 30 units which are the ending inventory for October, will incur their cost in the month if november)

Total cost = $6000000 + $35000 + $28000 + $26250 = $6089250

Month Demand Regular Production Ending Inventory No. of workers Hire Fire May 270 270 30 270 0 0 June 250 250 30 250 0 20 July 250 250 30 250 0 0 August 250 250 30 250 0 0 Sep 280 280 30 280 30 0 Oct 300 300 30 300 20 0 Total 1600 1600 180 1600 50 20

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