Computation of the workforce required for avoiding shortages

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Year Forecast Beginning Production Cumulative Cumulative Workers

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Inventory Requirement Production Units produced Required

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Requirement Per worker

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1 300000 20000 280000 280000 30000 10

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2 120000 120000 400000 60000 7

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3 200000 200000 600000 90000 7

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Workers hired 7 Initial hiring cost 3500

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Workers fired 0 Initial firing cost 0

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Total workers 10 Initial recruitment cost 3500 Straighttime cost 750000 ------------------------------------------------- cost -------------------------------------------------

Year Forecast Beginning Actual Ending Inventory

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Inventory Production Inventory Holding cost

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1 300000 20000 300000 20000 800

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2 120000 20000 300000 200000 8000

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3 200000 200000 300000 300000 12000

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Total cost 774300

c. Least cost production program:

Minimal Cost = 25000(wr) + 500(wh) + 1000(wf) + .04(ei)

wr = Workers Required = (Dn– ein-1)/30,000 ; round up to nearest integer.

D = Forecast/demand wh = Workers Hired = wrn- wrn-1 ; if <=0, then 0 wf = Workers fired = wrn-1- wrn ; if <= 0, then 0 ei = ending inventory = (wrn X 30,000) + ein-1 - Dn ; if <= 0, then 0

Question 2

(a) Find the total cost of the level plan.

level plan | forecast | beginning inventory | production requirement | cumulative production requirement | cumulative units produced | workers required | season | | | | | | | fall | 10000 | 520 | 9480 | 9480 | 240 | 42 | winter | 8000 | | 8000 | 17480 | 480 | 17 | spring | 7000 | | 7000 | 24480 | 720 | 10 | summer | 12000 | | 12000 | 36480 | 960 | 13 | | | | | | | | | | | | | | | workers hired | 12 | | hiring costs | 100 | | | workers fired | | layoff costs | 200 | | | total workers | 42 | | regular time | 5 | | | | | | hours per | 480 | | | | | | | | | | total hiring costs | 1200 | | | | | total firing costs | 0 | | | | | total salary | 100800 | | | | | total labor | 102000 | | | | | | | | | | | | | | | | | | | year | Forecast | beg invent | actual production | end. Inventory | inventory holding cost | 1 | 10000 | 520 | 10080 | 600 | 3000 | | 2 | 7000 | 600 | 10080 | 2680 | 13400 | | 3 | 8000 | 2680 | 10080 | 5760 | 28800 | | 4 | 12000 | 5760 | 10080 | 3840 | 19200 | | | | | | | 64400 | | | | | | | | | | | | | | total costs= 166400 | |

The total cost = Total Labor Cost + Total Holding Cost + Total Backorder Cost

Total Cost = 102,000 + 64,400 + 0

Total Cost = $166,400

(b) Total Costs of Chase Plan:

The total cost = Total Labor Cost + Total Holding Cost + Total Backorder Cost

Total Cost = 370,400 + 0 + 0

Total Cost = $166,400

(c) Formulate the problem as a linear program. Be sure to define all the variables.

The linear program would be created using the above tables Creating a well sized work force