Quantitative techniques used in advance decision making

Quantitative techniques play a critical role in advanced decision-making by providing a

structured, data-driven approach to analyzing and solving complex problems. Here are some
key quantitative techniques used in advanced decision-making:

1. Linear Programming (LP)

 Purpose: Optimizes a specific objective, like maximizing profit or minimizing cost,

subject to constraints.
 Applications: Resource allocation, production scheduling, and logistics.
 Techniques: Simplex method, duality theory, and sensitivity analysis.

2. Decision Trees and Decision Analysis

 Purpose: Helps visualize and analyze the outcomes of different decision paths,
especially under uncertainty.
 Applications: Risk assessment, investment decision-making, and project
management.
 Techniques: Expected monetary value (EMV), utility theory, and sensitivity analysis
on probabilities.

3. Simulation (Monte Carlo)

 Purpose: Models complex systems and evaluates the probability of various outcomes
by simulating a process multiple times.
 Applications: Financial forecasting, risk management, supply chain management.
 Techniques: Monte Carlo simulations, scenario analysis, and risk analysis.

4. Forecasting and Time Series Analysis

 Purpose: Predicts future trends based on historical data.

 Applications: Sales forecasting, stock market analysis, economic forecasting.
 Techniques: Moving averages, exponential smoothing, autoregressive integrated
moving average (ARIMA).

5. Queuing Theory

 Purpose: Analyzes waiting lines to improve service efficiency.

 Applications: Call centers, hospital emergency rooms, and manufacturing lines.
 Techniques: Poisson and exponential distributions, Markov processes.

6. Game Theory

 Purpose: Analyzes strategic interactions where the outcome depends on the actions of
multiple decision-makers.
 Applications: Competitive business strategies, auction design, and pricing.
 Techniques: Nash equilibrium, dominant strategies, zero-sum games, and mixed
strategies.

7. Network Models

 Purpose: Optimizes routes, flows, and connections in networks.

  Applications: Transportation, logistics, project management.
 Techniques: Shortest-path algorithms, maximum flow problems, critical path method
(CPM), and PERT (Program Evaluation Review Technique).

8. Regression Analysis

 Purpose: Examines relationships between variables to predict or understand their

association.
 Applications: Sales prediction, risk assessment, econometrics.
 Techniques: Simple and multiple regression, logistic regression, least squares
estimation.

9. Data Envelopment Analysis (DEA)

 Purpose: Measures the relative efficiency of decision-making units (e.g., departments

or companies).
 Applications: Performance benchmarking, resource allocation.
 Techniques: Efficiency frontier analysis using input-output data.

10. Inventory Control Models

 Purpose: Optimizes inventory levels to balance costs with service levels.

 Applications: Supply chain management, retail management.
 Techniques: Economic order quantity (EOQ), reorder point model, and just-in-time
(JIT) inventory.

11. Risk Analysis and Management

 Purpose: Identifies and quantifies risks to inform decision-making.

 Applications: Financial portfolios, project management, operations.
 Techniques: Value at Risk (VaR), scenario analysis, and sensitivity analysis.

12. Multicriteria Decision Analysis (MCDA)

 Purpose: Evaluates options based on multiple criteria to find the optimal solution.
 Applications: Policy decisions, resource allocation.
 Techniques: Analytic hierarchy process (AHP), weighted scoring models, and
outranking methods.

13. Cluster Analysis

 Purpose: Groups data points or decision units into clusters based on similarity.
 Applications: Market segmentation, customer profiling, and pattern recognition.
 Techniques: K-means clustering, hierarchical clustering.

These techniques, often used in combination, enable decision-makers to approach complex

scenarios systematically, enabling a higher degree of precision, risk management, and
outcome predictability.

Multi criteria decision making

Multi-Criteria Decision Making (MCDM), also known as Multi-Criteria Decision Analysis

(MCDA), is a set of techniques used for evaluating and prioritizing options based on
multiple, often conflicting criteria. It is especially useful when decisions are complex,
involving several quantitative and qualitative factors that need to be balanced against each
other. MCDM is commonly used in various fields, including business, engineering,
environmental management, and public policy.

Key Steps in Multi-Criteria Decision Making

1. Define the Decision Problem:

o Clearly identify the objectives, decision criteria, and constraints of the
problem.
o Define the alternatives available for evaluation.
2. Identify and Structure Criteria:
o List the relevant criteria that influence the decision. Criteria can be
quantitative (e.g., cost, time) or qualitative (e.g., user satisfaction,
sustainability).
o Structure these criteria hierarchically if necessary (e.g., breaking down main
criteria into sub-criteria).
3. Weight the Criteria:
o Assign weights to each criterion based on their relative importance. This step
may involve decision-makers or stakeholders to ensure that the weightings
reflect true preferences.
4. Evaluate the Alternatives:
o Score each alternative against the criteria. Scoring may involve qualitative
judgments, quantitative data, or both.
5. Aggregate Scores and Rank Alternatives:
o Combine the scores based on criteria weights to produce an overall score for
each alternative.
o Rank the alternatives based on the aggregated scores to determine the best
option.
6. Conduct Sensitivity Analysis:
o Test how changes in criteria weights or scores affect the outcome to assess the
robustness of the decision.

Common Techniques in Multi-Criteria Decision Making

1. Analytic Hierarchy Process (AHP)

o Description: AHP breaks down a complex decision into a hierarchy of goals,
criteria, sub-criteria, and alternatives. Pairwise comparisons are used to weigh
criteria and evaluate alternatives, which are then aggregated to produce
rankings.
o Applications: Project prioritization, supplier selection, resource allocation.
2. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)
o Description: TOPSIS ranks alternatives based on their distance from an ideal
solution (best criteria values) and a nadir (worst criteria values). The
alternative closest to the ideal solution and furthest from the nadir is preferred.
o Applications: Risk assessment, financial analysis, environmental
management.
3. Weighted Sum Model (WSM)
o Description: WSM is a straightforward method where scores of alternatives
are multiplied by their criteria weights, and the weighted scores are summed to
provide an overall score.
o Applications: Resource allocation, performance evaluation, and project
selection.
 4. Weighted Product Model (WPM)
o Description: WPM multiplies criteria scores by weights (raised to the power
of the weights) instead of summing them, making it suitable for criteria
measured in different units.
o Applications: Economic analysis, financial decision-making.
5. Multi-Attribute Utility Theory (MAUT)
o Description: MAUT provides a utility score for each alternative based on the
decision maker's preferences and risk tolerance. Utility functions are
developed to evaluate each criterion, and the overall utility is calculated.
o Applications: Policy analysis, environmental impact assessment.
6. PROMETHEE (Preference Ranking Organization Method for Enrichment
Evaluation)
o Description: PROMETHEE ranks alternatives by comparing them on each
criterion using a preference function. It evaluates the strengths and weaknesses
of each alternative without requiring strict weighting.
o Applications: Strategic planning, water resource management.
7. ELECTRE (Elimination and Choice Expressing Reality)
o Description: ELECTRE uses pairwise comparisons to rank alternatives,
emphasizing criteria that are more important or whose differences between
alternatives are significant.
o Applications: Environmental planning, project selection.

Advantages of MCDM

 Holistic Evaluation: Takes multiple factors into account, providing a more

comprehensive analysis than single-criteria methods.
 Transparency: Provides a structured approach for decision-making, making it easier
to understand why certain options were chosen.
 Flexibility: Allows for both quantitative and qualitative criteria, adapting to a wide
range of decision contexts.
 Stakeholder Involvement: Often includes stakeholder input, making decisions more
inclusive and aligned with preferences.

Challenges of MCDM

 Complexity: Requires detailed criteria selection, weighting, and scoring, which can
be time-consuming and complex.
 Subjectivity: Criteria weights and scores may reflect subjective judgments, leading to
potential biases.
 Data Requirements: Reliable data is needed to assess and compare alternatives,
which may not always be available.

MCDM techniques help decision-makers navigate complex situations by clarifying trade-

offs, structuring decisions, and evaluating options objectively, making it a valuable tool for
strategic decision-making across various fields.

Analytic hierarchic processing

The Analytic Hierarchy Process (AHP) is a popular decision-making technique developed

by Thomas Saaty in the 1970s. AHP is widely used for making complex decisions where
multiple criteria are involved. It helps break down a decision problem into a hierarchy,
making it easier to structure, analyze, and evaluate. AHP involves assigning weights to
criteria based on their importance and then using pairwise comparisons to score alternatives
against these criteria.

Key Steps in AHP

1. Define the Problem and Objective

o Identify the primary goal or objective of the decision.
o Define the criteria and sub-criteria that impact this decision.
o Identify the decision alternatives to be evaluated.
2. Structure the Decision Hierarchy
o Construct a hierarchy that visually represents the problem.
o The hierarchy usually has multiple levels:
 Level 1: Overall goal (e.g., "Select the Best Supplier").
 Level 2: Main criteria affecting the decision (e.g., cost, quality,
reliability).
 Level 3: Sub-criteria (optional), breaking down main criteria further
(e.g., for quality: durability, performance).
 Level 4: Decision alternatives (e.g., Supplier A, Supplier B, Supplier
C).
3. Pairwise Comparison of Criteria
o Compare each criterion with every other criterion in terms of importance to
the goal.
o Assign a numerical value based on a scale (typically 1 to 9), where:
 1 means both criteria are equally important.
 3, 5, 7, and 9 represent moderate, strong, very strong, and absolute
importance, respectively.
 Reciprocal values (e.g., 1/3, 1/5) represent the inverse relationship
when one criterion is less important than the other.
4. Calculate Criteria Weights
o Use the pairwise comparison data to create a matrix and compute normalized
weights for each criterion.
o Weights are usually calculated by normalizing the values and taking the
average of each row or through eigenvalue calculations.
o This weighting reflects the relative importance of each criterion.
5. Pairwise Comparison of Alternatives within Each Criterion
o For each criterion, perform pairwise comparisons of the alternatives.
o Rate each alternative relative to the others for that specific criterion.
o Compute a score for each alternative based on these comparisons.
6. Calculate Overall Scores for Each Alternative
o Combine the scores of each alternative by multiplying them by the criteria
weights and summing them up.
o The result gives an overall score for each alternative, indicating its suitability
relative to the goal.
7. Check Consistency of Judgments
o AHP includes a Consistency Ratio (CR) to check if the comparisons are
consistent.
o If CR is below 0.10, the consistency is acceptable. If it is higher, the
comparisons may need to be revised to improve consistency.

Example of AHP Application

Let's say a company needs to choose between three suppliers based on three criteria: cost,
quality, and reliability.
 1. Hierarchy Construction: The goal (selecting the best supplier) is at the top, followed
by criteria (cost, quality, reliability), and finally, the alternatives (Supplier A, B, and
C).
2. Pairwise Comparison of Criteria: The company compares cost vs. quality, cost vs.
reliability, and quality vs. reliability. If cost is moderately more important than
quality, they might assign it a 3, and so on.
3. Weight Calculation: The comparisons yield weights for each criterion, say: 50% for
cost, 30% for quality, and 20% for reliability.
4. Comparing Alternatives for Each Criterion: For the "cost" criterion, Supplier A
may be preferred over Supplier B and C. This is repeated for quality and reliability.
5. Scoring and Ranking: Each alternative’s scores under each criterion are weighted
and summed to get an overall score.
6. Choosing the Best Alternative: The alternative with the highest score is the most
suitable choice.

Advantages of AHP

 Structured and Transparent: AHP breaks down a complex problem into

manageable parts, making the process transparent.
 Incorporates Subjective and Objective Factors: AHP allows for both quantitative
and qualitative criteria.
 Consistency Check: The consistency ratio provides a way to validate judgments.

Disadvantages of AHP

 Subjectivity: Pairwise comparisons can be subjective, potentially leading to biases.

 Complexity in Large Problems: AHP becomes less manageable as the number of
criteria and alternatives increases.
 Requires Careful Judgment: Incorrect judgments can lead to inconsistencies,
requiring recalibration.

Applications of AHP

 Supplier selection
 Project prioritization
 Policy-making
 Risk assessment
 Product development and portfolio management

In summary, AHP is a powerful tool for structured decision-making, helping decision-makers

focus on critical factors and quantitatively compare complex choices.

Using excel solver for optimization techniques

Excel Solver is a powerful tool in Microsoft Excel that can solve various types of
optimization problems, including linear programming, integer programming, and nonlinear
programming. It's commonly used for problems involving maximizing or minimizing an
objective (e.g., profit, cost, time) under specific constraints.

Here's how to use Excel Solver for optimization techniques, along with an example:

Steps to Use Excel Solver for Optimization

 1. Define the Decision Variables
o Identify the cells in Excel that will represent the decision variables. These are the
values that Excel Solver will adjust to find the optimal solution.

2. Set Up the Objective Function

o Create a cell for the objective function, which is the formula that you want to
maximize or minimize (e.g., total profit, cost).
o The objective function will typically depend on the decision variables.

3. Define Constraints
o List the constraints that affect the decision variables. These could include things like
budget limits, resource capacities, or minimum/maximum requirements.
o Enter these constraints in separate cells to reference them in Solver.

4. Open Excel Solver

o Go to the Data tab in Excel and select Solver. If you don’t see Solver, you may need
to enable it by going to File > Options > Add-Ins > Solver Add-In.

5. Set Up Solver Parameters

o Set Objective: Select the cell containing the objective function.
o To: Choose whether you want to maximize, minimize, or set the objective function
to a specific value.
o By Changing Variable Cells: Select the cells that represent the decision variables.
o Subject to the Constraints: Click on Add to define each constraint. For each
constraint, select the cell(s) representing it, set the relation (e.g., ≤, =, ≥), and specify
the constraint value.

6. Choose a Solving Method

o Solver offers three main methods:
 Simplex LP: Best for linear programming problems.
 GRG Nonlinear: For nonlinear problems.
 Evolutionary: For complex problems or problems involving non-smooth
functions.
o Choose Simplex LP if you’re working with linear programming.

7. Solve the Problem

o Click Solve. Solver will search for the optimal solution and display the results in a
dialog box.
o If Solver finds a solution, it will offer to keep the solution or restore the original
values. Choose to keep the solution to see the results.

8. Review the Solution

o After Solver completes, review the adjusted values for the decision variables and the
objective function.
o Check whether the solution meets all constraints.

Example of Using Excel Solver for Optimization

Suppose you want to maximize the profit from producing two products, A and B. You have
limited resources: labor and materials. The following example walks you through setting up
and solving this problem in Excel.
Problem Setup

 Objective: Maximize total profit.

 Decision Variables: Quantity of Product A and Product B to produce.
 Constraints:
o Labor hours available: 500 hours.
o Material available: 400 units.

Data Table Setup in Excel

Product A Product B Total

Profit per Unit $40 $30

Labor Required (hrs/unit) 10 5 ≤ 500 hours

Material Required (units/unit) 4 6 ≤ 400 units

1. Decision Variable Cells: Assign cells (say B5 and C5) for the quantity of Product A
and Product B.
2. Objective Function Cell: In cell D5, calculate total profit as:
o =B5 * 40 + C5 * 30

3. Constraint Cells:
o Labor Used: =B5 * 10 + C5 * 5 (in cell D6)
o Material Used: =B5 * 4 + C5 * 6 (in cell D7)

4. Set Up Solver:
o Set Objective: D5 (total profit cell).
o To: Maximize.
o By Changing Variable Cells: B5 and C5.
o Constraints:
 D6 (labor used) ≤ 500.
 D7 (material used) ≤ 400.

5. Solve:
o Choose Simplex LP as the solving method.
o Click Solve.

After solving, Solver will give you the optimal quantities of Product A and Product B to
maximize profit under the given constraints.

Tips for Using Solver

 Constraints: Ensure that all constraints are set up accurately, as incorrect constraints may
lead to infeasible solutions.
 Solver Results: If Solver can’t find a feasible solution, check if the constraints are overly
restrictive.
 Nonlinear Problems: Use GRG Nonlinear for optimization with nonlinear relationships, like
squared terms or other non-linear functions.

Excel Solver is a powerful tool for solving optimization problems and is highly versatile for
real-world applications in finance, production, and logistics