Sunflower Ltd. needs to develop an aggregate production plan for next year. The
ID: 396260 • Letter: S
Question
Sunflower Ltd. needs to develop an aggregate production plan for next year. The demand forecast for each quarter in next year is Period Quarter 1 Quarter 2 Quarter 3 Quarter 4 The company has 70 workers and 1,000 units in the inventory at the beginning of quarter 1. According to the agreement with the union the company may lay off workers only once a year, at the beginning of quarter 2. The number of workers laid off at the beginning of quarter 2 should result in planned production levels for quarter 2 equal the demand forecast of quarter 2. The company may hire workers only at the end of quarter 2. The number of workers hired is sufficient to begin the regular work in the quarter 3. Overtime of two hours is allowed per worker per day. Following costs are given: » hiring $100 per new worker lay off - $ 200 per worker laid off holding $ 200 per unit quarter normal time labour- $ 30 per hour overtime - $ 50 per hour. One unit of production requires two labour hours. The company operates eight hours in regular time for twenty working days per month. Lost sales and back orders are not allowed. Develop an economical aggregate production plan. Calculate the total cost of the plan. Forecast 20,000 10,000 15,000 18,000-Explanation / Answer
Calculation for quarter 1
Opening inventory for first quarter is 1000 units
Inventory handling cost = 200 × 1000 = 2,00,000 $.…………(1)
Target for quarter 1 is 20000-1000 = 19000 units
Maximum labor hours available per month = 70 × 20 × 8 = 11200 labor hrs
So, maximum production per month = 11200/2 = 5600 units
Production cost 11200 × 30 × 3 = 10,08,000 $.............(2)
Production in 3 months = 5600 × 3 = 16800 units
The balance production will be met by providing overtime to workers
So, 19000-16800 = 2200 units balance
Overtime required = 2200 × 2 = 4400 hrs
4400/70 = 62.85 = approximately 63
So (70×63)/2 = 2205 units
So total production in Quarter 1 = 16800 + 2205 = 19005 units
Overtime cost = 70 × 63 × 50 = 2,20,500 $..........(3)
Adding equation (1), (2), (3)
Total cost for quarter 1 = 14,28,500 $
Calculation for quarter 2
Opening stock for quarter 2 = Opening stock for quarter 1 + Total production – Actual demand
= 1000 + 19005 – 20000
= 5 units
Inventory handling cost = 5 × 200 = 1000$..........(4)
Target production for quarter 2 = 10000-5 = 9995 units
Target per month = 9995/3 = approximately 3332 units
Number of labor required = (3332 ×2)/(20 × 8) = approximately 42
Therefore, 70 – 42 = 28 labors laid off
So, lay off cost = 28 × 200 = 5600$............(5)
Production per month = (42 × 20 × 8)/2 = 6720/20 = 3360
Total production for quarter 2 = 3360 × 3 = 10080
Production cost = 6720 × 3 × 30 = 6,04,800$.........(6)
Adding equation (4), (5), (6)
Total cost of production for quarter 2 = 6,11,400 $
Calculation for quarter 3
Opening stock for quarter 3 = Opening stock for quarter 2 + Total production – Actual demand
= 5 + 10080 – 10000
= 85 units
Inventory handling cost = 85 × 200 = 17,000$........(7)
Target for quarter 3 = 15000-85 = 14915
Production per month = 14915/3 = 4971.67 = approximately 4972
This target can be achieved by two ways
1 – Utilize 43 labor and provide over time
2 – Hire new labor based on new target
The first way will cost 3,62,800$ per month and the second alternative will cost 3,02,400$ per month
Production per month = 4972
Total labor hours required = 4972 × 2 = 9944
Total labor required per month = 9944/ (20×8) = 62.15 = Approximately 63 labor required
New labors to be hired = 63-42 = 21
Hiring cost = 21 × 100 = 2100$.......(8)
Total production = (63 × 20 × 8 × 3)/2 = 15120
Production cost = 63 × 20 × 8 × 30 = 3,02,400$
Production cost for 3 months = 302400 × 3 = 9,07,200$..........(9)
Adding equation (7), (8), (9)
Total cost of production for quarter 3 = 9,26,300$
Calculation for quarter 4
Opening stock for quarter 4 = Opening stock for quarter 3 + Total production – Actual demand
= 85 + 15120 – 15000 = 205 unit
Inventory handling cost = 205 × 200 = 41000$..........(10)
Target production for quarter 4 = 18000-205 = 17795 units
Target per month = 17795/3 = approximately 5932 units
Production per month = (63 × 20 × 8)/ 2 = 5040
Production cost = 10080 × 3 × 30 = 9,07,200$..........(11)
Overtime required = (5932-5040) × 2 = 1784 per month
For 3 months = 1784 × 3 = 5352
Overtime cost = 5352 × 50 = 2,67,600$........(12)
Adding equation (10), (11), (12)
Total cost of production for quarter 4 = 12,15,800 $
Total cost for the year = Sum of cost for all 4 quarters = 41,82,000$
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