Integral Logistics Management — Operations Management and Supply Chain Management Within and Across Companies

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.

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 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.       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 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