*Intended learning outcomes: Present qualitative findings of queuing theory for job shop production and, in part, for line production. Describe the measures indicated by the qualitative findings of queuing theory.*

It is not possible to apply quantitative results of queuing theory to job shop production directly, since some of the specified conditions are not satisfied. For example:

- The arrival process may be
*short term*, a purely random process. However, scheduling can shield production from large capacity utilization peaks, and the delivery rates of supplying nodes will limit arrival rates at a work center (= network node). Therefore, medium-term fluctuations will be somewhat smaller than in the case of a purely random process. - There is no independence between the execution and the arrival process. Since the negative consequences of large queues are undesirable, scheduling will spare no effort to avoid extreme situations. It manipulates the processes by:

- Subcontracting individual orders

- Subcontracting individual operations

- Raising the capacity of operating facilities with overtime or shift work

- Advancing or postponing individual operations

The result is not a stationary state, but rather a series of transitional states, which are characterized by varying values of the parameters and distributions that specify a queuing process. Nevertheless, queuing theory yields qualitative findings for job shop production and, in part, for line production:

1. *High capacity utilization <=> large queues:* In a rigid queuing system, particularly with a one-station model, it is not possible to achieve both good utilization of the capacities and short lead times simultaneously. The higher the capacity utilization desired (in the absence of capacity adjustments from planning interventions), the larger the average queue must be.

2. *High capacity utilization <=> (wait time *>>* operation time):* Wait time in the queue is significantly larger than operation time in the case of high capacity utilization.

3. *Shorter lead time <= fewer operations:* Fewer operations mean fewer queues. In industrial production, this is achieved by a greater versatility of machine tools, such as numerically controlled machines or machining centers, and in services and administration by a reduction of extreme division of labor. However, it is important to ensure that the total operation time with a reduced number of operations is shorter than that with a larger number of operations. Otherwise, no positive effect will result, since wait time increases with prolonged operation time.

4. Large queues result from a) prolonged operation time, b) extremely varied operation times, or c) few parallel workstations, or only one workstation

The qualitative findings of queuing theory indicate the following measures:

*A reduction of setup time**, which will reduce batch sizes and hence cut the average operation time.*However, direct reduction of batch size without reducing setup time increases manufacturing costs. It is only productive if the work center is not fully utilized, that is, if the larger setup time resulting from splitting the operations does not lead to overloading or nearly full utilization of the work center.*Equal contents for all operations, to avoid markedly different operation times.*Schedulers can reduce the coefficient of variation for operation times, that is, the difference in the duration of operations, by, for example, splitting up orders with long standard times. This results in a reduction in the mean operation time as well. However, in fully utilized production, increased setup can negate the positive

effect.*A reduction in utilization*,

All these measures are starting points or basic principles of the lean / just-in-time concept. The general, dominant tendency today is to move away from production as a system with fixed constraints. The more successful this move is, the shorter the wait times resulting from the queuing effect will be. As a result, organizational intent — rather than chance — increasingly determines lead times.

## Course section 13.2: Subsections and their intended learning outcomes

##### 13.2 Logistic Buffers and Logistic Queues

Intended learning outcomes: Explain wait time, buffers, the funnel model, and queues as an effect of random load fluctuations. Present conclusions for job shop production. Produce an overview on logistic operating curves.

##### 13.2.1 Wait Time, Logistic Buffers, and the Funnel Model

Intended learning outcomes: Describe inventory buffers to cushion disturbances in the production flow. Explain the buffer model, the reservoir model and the funnel model.

##### 13.2.2 Logistic Queues as an Effect of Random Load Fluctuations

Intended learning outcomes: Describe job shop production as a network with work centers as nodes.

##### 13.2.2b Wait Time as a Function of Capacity Utilization

Intended learning outcomes: Explain the average wait time as a function of capacity utilization.

##### 13.2.2c Queuing Theory: Relevant Formulas for the Average Case

Intended learning outcomes: Produce a summary of relevant formulas in queuing theory for the average case.

##### 13.2.3 Conclusions for Job Shop Production

Intended learning outcomes: Present qualitative findings of queuing theory for job shop production and, in part, for line production. Describe the measures indicated by the qualitative findings of queuing theory.

##### 13.2.4 LOC — Logistic Operating Curves

Intended learning outcomes: Produce an overview on logistic operating curves. Explain an example of logistic operating curves.