Management Science

Management Science
Presented by-
Mehedi Hasan
FBA, USTC
Submitted to
S M Salamotullah Bhuiyan
Adjunct Professor
FBA, USTC

Management science (MS, is an interdisciplinary branch of
applied mathematics, engineering and sciences that uses various
scientific research-based principles, strategies, and analytical
methods including mathematical modeling, statistics and
algorithms to improve an organization's ability to enact rational
and meaningful management decisions. The discipline is typically
concerned with maximizing profit, assembly line performance,
crop yield, bandwidth, etc or minimizing expenses, loss, risk, etc.

We consider a risk minimization
problem in a continuous-time
Markovian regime-switching
financial model modulated by a
continuous-time, observable and
finite-state Markov chain whose
states represent different market
regimes.

 Risk is the ultimate four-letter word of business,
investment and government. Entrepreneurs and political
leaders understand as well as anyone that if nothing is
ventured, nothing can be gained, and that therefore risk
can never be entirely eliminated. Nonetheless, the effort to
minimize, or at least manage risk, has become a major
focus of most corporate entities, and it's standard practice
for public companies to disclose their operating risks each
quarter in their public filings.

 Management science is the
science for managing and
involves decision making.
Management science uses
analytical methods to solve
problems in areas such as
production and operations,
inventory management,
and scheduling.

Management science decision techniques are used on a wide variety of
problems from a vast array of applications.
The scope of management science decision techniques is broad.These
techniques include:
 mathematical programming
 linear programming
 simplex method
 dynamic programming
 goal programming
 integer programming
 nonlinear programming
 stochastic programming
 Markov processes
 queuing theory/waiting-line theory
 transportation method
 simulation

Mathematical programming
 Mathematical programming deals
with models comprised of an
objective function and a set of
constraints. Linear, integer,
nonlinear, dynamic, goal, and
stochastic programming are all
types of mathematical
programming.

Linear programming
 Linear programming problems
are a special class of
mathematical programming
problems for which the objective
function and all constraints are
linear.

Media selection problem
 The local Chamber of Commerce periodically
sponsors public service seminars and programs.
Promotional plans are under way for this year's
program. Advertising alternatives include
television, radio, and newspaper. Audience
estimates, costs, and maximum media usage
limitations are shown in Exhibit 1.

Constraint Television Radio Newspaper
Audience per ad 100,000 18,000 40,000
Cost per ad 2,000 300 600
Maximum usage 10 20 10
Exhibit 1

Simplex method
 The simplex method is a specific
algebraic procedure for solving linear
programming problems.
 The simplex method begins with
simultaneous linear equations and
solves the equations by finding the best
solution for the system of equations.
 The simplex method can provide a
solution for the production allocation of
High Quality models and Medium
Quality models.

Dynamic
programming
Dynamic programming is a
process of segmenting a large
problem into a several smaller
problems. The approach is to
solve the all the smaller, easier
problems individually in order
to reach a solution to the
original problem.

Goal programming
 Goal programming is a technique
for solving multi-criteria rather
than single-criteria decision
problems, usually within the
framework of linear
programming.

Integer programming
• Integer programming is useful when values of one or more
decision variables are limited to integer values. This is
particularly useful when modeling production processes for
which fractional amounts of products cannot be produced.
• Areas of business that use integer linear programming
include capital budgeting and physical distribution.
 For example, faced with limited capital a firm needs to
select capital projects in which to invest. This type of
problem is represented inTable 1.

Integer programming
Project
Estimated Net
Return Year 1 Year 2 Year 3
New office 25,000 10,000 10,000 10,000
New warehouse 85,000 35,000 25,000 25,000
New branch 40,000 15,000 15,000 15,000
Available funds 50,000 45,000 45,000
Table1 1
Integer Programming Example

Nonlinear programming
Nonlinear programming is useful when the objective function
or at least one of the constraints is not linear with respect to
values of at least one decision variable.
 For example, the per-unit cost of a product may increase at
a decreasing rate as the number of units produced
increases because of economies of scale.

Stochastic programming
Stochastic programming is useful when the value of a
coefficient in the objective function or one of the constraints is
not know with certainty but has a known probability
distribution.
 For instance, the exact demand for a product may not be known, but its
probability distribution may be understood. For such a problem,
random values from this distribution can be substituted into the
problem formulation. The optimal objective function values associated
with these formulations provide the basis of the probability distribution
of the objective function.

Markov process models
Markov process models are used
to predict the future of systems
given repeated use.
 For example, Markov models are
used to predict the probability that
production machinery will function
properly given its past performance
in any one period. Markov process
models are also used to predict
future market share given any
specific period's market share.

Computer facility problem
The computing center at a state university has been
experiencing computer downtime. Assume that the trials of an
associated Markov Process are defined as one-hour periods
and that the probability of the system being in a running state
or a down state is based on the state of the system in the
previous period. Historical data in Table 2 show the transition
probabilities.

To
Running Down
From
Running .9 .1
Down .3 .7
Table 2

Queuing theory/waiting
Queuing theory is often referred to as waiting line theory. Both terms refer
to decision making regarding the management of waiting lines (or
queues). This area of management science deals with operating
characteristics of waiting lines, such as:
 the probability that there are no units in the system
 the mean number of units in the queue
 the mean number of units in the system (the number of units in the
waiting line plus the number of units being served)
 the mean time a unit spends in the waiting line
 the mean time a unit spends in the system (the waiting time plus the
service time)
 the probability that an arriving unit has to wait for service
 the probability of n units in the system

Transportation method
The transportation method is a
specific application of the
simplex method that finds an
initial solution and then uses
iteration to develop an optimal
solution. As the name implies,
this method is utilized in
transportation problems.

Simulation
Simulation is used to analyze complex
systems by modeling complex
relationships between variables with
known probability distributions.
Random values from these probability
distributions are substituted into the
model and the behavior of the system
is observed. Repeated executions of
the simulation model provide insight
into the behavior of the system that is
being modeled.

Management Science

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