*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.*

Nontechnical wait time before an operation is a difficult element of interoperation time to plan. It arises if the processing rhythm of the operations of a work center does not correspond to the rhythm of the receipt of the individual orders. This can happen in job shop production, for example, if the work center receives orders randomly from preceding operations. Queuing theory is a collection of models to deal with the resulting effects — buffers and queues.

A *buffer* or a *bank* is a quantity of materials awaiting further processing.

A buffer can refer to raw materials, semifinished stores or hold points, or a work backlog that is purposely maintained behind a work center (cf. [ASCM22]).

A *queue* in manufacturing is a waiting line of jobs at a given work center waiting to be processed.

As queues increase, so do average queue time (and therefore lead time) and work-in-process inventory (cf. [ASCM22]).

*Queuing theory* or *waiting line theory* is the collection of models dealing with waiting line problems, e.g., problems for which customers or units arrive at some service facility at which waiting lines or queues may build up ([ASCM22]).

## 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.

## Course 13: Sections and their intended learning outcomes

##### Course 13 – Time Management and Scheduling

Intended learning outcomes: Present the elements of time management. Explain in detail knowledge on buffers and queues. Disclose scheduling of orders and scheduling algorithms. Describe splitting and overlapping.

##### 13.1 Elements of Time Management

Intended learning outcomes: Describe the order of the operations of a production order, operation time and operation load, the elements of interoperation time, administrative time, and transportation time.

##### 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.

##### 13.3 Scheduling of Orders and Scheduling Algorithms

Intended learning outcomes: Describe the manufacturing calendar and the calculation of the manufacturing lead time. Differentiate between Backward Scheduling and Forward Scheduling. Explain network planning, central point scheduling, the lead-time stretching factor, and probable scheduling. Present scheduling of process trains.

##### 13.4 Order Splitting, Order Overlapping, and Extended Scheduling Algorithms

Intended learning outcomes: Explain order or lot splitting, and overlapping. Present an extended formula for manufacturing lead time and extended scheduling algorithms.

##### 13.5 Summary

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##### 13.6 Keywords

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##### 13.7 Scenarios and Exercises

Intended learning outcomes: Assess queues as an effect of random load fluctuations. Calculate examples for network planning, backward scheduling, forward scheduling, the lead-time stretching factor, and probable scheduling.

##### 13.8 References

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