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Calculation of production capacity
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Lesson "Calculation of production capacity of a workshop, enterprise"

  1. Kitchen production capacity
  2. Determine the annual production capacity of a workshop
  3. Determine the production capacity of a workshop and annual output of marketable products
  4. Determine the annual production capacity of an enterprise
  5. Determine the average annual production capacity of an enterprise
  6. Determine the utilization rate of production capacity

Task 1. Production capacity of the kitchen

Capacity of boilers 120 l. Filling coefficient of boilers 0.9. Average volume of one dish 0.5 l.
Average cooking time for one production cycle of boilers is 120 min. Organizational and technological downtime of equipment
per shift is 50 min. Time for preparatory and final operations on average for one cooking of food is 20 min. Duration of kitchen
work per day is 10 hours. The dining room works 305 days a year.

Calculate the daily production capacity of the kitchen and the annual production program of the dining room for the production
of first courses.

Webmaster Comment

The conditions of this task were sourced from a forum. While the task assumes a hypothetical "soup establishment" where the
same product is consistently consumed using the same recipe throughout the year, it does not account for seasonal fluctuations
in demand. The author has chosen to overlook these variations, and we will leave the semantic content to the author's discretion.

This task is presented primarily because the method of solving it is applicable to industrial enterprises with mass production. It
is important to note that the author does not consider the work schedule of the staff. In practice, this should be taken into account.
 Additionally, the phrase "per shift" requires clarification. If the kitchen operates for 10 hours, it is unclear whether this constitutes
one 10-hour shift or two 5-hour shifts. Given a 40-hour work week, it suggests a single shift with a flexible work schedule for
the staff, meaning that an individual can work no more than four days a week.

Given Data:

  • Capacity of boilers: 120 liters
  • Filling coefficient of boilers: 0.9
  • Average volume of one dish: 0.5 liters
  • Average cooking time for one production cycle: 120 minutes
  • Organizational and technological downtime per shift: 50 minutes
  • Time for preparatory and final operations per cooking: 20 minutes
  • Duration of kitchen work per day: 10 hours (600 minutes)
  • Number of working days per year: 305 days

Step-by-Step Solution:

  • Calculate the effective capacity of the boilers:
Effective Capacity=Capacity of Boilers×Filling Coefficient
Effective Capacity=120 liters×0.9=108 liters
  • Calculate the number of dishes per production cycle:
Number of Dishes per Cycle=Effective CapacityAverage Volume of One Dish
Number of Dishes per Cycle=108 liters / 0.5 liters per dish=216 dishes
  • Calculate the total time for one production cycle:
Total Time per Cycle=Cooking Time+Preparatory and Final Operations Time
Total Time per Cycle=120 minutes+20 minutes=140 minutes
  • Calculate the effective working time per day:
Effective Working Time per Day=Total Working Time per Day−Downtime
Effective Working Time per Day=600 minutes−50 minutes=550 minutes
  • Calculate the number of production cycles per day:
Number of Cycles per Day=Effective Working Time per Day / Total Time per Cycle
Number of Cycles per Day=550 minutes / 140 minutes per cycle≈3.93 cycles

Since we can't have a fraction of a cycle, we take the integer part:

Number of Cycles per Day=3
  • Calculate the daily production capacity of the kitchen:
Daily Production Capacity=Number of Cycles per Day×Number of Dishes per Cycle
Daily Production Capacity=3×216 dishes=648 dishes
  • Calculate the annual production program of the dining room:
Annual Production Program=Daily Production Capacity×Number of Working Days per Year
Annual Production Program=648 dishes per day×305 days=197,640 dishes

Summary:

  • Daily Production Capacity of the Kitchen: 648 dishes
  • Annual Production Program of the Dining Room: 197,640 dishes

Task 2. Determine the annual production capacity of the workshop


The workshop of a machine-building plant has three groups of machines: grinding - 5 units, planing - 11 units,
turret - 15 units. The standard time for processing a unit of product in each group of machines is 0.5 hours,
1.1 hours and 1.5 hours, respectively.
Determine the annual production capacity of the workshop, if it is known that the work mode is two-shift, the duration
of the shift is 8 hours;
regulated downtime of equipment is 7% of the regular time fund, the number of working days per year is 255.

Given Data:

  • Number of grinding machines: 5 units
  • Number of planing machines: 11 units
  • Number of turret machines: 15 units
  • Standard time for processing a unit of product:
    • Grinding machines: 0.5 hours
    • Planing machines: 1.1 hours
    • Turret machines: 1.5 hours
  • Work mode: two-shift
  • Duration of each shift: 8 hours
  • Regulated downtime of equipment: 7%
  • Number of working days per year: 255

Step-by-Step Solution:

  • Calculate the total working time per year:
Total Working Time per Year=Number of Shifts per Day×Duration of Each Shift×Number of Working Days per Year
Total Working Time per Year=2×8 hours×255 days=4080 hours
  • Calculate the effective working time per year (considering downtime):
Effective Working Time per Year=Total Working Time per Year×(1−Downtime Percentage)
Effective Working Time per Year=4080 hours×(1−0.07)=4080 hours×0.93=3794.4 hours

  1. Calculate the annual production capacity for each group of machines:

    Annual Production Capacity = (Effective Working Time per Year×Number of Machines) / Standard Time per Unit

  • Grinding Machines:
Annual Production Capacity (Grinding)=( 3794.4 hours×5 ) / 0.5 hours per unit=18972 / 0.5=37944 units
  • Planing Machines:
Annual Production Capacity (Planing)= ( 3794.4 hours×11) / 1.1 hours per unit=41738.4 / 1.1=37944 units
  • Turret Machines:
Annual Production Capacity (Turret)= (3794.4 hours×15) / 1.5 hours per unit=56916 / 1.5=37944 units

Summary:

  • Annual Production Capacity (Grinding Machines): 37,944 units
  • Annual Production Capacity (Planing Machines): 37,944 units
  • Annual Production Capacity (Turret Machines): 37,944 units

Task 3. Determine the production capacity of the workshop and the annual output
of marketable products

Determine the annual production capacity of the workshop and its annual output of marketable products,
if the utilization factor of production capacity is 0.95. The data for the calculation are given below.

Given Data:

  1. Number of machines: 25 pcs
  2. Workshop operation mode: 2 shifts
  3. Shift duration: 8 hours
  4. Standard time for product processing: 0.5 hours/piece
  5. Nominal working time: 230 days/year
  6. Regulated downtime of equipment under repair: 4%
  7. Utilization factor of production capacity: 0.95

Step-by-Step Solution:

  • Calculate the total working time per year:
Total Working Time per Year=Number of Shifts per Day×Shift Duration×Number of Working Days per Year
Total Working Time per Year=2×8 hours×230 days=3680 hours
  • Calculate the effective working time per year (considering downtime):
Effective Working Time per Year=Total Working Time per Year×(1−Downtime Percentage)
Effective Working Time per Year=3680 hours×(1−0.04)=3680 hours×0.96=3532.8 hours
  • Calculate the production capacity of the workshop:
Production Capacity= ( Effective Working Time per Year×Number of Machines ) / Standard Time per Unit
Production Capacity=( 3532.8 hours×25 ) / 0.5 hours per unit=88320 / 0.5=176640 units
  • Calculate the annual output of marketable products (considering the utilization factor):
Annual Output of Marketable Products=Production Capacity×Utilization Factor
Annual Output of Marketable Products=176640 units×0.95=167808 units

Summary:

  • Annual Production Capacity of the Workshop: 176,640 units
  • Annual Output of Marketable Products: 167,808 units

Task 4. Determine the annual production capacity of the enterprise

Determine the annual production capacity of the enterprise and the level of its utilization according to the following data.

Given Data:

  1. Production capacity of the enterprise at the beginning of the year: 10 USD million
  2. Production capacity increasing due to modernization and improvement of technology: 0.4 USD million
  3. Number of months of use of this capacity: 4 months
  4. Production capacity introduced as a result of new construction and reconstruction: 0.5 USD million
  5. Month of introduction: November
  6. Production capacity withdrawn from production: 0.3 USD million
  7. Month of withdrawal from production: February
  8. Production program of the enterprise: 9.4 USD million

Step-by-Step Solution:

  • Calculate the initial production capacity:
Initial Production Capacity= USD 10 million
  • Calculate the average annual production capacity increase due to modernization and improvement of technology:
Average Annual Increase= ( Increase×Number of Months of Use )  / 12
Average Annual Increase=0.4 USD million×4 / 12=1.6 / 12=0.1333 USD million
  • Calculate the average annual production capacity introduced as a result of new construction and reconstruction:
Average Annual Introduction= ( Introduction×Number of Months of Use ) / 12

Since the capacity is introduced in November, it will be used for 2 months (November and December):

Average Annual Introduction=0.5 USD million×2 / 12=1 / 12=0.0833 USD million
  • Calculate the average annual production capacity withdrawn from production:
Average Annual Withdrawal= ( Withdrawal×Number of Months of Use) / 12

Since the capacity is withdrawn in February, it will be used for 1 month (January):

Average Annual Withdrawal= ( 0.3 USD million×1 ) / 12=0.3 / 12=0.025 USD million
  • Calculate the average annual production capacity:
Average Annual Production Capacity = Initial Production Capacity +Average Annual Increase +Average Annual Introduction−Average Annual Withdrawal
Average Annual Production Capacity=10+0.1333+0.0833−0.025=10.1916 USD million
  • Calculate the production capacity utilization factor:
Utilization Factor=Production ProgramAverage /  Annual Production Capacity
Utilization Factor=9.4 / 10.1916 ≈ 0.922

Summary:

  • Average Annual Production Capacity of the Enterprise: 10.1916 USD million
  • Production Capacity Utilization Factor: 0.922 or 92.2%

Task 5. Determine the average annual production capacity of the enterprise

The capacity of the enterprise at the beginning of the year was 35,800 tons of final products.
During the year, the following capacity was introduced: in June - 3,500 tons, in August - 5,420 tons, in October - 2,750 tons.
The following capacities were withdrawn: in April - 2,250 tons, in November 8,280 tons.

It is necessary to determine: the average annual production capacity and the capacity of the enterprise at the end of the year.

Given Data:

  1. Capacity of the enterprise at the beginning of the year: 35,800 tons
  2. Capacity introduced during the year:
    • June: 3,500 tons
    • August: 5,420 tons
    • October: 2,750 tons
  3. Capacity withdrawn during the year:
    • April: 2,250 tons
    • November: 8,280 tons

Step-by-Step Solution:

  • Calculate the capacity at the end of the year:
 Capacity at the End of the Year=Initial Capacity+Total Introduced Capacity−Total Withdrawn Capacity
Total Introduced Capacity=3,500+5,420+2,750=11,670 tons
Total Withdrawn Capacity=2,250+8,280=10,530 tons
Capacity at the End of the Year=35,800+11,670−10,530=36,940 tons
  • Calculate the average annual production capacity:
  • For the capacity introduced in June (used for 7 months):
Average Annual Capacity (June)=3,500×7 / 12=24,500 / 12 = 2,041.67 tons
  • For the capacity introduced in August (used for 5 months):
Average Annual Capacity (August)=5,420×5 / 12=27,100 / 12 = 2,258.33 tons
  • For the capacity introduced in October (used for 3 months):
Average Annual Capacity (October)=2,750×3 / 12=8,250 / 12 = 687.5 tons
  • For the capacity withdrawn in April (used for 3 months):
Average Annual Capacity (April)=2,250×3 / 12=6,750 / 12 = 562.5 tons
  • For the capacity withdrawn in November (used for 10 months):
Average Annual Capacity (November)=8,280×10 / 12=82,800 / 12 = 6,900 tons
  1. Calculate the total average annual production capacity:
Total Average Annual Production Capacity = Initial Capacity+Average Annual Capacity (June)
+Average Annual Capacity (August)+ Average Annual Capacity (October)−Average Annual Capacity (April)−
Average Annual Capacity (November)
Total Average Annual Production Capacity=35,800+2,041.67+2,258.33+687.5−562.5−6,900=33,324 tons

Summary:

  • Average Annual Production Capacity of the Enterprise: 33,324 tons
  • Capacity of the Enterprise at the End of the Year: 36,940 tons

Task 6. Determine the production capacity utilization rate

The enterprise manufactures electric motors. Based on the data presented in the table, determine the initial
and average annual production capacity of the enterprise and the production capacity utilization rate.

Given Data:

  1. Production capacity of the enterprise at the beginning of the year: 12 USD million
  2. Production capacity that increases as a result of modernization and improvement of production technology
    (from October 1): 0.8 USD million
  3. Production capacity that is introduced from September 1 as a result of reconstruction: 0.6 USD million
  4. Production capacity withdrawn from March 1: 0.4 USD million
  5. Production program of the enterprise: 10 USD million

Step-by-Step Solution:

  • Calculate the initial production capacity:
Initial Production Capacity=12 USD million
  • Calculate the average annual production capacity increase due to modernization and improvement of production technology:
Average Annual Increase=Increase×Number of Months of Use / 12

Since the capacity is increased from October 1, it will be used for 3 months (October, November, December):

Average Annual Increase=0.8 USD million×3 / 12 = 2.4 / 12 = 0.2 USD million
  • Calculate the average annual production capacity introduced as a result of reconstruction:
Average Annual Introduction = Introduction×Number of Months of Use / 12

Since the capacity is introduced from September 1, it will be used for 4 months (September, October, November, December):

Average Annual Introduction= 0.6 USD million×4 / 12=2.4 / 12= 0.2 USD million
  • Calculate the average annual production capacity withdrawn from production:
Average Annual Withdrawal = Withdrawal×Number of Months of Use / 12

Since the capacity is withdrawn from March 1, it will be used for 2 months (January, February):

Average Annual Withdrawal=0.4 USD million×2 / 12=0.8 / 12 = 0.0667 USD million
  • Calculate the average annual production capacity:
Average Annual Production Capacity = Initial Production Capacity+ Average Annual Increase +
Average Annual Introduction −Average Annual Withdrawal
Average Annual Production Capacity=12+0.2+0.2−0.0667=12.3333 USD million
  • Calculate the production capacity utilization rate:
Utilization Rate=Production ProgramAverage / Annual Production Capacity
Utilization Rate=10 / 12.3333 ≈ 0.811

Summary:

  • Average Annual Production Capacity of the Enterprise: 12.3333 USD million
  • Production Capacity Utilization Rate: 0.811 or 81.1%
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 Production Capacity | Описание курса | Equipment operating time fund