Intended learning outcomes: Describe job shop production as a network with work centers as nodes.
With the exception of continuous production, there is no production type in which the capacities of machines and workstations following one another in the process are completely synchronized. As Figure 13.2.1.1 shows, even in other cases of line production, synchronization is not always possible. Thus, to a certain extent, buffers serve to balance the differing output rates of the work centers and to ensure continual load of the individual work centers over a certain period of time.
Fig. 13.2.2.1 Job shop production as a network with work centers as nodes.
These buffers are queues formed in front of a workstation; the size of the queues changes over time. Particularly in job shop production, there is great variation in the behavior of the buffer, since a queue is fed from many locations. We can view job shop production as a network with work centers as nodes, as represented in Figure 13.2.2.1. In the figure, the nodes represent work centers, which are classified as homogeneous. The arrows represent the flow of goods or information between these work centers. In the discussion below, the focus is on “Node I” of this network.
Input enters from various nodes and sometimes also from the outside (from a store or a receiving department, for example). This input arrives at a joint queue in front of one of the various workstations (S1, S2, . . . , Si) of work center i. After completion of the operation in Node i, the orders flow to other nodes or toward the outside, either in part or in their entirety (after a final operation), depending on the specification in the routing sheet. In line production, there is essentially a sequence of nodes rather than a network.
As mentioned above, determining the size of a buffer is an optimization problem. Queuing theory provides some fundamental insights into the way that job shop production functions and, to a certain extent, how line production functions as well. Here we limit our discussion to the stationary state of a queue, that is, the state after an infinite time period and with fixed constraints.
Continuation in next subsection (13.2.2b).
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.
