Principles of Sequencing and Scheduling, 2nd Edition

Appendix APractical Processing Time Distributions

A.1 Important Processing Time Distributions

Three distributions are prevalent in stochastic scheduling research – the uniform, exponential, and normal distributions. In addition to these three, we discuss two less prevalent distributions that may even be more important in practice: the lognormal distribution and the Parkinson distribution. Because the various properties of these two distributions are seldom covered among common probability distributions, we provide detailed coverage of each. In this section, we introduce all of these distributions and discuss how to simulate them. We also briefly discuss the Poisson distribution, which we need later. In Chapter 16 we introduce the beta distribution, but we omit it here because for our purposes it is not necessary to study its general properties or to simulate it. Some other distributions that we mention later are common in the literature but lack validation.

A.1.1 The Uniform Distribution

The uniform distribution describes a random outcome that is equally likely to occur anywhere between a minimum value a and a maximum value b. We denote the uniform distribution by U[a, b], where a is the minimum possible realization and b the maximum possible realization. This distribution has mean μ = (a + b)/2 and variance σ² = (b − a)²/12. An important special case, U[0, 1], can be simulated by computers very efficiently. For example, in Excel, this is done by the RAND function. If we wish ...