The monthly forecasts for Product X for January, February, and March are 1,200,

Question

     The monthly forecasts for Product X for January, February, and March are 1,200, 1,620, and 1,210, 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 510 units.

     Manufacturing cost is $220 per unit, storage cost is $4 per unit per month, standard pay rate is $6 per hour, overtime rate is $9 per hour, cost of stockout is $10 per unit per month, hiring and training cost is $220 per worker, layoff cost is $320 per worker, and worker productivity is 0.1 unit per hour. Assume that you start off with 41 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.)

January February March Forecast 1,200 1,620 1,210 Safety stock Beginning inventory Net production required Workers required Hired Laid off Actual production Ending inventory

Explanation / Answer

Safety stock is half of the forecast for that month:

The workers wil be paid hourly for the no. of working days in the month.

Beginning inventory is 510 so Net production required will be forcast - inventory already available/beginning inventory. So if 510 units are already available, then in January 690 more units need to be produced (forecast- inventory=1200 - 510)

1 worker productivity = 0.1 unit/hour

No. of hours a worker will work for in one day = 8 hrs.

No. of units produced by 1 worker in one day = 8*0.1 = 0.8 units

41 workers working for a 22 day January month will produce = 41*0.8*22 = 721.6 = 722 units.

Ending inventory = manufactured inventory + beginnning inventory - forecast

Inventory cost is manufacturing cost + storage cost.

Since no new orkers were hired or laid off - this cost will be 0.

units will be stored after one month if not used.

So in January, only labor cost and inventory cost are calculated.

Ending inventory of Jan will be beginning inventory of February.

Calculation of remanining months is also similar.

Since the cost of stockout is $10 and cost of storage is $4, we will be manufaturing units to meet the full forecast so as to avoid stock out scenario.

for February, if entire forecast has to be manufactured with 32 available as beginning inventory then there are 2 possible scenarios:

1. Increase the working hours to 10 and the productivity per day increase to 1 unit for each worker so to produce 1620-32= 1588 units, only 84 workers will be required. The cost of hiring and training is $220 for each new worker and each worker will be paid overtime.

Toral cost/day = (84-41)*220+84*6*8+84*2*9 = hiring cost + labor cost + extra hour working cost = 15004

2. while if we dont allow extra working hours and totally new workers are hired of 0.8 productivity to produce 1588 units then total of 105 workers will be required.

Total cost/day = (105-41)*220+105 *6*8= 19120.

So we choose first option

For March,1210 units have to be produced in 21 days at 0.8 productivity then 73 workers are required while we have 84 workers from February so 11 workers will be laid off.

January February March Forecast 1,200 1,620 1,210 Safety stock 600 810 605 No. of working days 22 19 21

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