13.7.1 Exercise: Queues as an Effect of Random Load Fluctuations (1)

Intended learning outcomes: Answer a number of questions using the relevant formulas in queuing theory.

Answer the following questions using the relevant formulas in queuing theory (refer to Figure 13.2.2.4):

a.    How many parallel workstations are needed to have an expected wait time of less than 10 hours, if capacity utilization is 0.95, the mean of the operation time is 2 hours, and the coefficient of variation of the operation time is 1?

b.    The capacity is 10 hours. How much does the expected wait time increase if load rises from 4 to 8 hours?

c.    How is the expected wait time affected when the coefficient of variation increases from 1 to 2?

Solutions:

a.    s = 0.95 / (1 – 0.95)  *  (1 + (1 * 1)) / 2  *  2 / 10) = 3.8. Thus, with four workstations, the expected wait time will be 9.5 hours.

b.    Capacity utilization increases from 4/10 to 8/10. Therefore, the respective factor in the formula for the expected wait time increases from 0.4 / (1 – 0.4) = 2/3 to 0.8 / (1 – 0.8) = 4. The new factor is 4 / (2/3) = 6 times greater than the old factor. Thus, the expected wait time increases by a factor of 6.

c.    The respective factor in the formula for the expected wait time increases from (1 + (1 * 1)) / 2 = 1 to (1 + (2 * 2)) / 2 = 2.5. Thus, the expected wait time increases by the factor 2.5.

Course section 13.7: Subsections and their intended learning outcomes

• 13.7 Scenarios and Exercises

Intended learning outcomes: Assess queues as an effect of random load fluctuations. Calculate examples for network planning, backward scheduling, forward scheduling, the lead-time stretching factor, and probable scheduling.

• 13.7.1 Exercise: Queues as an Effect of Random Load Fluctuations (1)

Intended learning outcomes: Answer a number of questions using the relevant formulas in queuing theory.

• 13.7.2 Scenario: Queues as an Effect of Random Load Fluctuations (2)

Intended learning outcomes: Experience average wait time as a function of capacity utilization in a job shop environment with random arrivals, execution of operations in order of arrival as well as operation times subject to a determinate distribution with mean and coefficient of variation.

• 13.7.3 Exercise: Network Planning

Intended learning outcomes: Calculate a scheduled network with incomplete data for six operations and a start operation (administration time. Determine the critical path.

• 13.7.4 Exercise: Backward Scheduling and Forward Scheduling

Intended learning outcomes: Explain and solve the forward and backward scheduling problems that is calculation of start and completion dates for the order and each operation, as well as the critical path and lead-time margin.

• 13.7.5 Exercise: The Lead-Time-Stretching Factor and Probable Scheduling

Intended learning outcomes: Explain and practice the use of the lead-time-stretching factor as well as probable scheduling.