Question

Develop a production schedule to produce the exact production requirements by varying the workforce size for the following problem.

The monthly forecasts for Product X for January, February, and March are 930, 1,550, and 1,220, respectively. Safety stock policy recommends that half of the forecast for that month be defined as safety stock. There are 22 working days in January, 19 in February, and 21 in March. Beginning inventory is 550 units.

Storage cost is $6 per unit per month based on ending inventory level, standard pay rate is $4 per hour, hiring and training cost is $280 per worker, layoff cost is $380 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 47 workers and that they work 8 hours per day. (Leave no cells blank - be certain to enter "0" wherever required. Input all values as positive values. Round Workers Required up to next higher whole number. Round all other variables to nearest whole number.)

Answer 1

We will sove this in 2 steps

1st step

Let us find with existing manpower can we meet the production requirement

If Yes - Then are we overstaffed

If no - How many excess manpower are required

Note - Daily Production rate = No. of workers * Productivity * no. of workings hours in day

Days taken to meet demand = Production demand / Daily production rate

If we hire in Jan then initial no. of workers for the month of feb will involve the newly hired workers as well  

Below is the working for Step 1

	PD	Jan	Feb	Mar
		930	1550	1220
Safety stock		465	775	610
On Hand inventory	550	465	775	610
Net Req. (Prod schedule)		845	1860	1055
No. of working days		22	19	21
No. of workers - Initial(Before hiring or firing)		47	49	123
Per day Production hours		8	8	8
Productivity per worker (unit /hr)		0.1	0.1	0.1
Per day Production rate (Units /day)		37	39	98
No. of Days taken to meet Production requirement		23	48	11
Will it meet demand (At optimum time)		No	No	No (It will meet prior to req. date)
Extra Manpower required - (+ Hired   - Fired)		2	73	-59

I arrived at extra manpower requirement by hit & trail method -- (Use excel --Just change No. of Workers in excel cell you will get whether the demand can be met at the exact required day)

Based on above table - You will see that - 2 , 73 people to be hired in Jan & Feb respectively & 59 people to be laid out in Mar

Step 2 )

Checking - Based on hiring or firing are we meetting the demand in exact no. of days

	PD	Jan	Feb	Mar
		930	1550	1220
Safety stock		465	775	610
On Hand inventory	550	465	775	610
Net Req. (Prod Schedule)		845	1860	1055
No. of working days		22	19	21
No. of workers - Initial		49	123	64
Per day Production hours		8	8	8
Productivity per worker (unit /hr)		0.1	0.1	0.1
Per day Production rate (Units /day)		39	98	51
No. of Days taken to meet Production requirement		22	19	21
Will it meet demand (At optimum dates)		Yes	Yes	Yes

So from above - you can see that we are meeting the demand requirements with optimum use of resources

Note - I have only focussed on resizing manpower as question mentions to focus on meeting exact production requirements and doesn't tell us to focus on resizing based on costing.

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