Risk Minimizing and

Decision Techniques

Management Science

Presented by-Mehedi Hasan

FBA, USTC

Submitted to

S M Salamotullah BhuiyanAdjunct Professor FBA, USTC

What is Management Science?

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.

Risk Minimizing and Decision Techniques

Risk minimizing

 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.

Decision techniques

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.

Decision techniques (cont...)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

Decision techniques (cont...)

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.

Decision techniques (cont...)

Linear programming 

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

Decision techniques (cont...)

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.

Decision techniques (cont...)

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

Decision techniques (cont...)

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.

Decision techniques (cont...)

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.

Decision techniques (cont...)

Goal programming 

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

Decision techniques (cont...)

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 in Table 1.

Decision techniques (cont...)

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

Decision techniques (cont...)

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.

Decision techniques (cont...)

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.

Decision techniques (cont...)

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.

Decision techniques (cont...)

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.

Decision techniques (cont...)

To

Running Down

FromRunning .9 .1

Down .3 .7

Table 2

Decision techniques (cont...)

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

Decision techniques (cont...)

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.

Decision techniques (cont...)

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.

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