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

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.

Continuation from previous subsection (13.2.2)

For the following discussion, Figure sets out several definitions of variables from queuing theory.

Fig.       Definitions of queuing theory variables.

To simplify the discussion, assume the following:

  • Arrivals are random; that is, they follow a Poisson distribution with the parameter λ. λ is the average number of arrivals per period under observation.
  • Arrivals and the operation process are independent of one another.
  • Execution proceeds either in order of arrival or according to random selection from the queue.
  • The duration of the operations is independent of the order of processing and is subject to a determinate distribution with mean M(OT) and coefficient of variation CV(OT).

Figure shows the average wait time as a function of capacity utilization for a model with one station (s = 1, where a queue feeds only one operation station, i.e., one workstation or one machine). We assume the coefficient of variation CV(OT) for the distribution to be 1, which is the case with a negative exponential distribution, for example.

Fig.       Average wait time as a function of capacity utilization: special case s = 1, CV(OT) = 1.

Exercise: Get used to the effect of queues by choosing different values for the queuing theory variables.

Continuation in next subsection (13.2.2c).

Course section 13.2: Subsections and their intended learning outcomes