Course Code : MBA-206

Course Title : Operations Research

Assignment No. : MBA-206/ 2022
Maximum Marks : 30

Q5. Discuss the decision tree analysis.

Ans. A decision tree is a flowchart that starts with one main idea and then branches out based on the consequences
of your decisions. It’s called a “decision tree” because the model typically looks like a tree with branches.

These trees are used for decision tree analysis, which involves visually outlining the potential outcomes, costs, and
consequences of a complex decision. You can use a decision tree to calculate the expected value of each outcome
based on the decisions and consequences that led to it. Then, by comparing the outcomes to one another, you can
quickly assess the best course of action. You can also use a decision tree to solve problems, manage costs, and reveal
opportunities.

The use decision tree analysis to make decisions in many areas including operations, budget planning, and project
management. Where possible, include quantitative data and numbers to create an effective tree. The more data you
have, the easier it will be for you to determine expected values and analyse solutions based on numbers.

For example, if you’re trying to determine which project is most cost-effective, you can use a decision tree to analyse
the potential outcomes of each project and choose the project that will most likely result in highest earnings.

The five steps to create a decision tree diagram to analyse uncertain outcomes and reach the most logical solution
are:

1. Start with your idea

Begin your diagram with one main idea or decision. You’ll start your tree with a decision node before adding single
branches to the various decisions you’re deciding between.

For example, if you want to create an app but can’t decide whether to build a new one or upgrade an existing one,
use a decision tree to assess the possible outcomes of each.

In this case, the initial decision node is:

 Create an app
 Building a new scheduling app
 Upgrading an existing scheduling app
 Building a team productivity app

2. Add chance and decision nodes

After adding your main idea to the tree, continue adding chance or decision nodes after each decision to expand
your tree further. A chance node may need an alternative branch after it because there could be more than one
potential outcome for choosing that decision.

For example, if you decide to build a new scheduling app, there’s a chance that your revenue from the app will be
large if it’s successful with customers. There’s also a chance the app will be unsuccessful, which could result in a
small revenue. Mapping both potential outcomes in your decision tree is key.

3. Expand until you reach end points

Keep adding chance and decision nodes to your decision tree until you can’t expand the tree further. At this point,
add end nodes to your tree to signify the completion of the tree creation process.

Once you’ve completed your tree, you can begin analysing each of the decisions.

4. Calculate tree values

Ideally, your decision tree will have quantitative data associated with it. The most common data used in decision
trees is monetary value.

For example, it’ll cost your company a specific amount of money to build or upgrade an app. It’ll also cost more or
less money to create one app over another. Writing these values in your tree under each decision can help you in
the decision-making process.

You can also try to estimate expected value you’ll create, whether large or small, for each decision. Once you know
the cost of each outcome and the probability it will occur, you can calculate the expected value of each outcome
using the following formula:

 Expected value (EV) = (First possible outcome x Likelihood of outcome) + (Second possible outcome x
Likelihood of outcome) - Cost

Calculate the expected value by multiplying both possible outcomes by the likelihood that each outcome will occur
and then adding those values. You’ll also need to subtract any initial costs from your total.

5. Evaluate outcomes

Once you have your expected outcomes for each decision, determine which decision is best for you based on the
amount of risk you’re willing to take. The highest expected value may not always be the one you want to go for.
That’s because, even though it could result in a high reward, it also means taking on the highest level of project risk.

Keep in mind that the expected value in decision tree analysis comes from a probability algorithm. It’s up to you and
your team to determine how to best evaluate the outcomes of the tree.

Q6. Discuss the significance and scope of operation research in modern management.

Ans. Scope of Operation Research

In recent years of organized development, OR has entered successfully in many different areas of research. It is
useful in the following various important fields

In agriculture

With the sudden increase of population and resulting shortage of food, every country is facing the problem of

 Optimum allocation of land to a variety of crops as per the climatic conditions

 Optimum distribution of water from numerous resources like canal for irrigation purposes

Hence there is a requirement of determining best policies under the given restrictions. Therefore a good quantity of
work can be done in this direction.

In finance

In these recent times of economic crisis, it has become very essential for every government to do a careful planning
for the economic progress of the country. OR techniques can be productively applied

 To determine the profit plan for the company

 To maximize the per capita income with least amount of resources

 To decide on the best replacement policies, etc.

In industry

If the industry manager makes his policies simply on the basis of his past experience and a day approaches when he
gets retirement, then a serious loss is encounter ahead of the industry. This heavy loss can be right away
compensated through appointing a young specialist of OR techniques in business management. Thus OR is helpful
for the industry director in deciding optimum distribution of several limited resources like men, machines, material,
etc. to reach at the optimum decision.

In marketing

With the assistance of OR techniques a marketing administrator can decide upon

 Where to allocate the products for sale so that the total cost of transportation is set to be minimum

 The minimum per unit sale price

 The size of the stock to come across with the future demand

 How to choose the best advertising media with respect to cost, time etc.?

 How, when and what to buy at the minimum likely cost?

In personnel management

A personnel manager can utilize OR techniques

 To appoint the highly suitable person on minimum salary

 To know the best age of retirement for the employees

 To find out the number of persons appointed in full time basis when the workload is seasonal

In production management

A production manager can utilize OR techniques

 To calculate the number and size of the items to be produced

 In scheduling and sequencing the production machines

 In computing the optimum product mix

 To choose, locate and design the sites for the production plans

In L.I.C

OR approach is also applicable to facilitate the L.I.C offices to decide

 What should be the premium rates for a range of policies?

 How well the profits could be allocated in the cases of with profit policies?

Role of Operations Research in Decision-Making

The Operation Research may be considered as a tool which is employed to raise the efficiency of management
decisions. OR is the objective complement to the subjective feeling of the administrator (decision maker). Scientific
method of OR is used to comprehend and explain the phenomena of operating system.

The benefits of OR study approach in business and management decision making may be categorize as follows

Better control

The management of large concerns finds it much expensive to give continuous executive supervisions over routine
decisions. An OR approach directs the executives to dedicate their concentration to more pressing matters. For
instance, OR approach handles production scheduling and inventory control.

Better coordination

Sometimes OR has been very helpful in preserving the law and order situation out of disorder. For instance, an OR
based planning model turns out to be a vehicle for coordinating marketing decisions with the restrictions forced on
manufacturing capabilities.
Better system

OR study is also initiated to examine a particular problem of decision making like setting up a new warehouse. Later
OR approach can be more developed into a system to be employed frequently. As a result the cost of undertaking
the first application may get better profits.

Better decisions

OR models regularly give actions that do enhance an intuitive decision making. Sometimes a situation may be so
complex that the human mind can never expect to assimilate all the significant factors without the aid of OR and
computer analysis.

Q8. Write the algorithm of simplex method.

Ans. The Simplex Method or Simplex Algorithm is used for calculating the optimal solution to the linear
programming problem. In other words, the simplex algorithm is an iterative procedure carried systematically to
determine the optimal solution from the set of feasible solutions.

Firstly, to apply the simplex method, appropriate variables are introduced in the linear programming problem, and
the primary or the decision variables are equated to zero. The iterative process begins by assigning values to these
defined variables. The value of decision variables is taken as zero since the evaluation in terms of the graphical
approach begins with the origin. Therefore, x1 and x2 is equal to zero.

The decision maker will enter appropriate values of the variables in the problem and find out the variable value that
contributes maximum to the objective function and removes those values which give undesirable results. Thus, the
value of the objective function gets improved through this method. This procedure of substitution of variable value
continues until any further improvement in the value of the objective function is possible.

Following two conditions need to be met before applying the simplex method:

1. The right-hand side of each constraint inequality should be non-negative. In case, any linear programming
problem has a negative resource value, then it should be converted into positive value by multiplying both
the sides of constraint inequality by “-1”.

2. The decision variables in the linear programming problem should be non-negative.

Thus, the simplex algorithm is efficient since it considers few feasible solutions, provided by the corner points, to
determine the optimal solution to the linear programming problem.

Q9. Define operation research. Discuss its uses in management.

Ans. Operations research is a subfield of applied mathematics that uses advanced mathematical principles or
analytical methods to solve the problems that business leaders and managers often experience. It encourages
businesspeople to use advanced analytical tools to make more informed and effective decisions for organizations.
This type of research has a variety of modern uses in business, and it uses data mining, statistical analysis and
mathematical modelling to formulate solutions to a wide variety of problems.

The problems it aims to solve may include scheduling, automation, routing, project planning, supply chain
management, transportation or network optimization issues. The operations research process involves considering
the different aspects of a specific problem individually and solving them using a defined set of steps. These steps
may include:

1. Identifying a problem that needs solving: The first step involves determining the problem that requires
solving, whether it's an internal or external problem.

2. Determining the constraints: After identifying the problem, it's necessary to determine the constraints or
limitations that are necessary for the solution to include.
 3. Constructing a model based on the problem: After identifying the variables involved, it's possible to develop
a cohesive mathematical model based on that specific problem that also accounts for the constraints.

4. Incorporating data into the model: To create solutions, it's useful to incorporate each additional piece of
relevant data into the model.

5. Testing each potential solution: After developing a set of solutions, it's beneficial to use the model to
analyse the success of each solution and determine which is the most effective.

6. Implementing the solution: The final step in the process involves implementing the solution within the
organization and revaluating it to ensure that it solves the problem adequately.

The application areas of operation research which used in management are

1. Allocation and Distribution in Projects:

(I) Optimal allocation of resources such as men materials machines, time and money to projects.

(ii) Determination and deployment of proper workforce.

(iii) Project scheduling, monitoring and control.

2. Production and Facilities Planning:

(I) Factory size and location decision.

(ii) Estimation of number of facilities required.

(iii) Preparation of forecasts for the various inventory items and computation of economic order quantities and
reorder levels.

(iv) Scheduling and sequencing of production runs by proper allocation of machines.

(v) Transportation loading and unloading,

(vi) Warehouse location decision.

(vii) Maintenance policy decisions.

3. Programmes Decisions:

(i) What, when and how to purchase to minimize procurement cost.

(ii) Bidding and replacement policies.

4. Marketing:

(i) Advertising budget allocation.

(ii) Product introduction timing.

(iii) Selection of advertising media.

(iv) Selection of product mix.

(v) Customer’s preference of size, colour and packaging of various products.

5. Organization Behaviour:

(i) Selection of personnel, determination of retirement age and skills.

(ii) Recruitment policies and assignment of jobs.

(iii) Recruitment of employees.

(iv) Scheduling of training programs.

6. Finance:

(i) Capital requirements, cash flow analysis.

(ii) Credit policies, credit risks etc.

(iii) Investment decision.

(iv) Profit plan for the company.

7. Research and Development:

(i) Product introduction planning.

(ii) Control of R&D projects.

(iii) Determination of areas for research and development.

(iv) Selection of projects and preparation of their budgets.

(v) Reliability and control of development projects thus it may be concluded that operation research can be widely
utilized in management decisions and can also be used as corrective measure.

Q10. Define game theory also define pure strategies and mixed strategies.

Ans. The game theory is said to be the science of strategies which comes under the probability distribution. It
determines logical as well as mathematical actions that should be taken by the players in order to obtain the best
possible outcomes for themselves in the games. The games studied in game theory may range from chess to tennis
and from child-rearing to takeovers. But there is one thing common that such an array of games is interdependent,
i.e. outcome for each player depends upon the strategies of all.

In other words, game theory deals with mathematical models of cooperation and conflicts between rational
decision-makers. Game theory can be defined as the study of decision-making in which the players must make
strategies affecting the interests of other players.

Mixed strategies are usually in the realm of Game against Nature as events are speculative, that is which are with
probabilities. For example if outcomes are dependent on coin tosses, then Game proceeds in the Probabilistic values.

Pure strategies are those with deterministic outcomes. Nash Games fall into this category as outcomes are all known
apriori or beforehand and loses to outcomes are all studied before Game begins. Like Nash games happen in
negotiations, where each party makes their choices based on their perception of minimal loses and maximum gains.
So, if 2 players are involved in a Nash game, Player As choices are on x axis and Bs on y axis. The choices can happen
at any point on a curve connecting maximum gain of A and maximum gain for B. So if A makes max gain then that
means B has forfeited any gain for himself by accepting maximum loses, which is irrational games or altruistic games
per se, which seldom happen in the realm of Materials. Similarly for B if he max gain outcomes. So these 2 points
when connected with a curve, then that curve will show the different trade-offs each make in reaching an
equilibrium.