Introduction to Uncertainty

Simulation of Operations

Rolf Harris: Jake the Peg, BBC 1969. Absolutely nothing to do with this course?

Introduction

• Most operational systems are subject to uncertainty– Timing, demand, availability of resource

• Simply using mean values may lead to inaccurate results

• Random sampling can be used to model uncertainty (stochastic processes)

• A stochastic model will produce results that are uncertain

Representing Uncertainty

• Time between part arrivals• Number of defective items in a batch• Time to failure of a piece of equipment• Time to repair a defective item or piece of equipment• Transport time between departments• Processing time for an item or batch • Expected customer demand in period• Expected supplier deliveries in period• Others….

One of the powerful functions of DES in process engineering is it ability to represent the uncertainty associated with many operations.

“but Statistics are too difficult!”

• Lack of understanding can lead to ‘dangerous’ oversimplification

• For example, ignoring the variation in process from natural causes and from poor management.

• Using the mean or average time when better representations are available– Example: using the ‘standard’ time for an activity.

The Joy of Stats

Simple Example

‘Server’(machine, activity etc.)

Mean cycle=0.98(an average!)

Inter-arrival timeIAT=1.0

(an average!)

IAT

Arriving jobs

t

0.02

0

Performance:Server Utilisation = 98%Average WIP <1Lead time=0.98

Queuing Theory

QT demonstrates why replacing a distribution with its mean can lead to inaccurate results, and should be avoided.

QT exampleThe problem of replacing a distribution with its meanBatches of work arrive on average every 1.0 hour and queue to be inspected. Inspection takes 58minutes and 48 seconds (0.98 hours) on average. How much WIP should we expect in front of inspection? If we assume that arrival and service processes are exponentially distributed with means of 1.0 and 0.98 hours respectively then 

i.e. the average delay time in the queue is 48.02 hours, equivalent to 48.02*0.98 or 47.05 batches.