Summary Logistics Management 344

Logistics Management 344
Queuing Theory, Simulation, Chi^2 Test & Linear
Programming




1. Queuing Theory
Key terms:

Wq  Time in the queue (e.g. time waiting to be serviced)
Ws  Time in service (e.g. time spent at the counter/washbay)
W  Time in the system (e.g. time spent in the premises)

Lq  Number of vehicles in the queue (e.g. number of vehicles waiting to be
served)
Ls  Number of vehicles in the service (e.g. number of vehicles at the washbay)
L  Number of vehicles in the system (e.g. number of vehicles in the premises)

p  Utilization factor
P0  Probability is ‘idle’


Kendall-Lee notation:




a  Nature of the interarrival times
b  Nature of the service times
c  Number of service points
d  Queuing rules
e  Number of customers allowable in the system
f  Number of customers in the calling population
GD=FIFO


Base assumptions for a M/M/1/GD/∞/∞ queuing model:

1. Queuing rules follow FIFO – first in first out
2. No balking or reneging

, 3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu


Base assumptions for a M/M/3/GD/∞/∞ queuing model:

1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Interarrival times are mutually independent & follow the exponential
distribution with lambda being known
4. Service times are mutually independent & follow the exponential
distribution with mu being known
5. Calling population in infinitely large & there is no space constraint
6. Lambda < mu


Base assumptions for a M/M/1/GD/9/9 queuing model:

1. Queuing rules follow FIFO – first in first out
2. No balking or reneging
3. Service times are mutually independent & follow the exponential
distribution with mu being known
4. The calling population in finite
5. Arrival times follow the poisson distribution

, Calculations/formulas:

*NB do all calculations using below formulas on excel to determine values!

*Determine probability that ‘1’ or more of the scanners are busy  P = ’1’ – P0
*Average number of ships being serviced at any time = L – Lq
M/M/1/GD/∞/∞
M/M/3/GD/∞/∞