Month# Forecast#
Jan 1800
Feb 1500
Mar 1100
Apr 1500
May 2100
June 1600

Name Value
Labor hours per unit (hr/unit) 5
Initial number of workers 30
Safety Stock (units) 0
Working hours in a day(hr/day) 6
Beginning inventory(units) 950

Month# Working Days available
Jan 20
Feb 20
Mar 20
Apr 20
May 20
June 19

The tables present forecasts, production, and cost information for aggregate planning. Using a level strategy with backorders to produce at average demand, how many workers are required each month? (Round up the calculated number of workers to the nearest whole number, and round the production rate to the nearest whole number.)

Question

Month#	Forecast#
Jan	1800
Feb	1500
Mar	1100
Apr	1500
May	2100
June	1600
 
Name	Value
Labor hours per unit (hr/unit)	5
Initial number of workers	30
Safety Stock (units)	0
Working hours in a day(hr/day)	6
Beginning inventory(units)	950
 
Month#	Working Days available
Jan	20
Feb	20
Mar	20
Apr	20
May	20
June	19

The tables present forecasts, production, and cost information for aggregate planning. Using a level strategy with backorders to produce at average demand, how many workers are required each month? (Round up the calculated number of workers to the nearest whole number, and round the production rate to the nearest whole number.)

BlackTom AI · Accepted Answer

We are given forecasts, initial inventory, and production constraints, and asked to apply a level production strategy with backorders to meet average demand. The key steps are:

- First, determine the monthly production quantity under a level (constant) production plan that allows backorders. A common approach is to set the monthly production so that the ending inventory after the entire horizon is zero, using the initial inventory to offset cumulative demand. This gives:  Beginning inventory + 6*Q - Total demand = Ending inventory. With Ending inventory = 0, Beginning inventory = 950, Total demand = 9600, we get 950 + 6*Q - 9600 = 0, so 6*Q = 8650, hence Q = 8650 / 6 ≈ 1441.666... units per month.

- Round Q to the nearest whole number as instructed. Q ≈ 1442 units per month.

- Now convert the monthly production quantity into required workers for each month, using the given labor and work-time data. Each unit requires 5 labor-hours. Therefore, monthly labor-hours required = Q * 5 = 1442 * 5 = 7210 hours.

- For each month, calculate the total available hours per worker: Working days available × 6 hours per day.
  - Jan: 20 days × 6 h = 120 hours per worker.
  - Feb: 20 × 6 = 120 hours per worker.
  - Mar: 20 × 6 = 120 hours per worker.
  - Apr: 20 × 6 = 120 hours per worker.
  - May: 20 × 6 = 120 hours per worker.
  - Jun: 19 × 6 = 114 hours per worker.

- The number of workers needed in a month is the ceiling of (total monthly hours required) / (hours available per worker that month): W = Ceil( (Q * 5) / (hours_per_worker_that_month) ).

- Compute for each month:
  - January: 7210 / 120 = 60.083..., ceiling to 61 workers.
  - February: 7210 / 120 = 60.083..., ceiling to 61 workers.
  - March: 7210 / 120 = 60.083..., ceiling to 61 workers.
  - April: 7210 / 120 = 60.083..., ceiling to 61 workers.
  - May: 7210 / 120 = 60.083..., ceiling to 61 workers.
  - June: 7210 / 114 ≈ 63.245..., ceiling to 64 workers.

- Interpreting the results: for the first five months, the same production rate (Q ≈ 1442 units) requires about 7210 hours each month, and with 120 hours available per worker, you need 61 workers (since 60 workers would provide 7200 hours, which is just under 7210). In June, with only 114 hours available per worker, you need more hands: 7210 / 114 ≈ 63.25, which rounds up to 64 workers.

- Note on rounding guidelines: the problem explicitly asks to round the production rate to the nearest whole unit, and to round the number of workers up to the nearest whole number. The monthly production quantity used here (Q = 1442) is rounded from 1441.666..., and the resulting worker counts are rounded up to the next whole number where necessary.

- If there were any alternative interpretations (for example, choosing a different ending inventory target or treating months differently), the required worker counts could change. However, under the stated level production with backorders and the common end-of-horizon zero-inventory assumption, the calculations above provide the consistent, month-by-month worker requirements.

- Summarizing the month-by-month worker requirements derived from the calculations:
  - January: 61 workers
  - February: 61 workers
  - March: 61 workers
  - April: 61 workers
  - May: 61 workers
  - June: 64 workers

- The key factors driving these results include the fixed monthly production quantity (Q ≈ 1442 units) and the varying monthly available working hours (120 hours per worker for five months vs. 114 hours per worker in June), which is why June necessitates an extra worker to meet the same production level.

BUS_105_001_25S Quiz_sop_part2

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