. 1.

How do decision models assist managers in making effective and data-driven

decisions?
Decision models help managers by providing a structured way to solve problems using data
and logic. They allow better analysis of options, outcomes, and risks. For example:
• Operations: A model can help schedule production to meet demand with minimal
cost.
• Finance: Forecasting cash flow helps in budgeting and investment planning.
• Marketing: Customer segmentation models help target the right audience.
• HR: Predictive models help in hiring by analyzing candidate performance data.
These models improve accuracy and support smarter decisions.

2. Application areas of Decision Models in Management

Decision models are used across different business functions:
• Supply Chain: Optimize inventory and delivery routes.
• Finance: Portfolio optimization and risk analysis.
• Marketing: Predict customer behavior and plan promotions.
• Operations: Resource allocation and production planning.
• HR: Workforce planning and performance analysis.
For example, Amazon uses models to manage warehouses, and banks use them to detect
fraud.

3. Difference between structured and unstructured decisions; use in semi-structured

decisions
• Structured decisions: Repetitive and routine, like reordering stock. Can be
automated.
• Unstructured decisions: Complex, with no clear process, like launching a new
product.
• Semi-structured decisions: A mix of both, such as pricing strategy.
Decision models help with semi-structured decisions by analyzing part of the problem using
data, while managers use judgment for the rest.

4. Use of Linear Programming (LPP) in business and two real-life applications

LPP is used to maximize or minimize objectives (like profit or cost) under resource limits.
Applications:
1. Production: A factory uses LPP to decide how many units of each product to make to
get maximum profit with limited labor and materials.
2. Supply Chain: A logistics company uses LPP to minimize transportation cost while
meeting delivery demands.
LPP helps in resource optimization.

5. Formulate a Linear Programming Problem

A company makes Product A and Product B. Each A needs 2 hours of labor, B needs 3 hours.
Total labor available is 120 hours. Profit is $40 for A, $50 for B.
Formulation: Let
x = units of A,
y = units of B.
Objective: Maximize Profit = 40x + 50y
Subject to:
2x + 3y ≤ 120 (labor constraint)
x ≥ 0, y ≥ 0 (non-negativity)

6. Assumptions and limitations of LPP

Assumptions:
• Linear relationships.
• Resources are limited and known.
• No uncertainty.
• Variables can be split (divisible).
Limitations:
• Real-world problems are not always linear.
• Assumes all data is certain.
• Cannot handle complex human factors.
• Solutions may not be practical if values must be whole numbers.

6. Explain the assumptions and limitations of Linear Programming in real-world

scenarios.
Assumptions of Linear Programming:
 1. Linearity: The objective function and constraints must be linear combinations of
decision variables.
2. Certainty: All input values (coefficients of variables, resource availability, etc.) are
known and constant.
3. Additivity: The total effect is the sum of individual effects, without interaction among
variables.
4. Divisibility: Variables can take any fractional values; assumes continuous production
(e.g., 2.5 units is possible).
5. Non-negativity: Decision variables cannot be negative, as producing negative
quantities is illogical.
Limitations of LP:
• Real-world complexity: Not all relationships are linear; real systems often involve
nonlinear dynamics.
• Integer constraints: LP cannot handle situations that require whole numbers (e.g.,
number of machines or employees).
• Lack of flexibility: It assumes fixed resource availability and does not consider
sudden changes.
• Ignores qualitative factors: It does not incorporate human behavior, brand value, or
market sentiment.
Example: In production, LP may suggest making 3.6 chairs, which is not possible — integer
programming is needed.

7. A company must choose between three investment options under different economic
conditions. Construct a payoff table and apply the Maximin and Maximax criteria.
Payoff Table (in ₹ Lakhs):

Investment Boom Normal Recession

A 120 80 30

B 100 90 60

C 150 70 20

Maximin Criterion (Pessimist):

• Find the minimum payoff in each row:
o A: 30, B: 60, C: 20
• Choose the maximum of these minimums = B (60)
Maximax Criterion (Optimist):
 • Find the maximum payoff in each row:
o A: 120, B: 100, C: 150
• Choose the maximum of these values = C (150)
Conclusion:
• A cautious manager would choose B using Maximin.
• A risk-taking manager would choose C using Maximax.

8. Explain the Minimax Regret and Laplace criteria for decision-making under
uncertainty. Provide a business scenario to illustrate.
Minimax Regret Criterion:
• Regret = difference between the best payoff and actual payoff in each state.
• Find the maximum regret for each decision.
• Choose the decision with the smallest maximum regret.
Laplace Criterion:
• Assumes all outcomes (states of nature) are equally likely.
• Calculate the average payoff for each alternative.
• Choose the decision with the highest average payoff.
Example: A garment retailer unsure about winter demand.
• Minimax Regret: Helps minimize the worst-case regret of stocking too much or too
little.
• Laplace: If the manager assumes mild, normal, and harsh winters are equally
probable, they can take the average sales from each and decide the order quantity
accordingly.
These criteria are used when no probabilities are available for future outcomes.

9. Discuss the relevance of Queuing Theory and Sequencing in business decision-

making. Support your answer with examples.
Queuing Theory:
• Deals with waiting lines and helps manage service systems efficiently.
• It is used to determine:
o Number of service counters required.
o Average waiting time and system capacity.
Example: In a bank, queuing models help decide how many tellers to deploy to keep wait
times under 10 minutes.
Sequencing:
• Refers to determining the best order in which tasks should be done.
• Objective: Minimize total processing time, delays, or cost.
Example: In a manufacturing unit, sequencing ensures that jobs are completed in the right
order to reduce machine idle time.
Importance:
• Helps in customer satisfaction by reducing wait times.
• Improves operational efficiency and resource utilization.
• Supports better scheduling in industries like healthcare, hospitality, and retail.

10. A ticket counter receives 5 customers per hour and serves 7 customers per hour.
Calculate Ls, Lq, Ws, and Wq using M/M/1 Queuing Model.
Given:
• Arrival rate (λ) = 5 per hour
• Service rate (μ) = 7 per hour
Formulas:
• Ls (Expected number in system) = λ / (μ - λ) = 5 / (7 - 5) = 2.5
• Lq (Expected number in queue) = λ² / [μ(μ - λ)] = 25 / (7×2) = 1.79
• Ws (Time in system) = 1 / (μ - λ) = 1 / 2 = 0.5 hours
• Wq (Time in queue) = λ / [μ(μ - λ)] = 5 / (7×2) = 0.36 hours
Interpretation:
• On average, 2.5 customers are in the system.
• Each customer spends around 30 minutes in the system and waits ~21.6 minutes in
queue.
• This helps in workforce and resource planning to reduce wait time.

11. Explain the difference between FCFS (First-Come-First-Served) and SPT (Shortest
Processing Time) sequencing rules. When is each more effective?
FCFS (First-Come-First-Served):
• Jobs are processed in the order of arrival.
 • Simple, fair, and easy to implement.
• Best used in service sectors like hospitals, banks, and retail where fairness is
important.
SPT (Shortest Processing Time):
• Jobs with the shortest duration are processed first.
• Minimizes average waiting and completion time.
• Best used in manufacturing and job shops to improve efficiency.
Comparison Table:

Feature FCFS SPT

Priority Arrival time Job duration

Efficiency Moderate High (reduces total processing time)

Fairness High Low

Application Service industries Production environments

12. What are the steps to solve a transportation problem using Vogel’s Approximation
Method (VAM)? Why is it more efficient than the North-West Corner Rule?
Steps in VAM:
1. Calculate penalty for each row and column: Difference between the two lowest costs.
2. Identify the row/column with the highest penalty.
3. Allocate as much as possible to the lowest-cost cell in that row/column.
4. Adjust supply and demand, strike out row/column if satisfied.
5. Repeat until all allocations are made.
Why VAM is Better than NWCR:
• NWCR starts from the top-left corner and ignores costs, leading to high initial costs.
• VAM considers cost differences and usually gives a better starting solution, closer
to optimal.
• Reduces iterations needed in optimization.
Example: In logistics, using VAM can help a company minimize total shipping cost across
multiple routes and warehouses.
13. Solve the following assignment problem to maximize profit: [Insert cost matrix in
actual paper].
Steps (assuming matrix is given):
1. Convert to Cost Matrix (if maximizing profit):
o Subtract each value from the highest value in the matrix to create a
minimization problem.
2. Apply Hungarian Method:
o Subtract row minimum from each row.
o Subtract column minimum from each column.
o Cover all zeros using the minimum number of lines.
o If the number of lines = number of rows, optimal solution is reached.
o If not, adjust the matrix and repeat.
3. Assign tasks to zero cells without conflicts.
Result: The final assignment gives the combination that maximizes total profit.
Use this step-by-step process in the exam once the matrix is provided.

14. What is simulation in decision models? Discuss its use in project management or
inventory management with a real-life example.
Simulation is a technique used to imitate the operations of a real-world system. It allows
decision-makers to observe how a system behaves under different conditions by running
virtual experiments.
Use in Project Management:
• Monte Carlo Simulation helps forecast project completion time by considering
uncertainty in task durations.
• Identifies probability of delay and helps in risk mitigation.
Example: A construction firm simulates weather delays to estimate buffer times for project
deadlines.
Use in Inventory Management:
• Simulates demand fluctuations to determine reorder levels and safety stock.
• Helps in reducing stockouts and overstocking.
Example: A supermarket uses simulation to predict demand during festive seasons to
optimize stock levels.
Simulation improves planning and reduces risks in uncertain environments.
15. Explain how Game Theory can be used in competitive decision-making. Illustrate
with a two-player zero-sum game.
Game Theory studies strategic interactions between two or more players (companies,
individuals) where each player’s payoff depends on the actions
of others.
Use in Business:
• Helps in pricing strategies, advertising decisions, or launching new products.
• Useful when competitors’ actions affect your outcomes.
Zero-Sum Game:
• One player's gain = another player's loss.
• Players try to maximize their minimum gain (Minimax strategy).
Example:

Competitor B: High Price Competitor B: Low Price

A: High Price (40, 40) (10, 60)

A: Low Price (60, 10) (30, 30)

• Firm A and B must decide price strategies.

• They analyze payoffs and try to select strategies to maximize their outcome assuming
the worst-case move from the competitor.
Conclusion: Game theory supports strategic decisions in competitive environments by
predicting opponents’ responses and choosing optimal strategies.

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