CALCU-A government office is responsible for revie

Solution by Steps

step 1

To find the capacity of each individual stage, we first calculate the effective capacity for each stage using the formula:

\text{Capacity} = \left(\frac{\text{Number of Employees} \times \text{Hours per Day per Employee}}{\text{Unit Processing Time (in hours)}}\right) \times (1 - \text{Rejection Rate})

step 2

For the Clerk stage:

\text{Capacity}_{\text{Clerk}} = \left(\frac{5 \times 8}{\frac{10}{60}}\right) \times (1 - 0.10) = 40 \times 0.90 = 36 \text{ units/day}

step 3

For the Review <$1K stage: \[ \text{Capacity}_{\text{Review <1K}} = \left(\frac{12 \times 8}{\frac{30}{60}}\right) \times (1 - 0.60) = 32 \times 0.40 = 12.8 \text{ units/day} \]

step 4

For the Review >$1K stage: \[ \text{Capacity}_{\text{Review >1K}} = \left(\frac{15 \times 8}{\frac{45}{60}}\right) \times (1 - 0.50) = 24 \times 0.50 = 12 \text{ units/day} \]

step 5

For the Commercial Review stage:

\text{Capacity}_{\text{Commercial Review}} = \left(\frac{20 \times 4}{\frac{90}{60}}\right) \times (1 - 0.10) = 16 \times 0.90 = 14.4 \text{ units/day}

step 6

For the Electrician stage:

\text{Capacity}_{\text{Electrician}} = \left(\frac{24 \times 5}{\frac{60}{60}}\right) \times (1 - 0.15) = 120 \times 0.85 = 102 \text{ units/day}

step 7

For the Approval stage:

\text{Capacity}_{\text{Approval}} = \left(\frac{8 \times 3}{\frac{10}{60}}\right) \times (1 - 0.05) = 144 \times 0.95 = 136.8 \text{ units/day}

step 8

Now, we summarize the capacities for each stage: - Clerk: 36 units/day - Review <1K: 12.8 units/day - Review >1K: 12 units/day - Commercial Review: 14.4 units/day - Electrician: 102 units/day - Approval: 136.8 units/day

step 9

To find the overall process capacity, we take the minimum capacity from all stages:

\text{Process Capacity} = \min(36, 12.8, 12, 14.4, 102, 136.8) = 12 \text{ units/day}

Answer

The capacity of each individual stage is as follows: Clerk: 36, Review <1K: 12.8, Review >1K: 12, Commercial Review: 14.4, Electrician: 102, Approval: 136.8. The overall process capacity is 12 units/day.

Key Concept

Capacity analysis in a process helps identify bottlenecks and optimize workflow.

Explanation

The capacity of each stage is calculated based on the number of employees, their working hours, processing time, and rejection rates, leading to the identification of the overall process capacity.

Solution by Steps

step 1

To find the capacity of each individual stage, we first calculate the effective capacity for each stage using the formula:

\text{Capacity} = \left(\frac{\text{Number of Employees} \times \text{Hours per Day per Employee}}{\text{Unit Processing Time (in hours)}}\right) \times (1 - \text{Rejection Rate})

step 2

For the Clerk stage: Number of Employees = 5, Hours per Day = 8, Unit Processing Time = 10 min (which is

\frac{1}{6}

hours), Rejection Rate = 10\%. Thus, the capacity is:

\text{Capacity}_{\text{Clerk}} = \left(\frac{5 \times 8}{\frac{1}{6}}\right) \times (1 - 0.1) = 240 \times 0.9 = 216 \text{ units/day}

step 3

For the Review <

1K

stage: Number of Employees = 12, Hours per Day = 8, Unit Processing Time = 30 min (which is

\frac{1}{2}

hours), Rejection Rate = 60\%. Thus, the capacity is:

\text{Capacity}_{\text{Review < 1K}} = \left(\frac{12 \times 8}{\frac{1}{2}}\right) \times (1 - 0.6) = 192 \times 0.4 = 76.8 \text{ units/day}

step 4

For the Review >

1K

stage: Number of Employees = 15, Hours per Day = 8, Unit Processing Time = 45 min (which is

\frac{3}{4}

hours), Rejection Rate = 50\%. Thus, the capacity is:

\text{Capacity}_{\text{Review > 1K}} = \left(\frac{15 \times 8}{\frac{3}{4}}\right) \times (1 - 0.5) = 160 \times 0.5 = 80 \text{ units/day}

step 5

For the Commercial Review stage: Number of Employees = 20, Hours per Day = 4, Unit Processing Time = 1.5 hours, Rejection Rate = 10\%. Thus, the capacity is:

\text{Capacity}_{\text{Commercial Review}} = \left(\frac{20 \times 4}{1.5}\right) \times (1 - 0.1) = \frac{80}{1.5} \times 0.9 \approx 48 \text{ units/day}

step 6

For the Electrician stage: Number of Employees = 24, Hours per Day = 5, Unit Processing Time = 1 hour, Rejection Rate = 15\%. Thus, the capacity is:

\text{Capacity}_{\text{Electrician}} = \left(\frac{24 \times 5}{1}\right) \times (1 - 0.15) = 120 \times 0.85 = 102 \text{ units/day}

step 7

For the Approval stage: Number of Employees = 8, Hours per Day = 3, Unit Processing Time = 10 min (which is

\frac{1}{6}

hours), Rejection Rate = 5\%. Thus, the capacity is:

\text{Capacity}_{\text{Approval}} = \left(\frac{8 \times 3}{\frac{1}{6}}\right) \times (1 - 0.05) = 144 \times 0.95 = 136.8 \text{ units/day}

step 8

The overall process capacity is determined by the stage with the minimum capacity. The capacities are: Clerk: 216, Review <

1K

: 76.8, Review >

1K

: 80, Commercial Review: 48, Electrician: 102, Approval: 136.8. Thus, the overall process capacity is:

\text{Overall Capacity} = \min(216, 76.8, 80, 48, 102, 136.8) = 48 \text{ units/day}

Answer

The utilization among electricians is 48 units/day.

Key Concept

Utilization is the measure of how much of a resource is being used compared to its total capacity.

Explanation

The utilization among electricians is determined by the capacity of the stage with the lowest throughput, which in this case is the Commercial Review stage with a capacity of 48 units/day.

Supposing that the entrance flowrate is actually 200 applications per day, what is the utilization among electricians as a percentage value?

Solution by Steps

step 1

To find the utilization among electricians, we first need to determine the capacity of the electricians. The capacity is calculated using the formula:

\text{Capacity} = \left( \frac{\text{Number of Employees} \times \text{Hours per Day per Employee}}{\text{Unit Processing Time (in hours)}} \right) \times (1 - \text{Rejection Rate})

step 2

For the Electrician stage: Number of Employees = 20, Hours per Day = 5, Unit Processing Time = 1.5 hours, Rejection Rate = 10\%. Thus, the capacity is:

\text{Capacity} = \left( \frac{20 \times 5}{1.5} \right) \times (1 - 0.10) = \left( \frac{100}{1.5} \right) \times 0.90 = 60 \text{ units/day}

step 3

Given that the entrance flowrate is 200 applications per day, the utilization among electricians can be calculated as:

\text{Utilization} = \frac{\text{Flowrate}}{\text{Capacity}} = \frac{200}{60} \approx 3.33 \text{ or } 333\%

step 4

Since utilization cannot exceed 100%, this indicates that electricians are over-utilized, and we need to express this as a percentage of their capacity:

\text{Utilization Percentage} = \left( \frac{200}{60} \right) \times 100 \approx 333\%

Answer

The utilization among electricians is approximately 333%.

Key Concept

Utilization measures how effectively resources are being used in a process.

Explanation

In this case, the utilization percentage indicates that electricians are overwhelmed with the number of applications compared to their processing capacity.

what assumption is made to know that that the enterance flowrate is constant throughout ?

Solution by Steps

step 1

To find the utilization among electricians, we first need to determine the capacity of the electricians. The capacity is calculated using the formula:

\[ \text{Capacity} = \left( \frac{\text{Number of Employees} \times \text{Hours per Day per Employee}}{\text{Unit Processing Time (in hours)}} \right) \times (1 - \text{Rejection Rate}) \]

step 2

For the Electrician stage: Number of Employees = 20, Hours per Day = 5, Unit Processing Time = 1.5 hours, Rejection Rate = 10\%. Thus, the capacity is:

\[ \text{Capacity} = \left( \frac{20 \times 5}{1.5} \right) \times (1 - 0.1) = \left( \frac{100}{1.5} \right) \times 0.9 = 60 \text{ units/day} \]

step 3

Given that the entrance flowrate is 200 applications per day, the utilization among electricians is calculated as:

\[ \text{Utilization} = \frac{\text{Flowrate}}{\text{Capacity}} = \frac{200}{60} \approx 3.33 \text{ or } 333\% \]

Answer

The utilization among electricians is approximately 333%.

Key Concept

Utilization measures how much of a resource's capacity is being used.

Explanation

In this case, the utilization of electricians is calculated by comparing the actual flowrate of applications to their processing capacity, resulting in a utilization of 333%, indicating they are over capacity.

Generated Graph

Solution by Steps

step 1

To find the capacity of each individual stage, we first calculate the effective capacity for each stage using the formula:

\text{Capacity} = \left(\frac{\text{Number of Employees} \times \text{Hours per Day per Employee}}{\text{Unit Processing Time (in hours)}}\right) \times (1 - \text{Rejection Rate})

step 2

For the Clerk stage: Number of Employees = 5, Hours per Day = 8, Unit Processing Time = 10 min (which is

\frac{1}{6}

hours), Rejection Rate = 10%. Thus, the capacity is:

\text{Capacity}_{\text{Clerk}} = \left(\frac{5 \times 8}{\frac{1}{6}}\right) \times (1 - 0.1) = 240 \text{ units/day}

step 3

For the Review <

1K

stage: Number of Employees = 12, Hours per Day = 8, Unit Processing Time = 30 min (which is

\frac{1}{2}

hours), Rejection Rate = 60%. Thus, the capacity is:

\text{Capacity}_{\text{Review < 1K}} = \left(\frac{12 \times 8}{\frac{1}{2}}\right) \times (1 - 0.6) = 48 \text{ units/day}

step 4

For the Review >

1K

stage: Number of Employees = 15, Hours per Day = 8, Unit Processing Time = 45 min (which is

\frac{3}{4}

hours), Rejection Rate = 50%. Thus, the capacity is:

\text{Capacity}_{\text{Review > 1K}} = \left(\frac{15 \times 8}{\frac{3}{4}}\right) \times (1 - 0.5) = 60 \text{ units/day}

step 5

For the Commercial Review stage: Number of Employees = 20, Hours per Day = 4, Unit Processing Time = 1.5 hours, Rejection Rate = 10%. Thus, the capacity is:

\text{Capacity}_{\text{Commercial Review}} = \left(\frac{20 \times 4}{1.5}\right) \times (1 - 0.1) = 106.67 \text{ units/day}

step 6

For the Electrician stage: Number of Employees = 24, Hours per Day = 5, Unit Processing Time = 1 hour, Rejection Rate = 15%. Thus, the capacity is:

\text{Capacity}_{\text{Electrician}} = \left(\frac{24 \times 5}{1}\right) \times (1 - 0.15) = 102 \text{ units/day}

step 7

For the Approval stage: Number of Employees = 8, Hours per Day = 3, Unit Processing Time = 10 min (which is

\frac{1}{6}

hours), Rejection Rate = 5%. Thus, the capacity is:

\text{Capacity}_{\text{Approval}} = \left(\frac{8 \times 3}{\frac{1}{6}}\right) \times (1 - 0.05) = 136.8 \text{ units/day}

step 8

The overall process capacity is determined by the bottleneck stage, which is the stage with the lowest capacity. In this case, the bottleneck is the Review <

1K

stage with a capacity of 48 units/day

Answer

The overall process capacity is 48 units/day.

Key Concept

Capacity calculation in a process flow

Explanation

The capacity of each stage is calculated based on the number of employees, hours worked, processing time, and rejection rates, with the overall capacity determined by the bottleneck stage.

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