Calculating the Optimal Number of Machines for an Operator

Introduction

In work processes, it is common for an operator to attend to one or more machines to perform their job. The number of machines an operator should attend to will depend on various factors, such as cycle time, manual work time, machine work time, and the operator’s rest percentage. In this article, we will explain step by step and with examples how to calculate the optimal number of machines an operator should handle.

Basic Concepts

Before starting with the calculations, it is necessary to know some basic concepts:

• Cycle time (C): is the total time it takes to complete an operation, including manual work time and machine work time.

• External manual work time (C1): is the time the operator works outside the machine cycle, that is, with the machine stopped.

• Machine work time (Tm): is the time the machine works without operator intervention, the automatic work time of the machine.

• Internal manual work time (C2): is the time the operator works within the machine cycle time, working with the machine running.

• Operator saturation percentage (So): is the percentage of time the operator is working in relation to the total cycle time.

• Machine saturation percentage (Sm): is the percentage of time the machine is working in relation to the total cycle time.

• Rest percentage (D): is the percentage of time the operator is not working, either due to scheduled breaks or waiting between operations.

Calculation of the Number of Machines

To calculate the optimal number of machines an operator should handle, the following steps must be followed:

Step 1: Calculate the Cycle Time (C)

The cycle time is calculated by adding the work time with the machine stopped (C1) and the longer work time between working with the machine running or the machine time once the times are normalized.

Normal Cycle = MP+The longest of MM or TM

Example: In a part machining process, the external manual time is 60 seconds and the machine time is 100 seconds. What is the cycle time?

C = 60 + 100 = 160 seconds

Step 2: Calculate the Operator Saturation Percentage (So) and Machine Saturation Percentage (Sm)

The operator saturation percentage working at a normal pace is calculated by dividing the manual work time C1 + C2 by the cycle time (C) and multiplying by 100.

Normal Operator Saturation = [(MM+MP)/Normal Cycle]*100

The operator saturation percentage working at an optimal pace is calculated by dividing the optimized manual work time C1 + C2 by the optimized cycle time (C) and multiplying by 100.

Optimal Operator Saturation = [(MMi + MPi)/Optimal Cycle]*100

The machine saturation percentage is calculated by dividing the machine work time (Tm) by the cycle time (C) and multiplying by 100.

Sm = (Tm / C) x 100

Example: In the previous part machining process, what is the operator and machine saturation percentage?

So = (60 / 160) x 100 = 37.5%

Sm = (100 / 160) x 100 = 62.5%

Step 3: Calculate the Rest Percentage (D)

The rest percentage is calculated by subtracting the operator and machine saturation percentage from 100.

D = 100 - So - Sm

Example: In the previous part machining process, what is the rest percentage?

D = 100 - 37.5 - 62.5 = 0

In this case, the rest percentage is 0 because the operator and the machine are working at 100% of their capacity.

Step 4: Calculate the Number of Machines

The number of machines an operator can attend to is calculated with the following formula:

N = (100 x D) / (A1 + A2)

Where:

• N is the number of machines.
• D is the rest percentage.
• A1 is the external manual time percentage.
• A2 is the internal manual time percentage.

The external and internal manual time percentages are calculated by dividing the external and internal manual work time by the cycle time and multiplying by 100.

A1 = (C1 / C) x 100

A2 = (C2 / C) x 100

Example: An operator works with an undetermined number of electronic material assembly machines. The time allocated for analysis is 2 minutes and 24 seconds; the time the machine works is 40 seconds and the time the operator works is 2 minutes and 12 seconds. If the rest percentage is 8%, how many machines can the operator attend to?

Step 1: Calculate the cycle time (C)

C = C1 + Tm

C = 2 minutes and 12 seconds + 40 seconds = 2 minutes and 52 seconds = 172 seconds

Step 2: Calculate the operator saturation percentage (So) and machine saturation percentage (Sm)

So = (C1 / C) x 100

So = (132 / 172) x 100 = 76.74%

Sm = (Tm / C) x 100

Sm = (40 / 172) x 100 = 23.26%

Step 3: Calculate the rest percentage (D)

D = 100 - So - Sm

D = 100 - 76.74 - 23.26 = 0

In this case, the rest percentage is 0 because the operator and the machine are working at 100% of their capacity. However, the problem statement indicates that the rest percentage is 8%. Therefore, it is necessary to adjust the cycle time to include the rest time.

C = C1 + Tm + D

C = 132 + 40 + (0.08 x 172) = 181.36 seconds

Step 4: Calculate the number of machines (N)

A1 = (C1 / C) x 100

A1 = (132 / 181.36) x 100 = 72.78%

A2 = (C2 / C) x 100

A2 = (0 / 181.36) x 100 = 0%

N = (100 x D) / (A1 + A2)

N = (100 x 8) / (72.78 + 0) = 1.10

In this case, the number of machines is 1.10. However, a fraction of a machine cannot be attended to. Therefore, it is necessary to adjust the number of machines to the nearest integer. In this case, the operator can attend to 1 machine.

Conclusion

In this article, we have explained step by step and with examples how to calculate the optimal number of machines an operator should handle. To do this, it is necessary to know the cycle time, manual work time, machine work time, and the operator’s rest percentage. With this information, the operator and machine saturation percentage, the rest percentage, and finally, the number of machines the operator can attend to can be calculated. It is important to keep in mind that the number of machines must be an integer, as a fraction of a machine cannot be attended to.