Multi-criteria decision making helps tackle complex problems with multiple, often conflicting factors. It's a key tool in prescriptive analytics, allowing managers to systematically evaluate options and make informed choices in uncertain situations.

This approach involves identifying criteria, prioritizing them, and using methods like weighted scoring to assess alternatives. It also considers stakeholder preferences and uses sensitivity analysis to test the robustness of recommendations, ensuring more reliable decision-making processes.

Multi-criteria decision-making

Identifying criteria for complex decisions

• Complex decisions often involve multiple, sometimes conflicting, criteria that need to be considered simultaneously to reach an optimal solution
• Criteria are the factors, attributes, or objectives that are relevant to the decision problem and used to evaluate the desirability of alternatives
• Identifying criteria involves brainstorming, research, and stakeholder input to determine the most important factors influencing the decision outcome
• Criteria should be:
  • Complete: Covering all important aspects
  • Operational: Measurable and meaningful
  • Decomposable: Can be broken down into sub-criteria if needed
  • Non-redundant: Avoiding double-counting of similar factors
  • Minimal: Keeping the number of criteria manageable

Prioritizing criteria based on importance

• Prioritizing criteria assesses their relative importance to the decision-maker(s) and stakeholders
• Methods for prioritizing criteria include:
  • Pairwise comparison: Decision-makers judge the importance of each criterion relative to others in a series of one-to-one comparisons (analytic hierarchy process)
  • Swing weighting: Considers both the importance of a criterion and the range of differences in the alternatives' performance on that criterion
  • Direct rating: Assigning weights or scores to criteria on a predetermined scale (1-5, 1-100)
  • Point allocation: Distributing a fixed number of points among criteria based on their perceived importance
• The resulting weights reflect the relative priority of each criterion in the decision-making process

Evaluating alternatives

Multi-criteria decision-making (MCDM) methods

• MCDM methods provide structured approaches to evaluate alternatives on multiple criteria and determine the best option(s)
• Common MCDM methods include:
  • Weighted sum model (WSM): Calculates an overall score for each alternative by multiplying its performance on each criterion by the criterion's weight and summing these weighted scores
  • Analytic hierarchy process (AHP): Uses pairwise comparisons to determine criteria weights and alternative preferences, synthesizing these judgments to derive overall priority scores
  • Outranking methods (ELECTRE, PROMETHEE): Compare alternatives pairwise on each criterion to determine preference relations, using concordance and discordance indexes to model decision-maker preferences
  • Compromise programming: Identifies the alternative closest to an ideal solution by minimizing the distance between the alternative's criteria values and the optimal values
  • Technique for Order Preference by Similarity to Ideal Solution (TOPSIS): Ranks alternatives based on their relative closeness to the positive ideal solution and distance from the negative ideal solution in a multi-dimensional criteria space

Applying weighted scoring models

• Weighted scoring models assign weights to criteria to reflect their relative importance and calculate overall scores for alternatives based on their weighted performance
• Steps in applying weighted scoring models:
  1. Define criteria and alternatives
  2. Determine criteria weights based on stakeholder preferences (direct rating, point allocation, pairwise comparison)
  3. Score alternatives' performance on each criterion using a standard scale (1-5, 1-100)
  4. Calculate weighted scores by multiplying weights and scores for each criterion and alternative
  5. Sum weighted scores to obtain an overall score for each alternative
  6. Rank alternatives based on their overall scores
• Examples of weighted scoring models in practice include:
  • Project prioritization: Evaluating potential projects based on criteria like strategic fit, financial return, risk, and resource requirements
  • Vendor selection: Comparing suppliers based on factors such as cost, quality, delivery time, and customer service

Stakeholder preferences in decision-making

Incorporating stakeholder preferences

• Stakeholder preferences represent the relative importance of different criteria to various individuals or groups affected by the decision
• Methods for eliciting stakeholder preferences:
  • Direct rating: Asking stakeholders to assign weights or scores to criteria on a predetermined scale
  • Point allocation: Having stakeholders distribute a fixed number of points among criteria based on their perceived importance
  • Pairwise comparison: Asking stakeholders to judge the relative importance of criteria in a series of one-to-one comparisons
• Stakeholder preferences can be incorporated into the decision model by using their input to determine criteria weights

Aggregating individual preferences in group decision-making

• Group decision-making often requires aggregating individual stakeholder preferences into a collective weighting
• Approaches for aggregating preferences include:
  • Arithmetic mean: Calculating the average weight for each criterion across all stakeholders
  • Geometric mean: Taking the nth root of the product of n stakeholders' weights for each criterion
  • Consensus-building: Facilitating discussion and negotiation among stakeholders to reach agreement on criteria weights
• The choice of aggregation method depends on factors such as the level of stakeholder agreement, the desired balance between individual and group preferences, and the decision-making context

Sensitivity analysis for decisions

Assessing robustness of decision recommendations

• Sensitivity analysis assesses how changes in the inputs (criteria weights and alternative scores) affect the outputs (alternative rankings) of a multi-criteria decision model
• It helps determine the robustness of the model's recommendations and identifies critical factors that significantly impact the decision outcome
• Types of sensitivity analysis:
  • One-way sensitivity analysis: Varies one input parameter at a time while holding others constant, plotting the effect on alternative scores or rankings
    • Reveals influential criteria weights or performance scores
    • Identifies thresholds where the preferred alternative changes
  • Multi-way sensitivity analysis: Varies multiple input parameters simultaneously to explore their joint effect on decision recommendations
  • Scenario analysis: Compares the model's results under different sets of weights or scores representing plausible future scenarios or stakeholder perspectives

Integrating sensitivity analysis into the decision-making process

• Sensitivity analysis should be an integral part of the decision-making process to:
  • Enhance understanding of the decision problem and the relationships between inputs and outputs
  • Stimulate critical thinking about the assumptions, uncertainties, and value judgments underlying the model
  • Provide a basis for refining the model, gathering additional information, or exploring alternative scenarios
  • Build confidence in the decision recommendations by demonstrating their robustness or identifying areas for further analysis
• Examples of sensitivity analysis in practice:
  • Investment decisions: Analyzing the sensitivity of financial metrics (NPV, IRR) to changes in key assumptions like discount rates, growth rates, or market conditions
  • Environmental policy: Examining how different stakeholder weights or performance scores affect the ranking of policy options for reducing greenhouse gas emissions