Appunti di Service Design & Management

-> LA PROBABILITA’ SI FA INTEGRANDO (DOMANDA

ESAME)

Cumulative Density Function

Preso un valore sull’asse x, la funzione ci dice qual è

la probabilità che il tempo di interarrivo sia minore o

uguale a quel valore.

e.g. in an ER, patient interarrival times

follow an exponential distribution. The

MTBA is 2.4 minutes. The probability that

if a customer has already arrived at least

another patient will arrive in the next five

minutes is: −04167(5)

(5) = 1 − = 0.8754

= 87,5% 50

Poisson Distribution The Poisson Distribution tells exactly what the

probability of having n arrivals is.

Unlike the previous ones, this is a discrete

distribution.

Interarrival time: continuous variable

Number of arrivals: discrete variable

e.g. MTBA = 2.4 min, Arrival rate = 0.4167 min^(-1)

The probability that no patients will arrive during a hour interval is:

0 −0.4167∗

(0.4167 ∗ 60) −11

(0) = = 1.39 ∗ 10

0!

Possiamo mettere a confronto la distribuzione di Poisson e quella esponenziale:

sulla parte superiore (top

view) abbiamo la

distribuzione di Poisson,

mentre nella parte inferiore

(bottom view) quella esponenziale.

Poisson processes can be:

• Homogeneous: they’re characterized by an intensity that doesn’t change overtime

λ

• Non-homogeneous: is time dependant:

λ λ = λ(t) 51

Queue configurations

Queues can be of different types:

• Single queue

Finite

o Unlimited

o

• Take a number

Finite

o Unlimited

o

• Multiple queues

Finite

o Unlimited

o Jockeying allowed

o Jockeying not allowed

o Express lane

o

Pros & Cons:

• Multiple queue

The service can be differentiated (e.g. express lanes in supermarkets)

o Labour can be divided

o The customer can choose based on his preferences

o Balking can be avoided

o

• Single queue

It’s fair

o No anxiety to look for the faster lane

o Enhanced privacy

o More efficient in terms of Wq

o

• Take a number

Customers are free to pursue some kind of diversion (= svago)

o Customers risk missing their turn

o Impulse sales

o Waiting area could be inadequate

o 52

[Single queue:

Ho una sola coda, o più server, ma tutti i server possono servire tutti i clienti che vengono messi

tutti in una stessa fila e poi via via il primo della fila raggiungerà il primo server disponibile

→

Garantiscono equità (FCFS applies to all arrivals) garantisce equità perché si applica first

come first served quindi chi prima arriva meglio alloggia, diminuiscono lo stato d’ansia perché

la coda accanto va più forte →

No cutting-in problem and reneging made difficult si scoraggia cutting in: quando sono in

coda e si libera un’altra coda qualcuno ci va e viene servito prima, ad esempio al supermercato

quando si apre una cassa e quelli dietro di te ci vanno e vengono subito serviti

→

Privacy maggiore ci si stacca da una coda e si va ad essere serviti senza avere dietro gli altri

che aspettano per lo stesso server. →

Sono più efficienti dei multiple queue in termini di tempo di attesa se una coda non ha

nessun cliente da servire rimane ferma. Wq = tempo medio di attesa in coda

Multiple queues

Ho più server e il cliente quando entra può scegliere una coda,

decide il provider se permettere cambio coda, (Jockeying), se

non vuole, può mettere pioli, (casello autostradale).

Servizio differenziato (supermercati express line per anziani,

donne in gravidanza, telepass)

→

Divisione del lavoro divisione del lavoro è possibile perché server diversi possono fare

operazioni diverse e i clienti possono essere dirottati nelle code in cui l’operatore ha le skills

necessarie a erogarli il servizio

Il cliente sceglie il provider che vuole →

Disencintiva il fenomeno del bulcking scoraggiano bulking perchè se vedo tante code

piccole tendo a mettermi in coda

Takes a number

Posso avere più server che possono servire tutti i clienti, ma

prendono un numerino e possono non stare in coda ma quando

avviene il numerino deve essere lì.

→

Cliente può distrarsi cliente mentre è in attesa in coda può

essere libero di distrarsi così da rendere l’attesa in coda più

leggero e intanto faccio altra spesa (caso supermercato)

→

Customers risk missing their turns for service cliente può rischiare di perdere il proprio turno

e ansia di non essere servito mi fa comunque aspettare lì

→

Increase impulse sales invoglia acquisti impulsivi, mentre siamo in attesa al banco della

gastronomia vedo tutto ciò che è venduto e alla fine acquisterò di più di quello che avevo

previsto

problems if the waiting area is inadequate (finite queue) 53

Concealment of the waiting line

Strategia che molti server povider implementano per allietare il tempo di attesa in fila o per farlo

percepire più breve è quella di nascondere le code.

Es. parchi a tema in cui si vede solo una parte della coda dall’esterno.

Così percepiamo l’attesa in coda più breve e si minimizza il rischio che i clienti non entrino in

coda]

Queue discipline can be:

• Static (First Come, First Serve – FCFS)

• Dynamic

Selection based on status of queue

o Number of customers waiting

▪ Round robin

▪

Selection based on individual customer attributes

o Priority

▪ Pre-emptive

▪ Processing time of customers (SPT rule)

▪

Service processes can be:

• Static Self-service

o Machine-paced

o

• Dynamic

Varying service rate

o Closing and opening service lanes

o

Poisson arrivals can be:

• Infinite queue

Exponential service time

o Single server M/M/1

▪ Multiple servers M/M/c

▪

General service time

o Single server M/G/1

▪ Self-service M/G/∞

▪

• Finite queue

Exponential service times

o 54

Single server M/M/1

▪ Multiple servers M/M/c

▪

Kendal notation: A/B/c where A: distribution of time between arrivals, B: distribution of service

times, c: number of servers.

A, B can assume: M – exponential distribution (memoryless), G – general distribution with

known mean and variance, D – deterministic distribution, Ek – Erlang distribution

QUANTO è PIU EFFICIENTE IL SUPERSERVER DEL SERVER?

Transient VS Steady state

We define:

• Transient state: it’s when the value of the operating characteristics (which refer to mean

values) depends on time

• Steady state: it's when the operating characteristics do not depend on time; the system

can be considered to be in statistical equilibrium (-> the mean value is stable)

When the system is warming up, its characteristics are usually transient. After a while, it can

achieve a statistical equilibrium in which the number of queues assumes a distribution that is

independent of the starting condition.

For any queuing system that’s reached a steady state, the following formulas apply (DA SAPERE

PER ESAME): 55

56

Sampson’s case studies

Case study #1: higher education

Higher education has expanded in recent years, mostly thanks to distance learning and for-

profit institutions. In 2005, almost 900.000 students enrolled in for-profit schools, while in 2010

they were 1.900.000.

Many of these schools now deliver online education courses and this is a classic illustration of

deservitization, which can provide higher value proposition to some customer segments.

In traditional education (universities), which is affected by costly labour and interactions,

budget constraints often lead to large lecture courses to improve efficiency. In its PCN diagram,

the provider is the university (university professor, employed as a topic expert) and the

customer is the student, who enrolls in because he is in need of knowledge. The student’s

activities are: acquire the lecture book, go to classes, take notes and, if the size class allows it,

ask questions for clarification. At the end of the semester, the student acquires the knowledge

needed for the exam and gets a grade that counts for his graduation.

This process shows some inefficiency due to the requirement for the teacher and the student

to co-locate during lessons. If the class is too big to allow questions, recording the lesson to

listen to it on a later time could give some benefit.

Professor Norm from BYU started recording his lessons and made some CDs to provide to

students so that they could rewatch the lessons at the speed they wanted and as many times

as they wanted. Even though he retired in 2011, his CDs are still around and are marketed to

universities around the world. This process proved to be superior to the previous one both in

terms of efficiency and customization, since the viewing of the lecture moved to the

independent area of the student. Also, the quality of the material on the CDs was high enough

to reduce the need of questions (direct interactions).

Finally, the internet has had a great impact on education. On-line learning is slightly different

from Norm’s one. Lessons are now served interactively, meaning that each student has to log

in into the system: students can’t sell or exchange CDs anymore, so the provider has a higher

control on the process and higher revenues. Also, by logging in, the provider can track the

students’ progress and know if they’re on schedule. Interactions are now mostly surrogate and

this is a great way to balance the trade-off between process efficiency and customization.

Traditional education institutions that rely on on-campus interactions may feel threatened by

on-line learning. Some of them are trying to fight back by making their professors port their

courses on online learning systems, which may somewhat help reduce the problem, but not

solve it: universities which do so are at a competitive disadvantage to firms that have greater

economies of scale. Professors who work in the region of direct interactions and move to the

independent one are likely to be dominated by the ones who have greater economies of scale.

57

When switching from an interactive process to an independent one, those with great

economies of scale have clear advantage. The large fixed cost of developing a high-quality

online course must be offset by a large customer base.

An alternative to moving toward independent processes is to focus on an education market that

is more resistant to deservitization.

An example of this is the “case method” developed by the Harvard Business School. Here, the

professor acquire