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

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.


Scheduling may deliberately plan in buffers and wait times before a work center for organizational purposes.

Inventory buffer is inventory used to protect the throughput of an operation or the schedule against the negative effects caused by statistical fluctuations (cf. [APIC16]).

Such buffers should absorb potential disturbances in the production process, that occur, for example, in line production or Kanban chains. Figure 13.2.1.1 considers two adjacent workstations.

Fig. 13.2.1.1       Inventory buffers to cushion disturbances in the production flow.

If both workstations were perfectly synchronized, a waiting line would be unnecessary. However, a disturbance may occur at either of the two work systems as a result of, for example

  • Overloading, scrap, or reworking
  • Material shortage, breakdown, or absence of workers

The size of the inventory buffer in front of a work center depends on the degree of synchronization that can be maintained with the previous workstation in practice.

  • If the work process on the first machine is disrupted, the queue waiting for the second machine is reduced. In this case, the second machine may become idle.[note 1304]
  • If the work process on the second machine is disrupted, the queue waiting for the second machine increases, as does the buffer before the second workstation. This may lead to a bottleneck at the second machine.

Scheduling may also plan buffers for economic reasons. By skillfully sequencing operations from the buffer inventory, you can save valuable setup times. Such setup time savings may occur, for example, in processing products from a single product family. Depending on the circumstances, it is possible to provide directly for such sequencing in detailed planning and scheduling. In practice, however, order lead times of unequal length or highly varied order structures limit the extent to which you can plan. As a result, you can often only optimize the sequence of operations at the workstation itself via finite forward scheduling.

Another economic reason for having a buffer in front of a work center is the psychological effect of the buffer on the efficiency of the workers:

  • If the buffer is too small, the workers begin to slow down, fearing that their hours will be cut or even that they will not be needed at the work center. Small buffers make it look like there is not enough work. Therefore, efficiency decreases.
  • Up to a certain point, long queues have a positive influence on efficiency. However, if the queue is too long, it can have a demoralizing effect on workers. The quantity of work to be performed seems insurmountable. Efficiency sinks.

In summary, a buffer in front of a work center is often tolerated or even planned deliberately. However, in evaluating buffers, and in particular their economic repercussions, it is important to take into account the double-negative effect of buffers, specifically 1.) an increase in lead time, and 2.) an increase in work in process and thus tied-up capital.

The buffer model and the funnel model below are concepts of the levels of work in process that are waiting at the workstations.

Figure 13.2.1.2 shows the buffer as a reservoir. This conceptualization is quite old (see [IBM75]).

Fig. 13.2.1.2       Reservoir model.

A more recent conceptualization of the buffer is the funnel model (see [Wien95]). Each work center is viewed as a funnel, as illustrated in Figure 13.2.1.3.

Fig. 13.2.1.3       Funnel model.

The objective is to align the mean output of the work center with its mean load. The funnel volume is used to bring variations of the mean load under control. This means that there must be continual measurement of the mean load, its variation, and the mean output.

If we see total production as a system of work centers, or funnels, that are linked together by output flows, it becomes evident that there are basically two ways to adjust the system:

  • Change capacity, or rather the capacity utilized for each individual funnel. However, it is not always possible to alter capacity short-term.
  • Regulate the number of orders that enter into the system. If too many orders are on hand, individual funnels can overflow, resulting in blocked shop floors and poor delivery reliability. In this case, schedulers should decide what orders to withhold from production. Again, this measure is not always possible.


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. Explain the average wait time as a function of capacity utilization. Produce a summary of relevant formulas in queuing theory.

  • 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.

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