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

*Logistic operating curves* *(LOC)* are ways to summarize the facts of an operation, as shown in Figure 13.2.4.1 (see [Wien95]).

Logistic operating curves aid evaluation of production processes in the framework of production control. Logistic operating curves express a comparison of logistic performance indicators.

- In Figure 13.2.4.1,
*performance*is the output, that is, the load processed by the work center (see also [Wien95]). Thus, the performance curve corresponds to the*capacity utilization*curve(see also Figure 1.4.3.4 or Figure 1.4.4.4). A particular output is achievable only if the waiting work in process is of a particular size. As output approaches its maximum, you can only increase it if you increase the inventory of work in the queue over proportionally. This logistic operating curve shows in its upper part roughly the same situation as in Figure 13.2.2.3, where the axes are reversed. - The
*range (of inventory)*is the length of time required to process the inventory at the workstation. Accordingly, the*mean range*is the mean of the wait time, as in Figure 13.2.2.4, plus the operation time. This mean has a minimum, which is influenced, among other things, by the operation times and their variances. For job shop production, the level of waiting work determines the inventory or work-in-process to a large degree. See also the performance indicator*work-in-process-inventory turnover*in Figure 1.4.3.2.

**Fig. 13.2.4.1** An example of logistic operating curves (following [Wien95]).

From capacity utilization, then, we arrive at work-in-process and from there to the mean wait time (which, in job shop production, makes up a large proportion of lead time). The three inventory levels I, II, and III represent, respectively, an underloaded work center, an appropriately loaded work center, and an overloaded work center. Thus, the logistic operating curves indicate how much play there is to reduce queues, and hence wait times, without endangering capacity utilization.

In the following, we present suitable measures to alter the logistic operating curve so that the dangerous curve occurs as late as possible. In addition, the slope of the straight lines representing mean work on hand should be as small as possible. Lean/JIT concepts (see Chapter 6), for example, can create the potentials for achieving these aims. Through the use of these potentials, the logistic operating curves change, and new degrees of freedom arise that allow for a decrease in orders waiting to be processed.

## 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.