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# Tag Archives: Utilization

## Calculation of the time in the queue / waiting time

The **time in the queue** is calculated as follows:

*time in queue = activity time * (utilization / 1 – utilization) * ((Cv_a^2 + Cv_p^2) / 2)*

with:

activity time = service time factor (average processing time p)

(utilization / 1 – utilization) = utilization factor

((Cv_a^2 + Cv_p^2) / 2) = variability factor

Since the utilization factor is calculated as (u / 1-u), this means that as the waiting time gets higher, the utilization gets closer and closer to 1. The formula for the time in the queue always delivers an average value. This so-called waiting time formula can only be used if the demand is lower than the capacity. If the demand is higher than the capacity, the waiting time will ultimately not be driven by variability, but rather by insufficient capacity.

The **total flow time** of a flow object can be calculated as:

*total flow time = time in the queue + processing time*

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org. |

## Average labor utilization and cost of direct labor

Two important performance measures are the average labor utilization and the cost of direct labor.

**Average labor utilization**: The average labor utilization is defined as the total labor content divided by the sum of labor content and total idle time. If, for example, the total labor content is 30 minutes and the total idle time is 10 minutes, the average labor utilization is 30 / 40 = 0,75 = 75%. The average labor utilization thus tells us the overall performance or productivity of the process.

**Cost of direct labor:** The cost of direct labor is defined as the total wages per unit of time divided by the flow rate per unit of time. It tells us, how many Dollars (or Euros) are being spent in order to get one flow unit through a process (e.g. to treat one patient or to serve one customer).

Looking at the direct labor costs is very important, even though labor costs seem to make up – at least at first glance – only a tiny part of the overall costs. But since labor costs are hidden in all supplies and materials a company buys (that is, the labor costs of the suppliers), a company that might on the sheet be only paying for materials does in fact pay for externalized labor.

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org. |

## Capacity, bottleneck, process capacity, flow rate and utilization

In order to perform the following calculations, processing time has to be defined as the time that is spent on a certain task (e.g. one station in a sandwich restaurant). We will also need the previously introduced definitions of flow rate and flow time.

**Capacity**: The capacity can be calculated for every station in a business process. It is always m / processing time with m being the number of resources (e.g. workers) being devoted to the station. If, for example, one worker needs 40 seconds to put together a sandwich, the capacity of this station is 1/40 per second or 1,5 sandwiches per minute. If there are two workers on the same station, the capacity increases to 2/40 per second or 3 sandwiches per minute.

**Bottleneck**: The bottleneck is defined as the process step (station) in the flow diagram with the lowest capacity (the “weakest link”). Although the bottleneck is often the process step with the longest processing time, it is important to always look at the capacities for making a judgement.

**Process capacity**: The process capacity is always equivalent to the capacity of the bottleneck. It is useful, to calculate a comprehensible number, such as customers per hour or parts per day (instead of a hard to comprehend number such as 1/40 customer per second or 1/345 part per second).

**Flow rate**: Even though the flow rate was previously defined, the definition needs to be augmented as the flow rate being the minimum of demand and process capacity. While the flow rate logically can never be higher than the capacity of the bottleneck, it can very well be lower, if the demand is insufficient.

**Utilization**: The utilization tells us, how well a resource is being used. It is calculated as flow rate divided by capacity (e.g. 1/40 / 1/25). The utilization always lies between 0% and 100%.

These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org. |