1. Randomservicing
Thismethodapplieswhenyouhave one personhandlingseveralmachines(orthings)that:
– Do not run fora setlengthof time,
– Needservicingat irregularintervals
Examples:
– Machine repair:machinesbreakat randomtimes.
– Call center, callscome inat random times.
Randomservicing:approach
The proportionof time, p,that a machine isup or downcan be estimatedthrougha time study
(Chapter9) or a worksampling study (Chapter14)
q = 1 - p
P = the probabilitythat moutof n total machinesare downis:
P (mof n) = n! x pm
qn-m
m! (n – m)!
Randomservicing:Example
Suppose ata call service center you have one phone operatortoanswer:
– n = 4 phone lines
– p = 0.10 = probabilitythata phone line is in useis.
– q = 1 – p = 0.9 = the probabilitythatagivenphone line is unused,e.g.noone onthe line.
“In use”meansthat a callermay be either:
– waitingonthe line,or
– speakingwiththe phone operator.
If calls come intothe centerat random,whatisthe probabilitythatthere will be exactly three
phone linesinuse? (e.g.One callerspeakingwiththe operator,twocallerswaiting).
Randomservicing
No callers 4! x (.10
) (.94
) = .66
0! (4 – 0)!
One caller 4! x (.11
) (.93
) = .29
1! (4 – 1)!
2. Two callers 4! x (.12
) (.92
) = .05
2! (4 – 2)!
Three callers 4! x (.13
) (.91
) = .0036
3! (4 – 3)!
Four callers 4! x (.14
) (.90
) = .0001
4! (4 – 4)!
Randomservicing
In otherwords,inthissituation:
66 % of the time,the salesassistanthasnocalls;
29 % of the time,exactlyone call;
5 % of the time,exactlytwocalls, e.g.the assistanthelpsone customerwhileone customer
waits,
Lessthan a half a percentof the time (0.36 %),exactlythree calls: one customerisbeinghelped
while twocustomerslistentoMusak.
The probabilitythatall 4 linesare inuse at once isalmostnon-existent.
Probability of exactly n calls
0.6561
0.2916
0.0486
0.0036 0.0001
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4
Number of calls
Probability
3. Line balancing
Line Balancing(LB) is a classic,well-researchedOperationsResearch(OR) optimizationproblem
of significantindustrial importance.Itisone of those problemswheredomainexpertisedoes
not helpverymuch:whateverthe numberof yearsspentsolvingit,one iseachtime facingan
intractable problemwithanastronomicnumberof possible solutionsandnoreal guidance on
howto solve itinthe bestway,unlessone postulatesthatthe oldwayisthe bestway
