Short intro, Jan 12, 2009, by Krister Svanberg.

Welcome to the course "Stochastic decision support models".

The book, which is crucial for the course, is called
Introduction to operations research, 8th edition,
and is written by Frederick Hillier and Gerald Lieberman.
By the expression "Operation research" (OR) is meant a
scientific approach to "operations", or "activities".
OR was born during World war II but is nowdays used mainly 
by civil organization like profit-making companies.

The first half of the book, but NOT this course, deals with
certain deterministic mathematical models and methods which
we presume that you are already somewhat familiar with,
e.g. linear and nonlinear optimization:
minimize f(x_1,...,x_n)
subject to g_i(x_1,...,x_n) =< b_i, i=1,...,m.

The second half of the book -- AND ALSO THIS COURSE -- deals
with models where the uncertainty of reality is represented by 
random variables. In some situations it may be acceptable to 
replace these random variables by their expected value and use 
a deterministic model, but in many situations this is not so.

As an example, consider a simple queue where customers arrive
according to some random process with, on the average, 10 arriving
customers per hour, and the service times are random variables
with mean 5 minutes (the service rate is 12 customers per hour).
If we remove the randomness and state that one customer arrives
every 6th minute and is served during exactly 5 minutes then
there will be no queue at all. But this is a worthless approximation
of reality where there certainly will be a queue now and then!
Stochastic models of queues is one important part of this course.

Another part of the course deals with inventory theory.
Consider a car-producing company called Volov.
Within each car, there should be a certain electronic item
which Volov buys from another company called Electro. Let 
d = Volovs demand for the item (number of units per week),
Q = the batch size (order quantity) each time Volov
    orders the items from Electro,
T = time between the orders.
Then we have the relation T = Q/d (see the figure)
and the aim is to choose Q such that the sum of the holding
costs, the setup costs for the orders, and the shortage
costs (if any) is minimized.
If the demand and the lead time (between order and delivery)
are exactly known then a deterministic model could be used,
while if there are significant uncertainties in the demand
or the lead time then a stochastic model is needed.

Several of the other parts of the course are more or less
devoted to SEQUENTIAL decision making under uncertainty.
Here is an example which is easy to state but not so easy
to solve (or can you solve it already now?):
Assume that we are to interview N candidates for a job.
At the end of each interview we must either hire or reject
the candidate we have just seen, and this decision cannot be
changed later. Candidates are seen in a completely random order,
and each candidate can be ranked against those seen previously.
The aim is to maximize the probability of choosing the candidate
of greatest rank.


The lectures, which do not cover all the material in the book,
will concentrate on the mathematical theory, models and methods.
Applications will be described only in relatively general terms.
The book, however, presents a lot of specific and detailed
applications of the theory! You should read the book, and we hope
that the lectures should make it easier for you to do that.