IE 334 • Final • Operations Research III

Counting Processes

Assumptions of Poisson Processes

Example 1

Memoryless Property

Example 2

Minimum of Exponential Random Variables

Example 3

Thinning

Example 4

Superposition

Example 5

Non-homogenous Poisson Processes

Example 6

Continuous Time Markov Chain

Example 1

Example 2

Example 3

Steady State Distribution

Birth and Death Process

Random Rates, Finite Chain

Example 4

Random Rates, Infinite Chain

Example 5

Equal Rates, Infinite Chain, Single Server

Example 6

Equal Rates, Finite Chain, Single Server

Example 7

Equal Rates, Finite Chain, Multiple Servers

Example 8

Kendall's Notation

Terminology

M/M/1 Queue

Example 1

M/M/s Queue

Example 2

M/M/1/K Queue

Example 3

M/M/s/K Queue

Example 4

Newsvendor Problem

Cost Calculation and Optimal Solution

Example 1

Additional Values

Example 2

Lot Size-Reorder Level (Q, R) Model

Optimal Solution

Example 1

Extra Quantities

Example 2

Service Levels

Given Type 1 Service Level

Given Type 2 Service Level

Lead Time Variability

(s, S) Policy

Service Levels in (s, S) Policy

Poisson Processes 1

Poisson Processes 2

Poisson Processes 3

Poisson Processes 4

Birth and Death 1

Birth and Death 2

Birth and Death 3

Birth and Death 4

Queueing Theory 1

Queueing Theory 2

Queueing Theory 3

Queueing Theory 4

Queueing Theory 5

Queueing Theory 6

Queueing Theory 7

Queueing Theory 8

Newsvendor Model 1

Newsvendor Model 2

Newsvendor Model 3

Newsvendor Model 4

Newsvendor Problem 5

(R, Q) Model 1

(R, Q) Model 2

(R, Q) Model 3

(R, Q) Model 4

Service Levels 1

Service Levels 2

Lead Time Variability & (s, S) Policy

Service Levels in (s, S) Policy