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Author: Ivchenko, Oleh Affiliation: Odessa National Polytechnic University Series: AI Portfolio Optimisation Year: 2025

Abstract #

The Decision Readiness Levels (DRL) framework prescribes one of five optimization strategies for each pharmaceutical portfolio segment, conditioned on that segment’s Decision Readiness Index (DRI) score. This paper provides a complete specification of DRL-1 through DRL-5: the conditions under which each level is appropriate, the optimization methods employed at each level, the mathematical formulations, and the implementation considerations. We demonstrate that the five-level taxonomy covers the full spectrum from information-constrained abstention (DRL-1) to sophisticated multi-objective AI optimization (DRL-5), providing a principled path from conservative to aggressive portfolio management as information conditions improve. Worked examples illustrate strategy selection and expected outcomes at each level.

1. Introduction #

Portfolio optimization has produced a rich body of methods: linear programming, mean-variance optimization, CVaR minimization, genetic algorithms, multi-objective evolutionary methods. What has been lacking is a principled framework for deciding which method is appropriate when. The common practice of selecting an optimization algorithm based on organizational habit, available software, or analyst preference — rather than on the actual information environment — is a significant source of portfolio management error.

The Decision Readiness Levels (DRL) framework addresses this gap. DRL maps DRI scores (as defined in Article 2) to five strategy tiers, each with a specific optimization algorithm, mathematical formulation, and applicability condition. The result is a decision tree that is explicit, auditable, and calibrated to information quality.

flowchart TD
    A[Portfolio Segment] --> B{Compute DRI Score}
    B -->DRI < 0.20| C[DRL-1: Abstention
Freeze allocations
Collect data]
    B -->|0.20 ≤ DRI < 0.40| D[DRL-2: Proportional Rebalancing
Ordinal ranking rules]
    B -->|0.40 ≤ DRI < 0.60| E[DRL-3: Linear Programming
Constrained LP optimization]
    B -->|0.60 ≤ DRI < 0.80| F[DRL-4: CVaR Optimization
Stochastic risk-aware LP]
    B -->DRI ≥ 0.80| G[DRL-5: Multi-Objective AI
NSGA-II + preference learning]
    C --> H[Monitor & Improve DRI]
    H --> B
    style C fill:#ffcccc
    style D fill:#ffe0cc
    style E fill:#fff4cc
    style F fill:#ccf0cc
    style G fill:#cce0ff

2. DRL-1: Abstention #

2.1 Trigger Condition #

DRL-1 applies when DRI < 0.20. At this level, information quality is so low that any optimization — however conservative — is more likely to degrade portfolio performance than improve it. The only rational strategy is to maintain current allocations unchanged.

2.2 Rationale #

The abstention decision is counterintuitive in a culture that equates action with competence. However, the operations research literature provides strong theoretical support: when the uncertainty set is unbounded or uncharacterizable, robust optimization degenerates and expected utility maximization is undefined. In practical terms: if you cannot reliably estimate demand, costs, or risks for a portfolio segment, any optimization model you build is fitting noise.

2.3 Implementation #

DRL-1 implementation requires:

• Freezing all allocation changes for the affected segments
• Initiating active data collection to improve DRI dimensions
• Setting a monitoring schedule to re-evaluate DRI at defined intervals
• Documenting the DRL-1 designation for audit purposes

DRL-1 is not permanent. The correct response to a DRL-1 designation is to identify which DRI dimensions are lowest and invest in improving them. Article 2 provides guidance on dimension-specific improvement strategies.

2.4 Example #

A pharmaceutical company managing orphan disease products in a conflict-affected region has DRI = 0.12 for this segment: R1 = 0.20 (most patient records inaccessible), R5 = 0.05 (distribution network destroyed), R3 = 0.10 (supplier status unknown). The HPF system designates DRL-1 and halts all optimization attempts while humanitarian data collection efforts proceed.

3. DRL-2: Proportional Rebalancing #

3.1 Trigger Condition #

DRL-2 applies when 0.20 ≤ DRI < 0.40. At this level, some reliable information is available but insufficient to support model-based optimization. Simple proportional rules can extract value without requiring reliable forecasts.

3.2 Mathematical Formulation #

The DRL-2 strategy applies a proportional rebalancing rule:

where is the allocation to product , is a simple rank-order estimate of relative performance (not a precise forecast), and is the total budget. Allocations are adjusted proportionally to relative performance rankings, subject to minimum and maximum bounds.

3.3 Key Properties #

DRL-2 does not require:

• Precise demand forecasts
• Accurate cost models
• Risk quantification

It requires only:

• Relative ranking of products by recent performance indicators
• Minimum and maximum allocation bounds
• Total budget

This minimal data requirement makes DRL-2 appropriate for high-uncertainty environments where some ordinal information is available but cardinal estimates are unreliable.

3.4 Example #

A segment with DRI = 0.33 (R1 = 0.65, R2 = 0.28, others low due to post-shock recovery) can be managed with DRL-2: products with the best recent sell-through ratios receive proportionally more allocation, without requiring precise forecast models.

4. DRL-3: Linear Programming #

4.1 Trigger Condition #

DRL-3 applies when 0.40 ≤ DRI < 0.60. At this level, demand forecasts and cost estimates are available with meaningful accuracy, supporting constrained linear optimization.

4.2 Mathematical Formulation #

Subject to:

where is the expected profit per unit for product , is the allocation, is the unit cost, is the total budget, and encode category-level constraints.

4.3 Data Requirements #

DRL-3 requires:

• Point estimates of demand (not distribution estimates — those come at DRL-4)
• Unit cost estimates with accuracy within ±15%
• Hard constraints (budget, storage capacity, regulatory minimums)

4.4 Risk Handling #

At DRL-3, risk is handled conservatively through constraint tightening: budget constraints are set at 90% of actual budget, minimum allocations are set slightly above regulatory minimums, and demand estimates are discounted by a fixed percentage (default 10%) to provide a buffer against forecast error. This approach is less sophisticated than DRL-4’s CVaR optimization but appropriate for the available information quality.

4.5 Example #

A mature OTC portfolio recovering from a supply disruption has DRI = 0.52: sufficient demand history is now available (6 months post-disruption), costs are known, regulatory status is clear, but market conditions remain somewhat uncertain. LP optimization identifies an allocation that increases expected profit by 8% over the status quo while respecting all operational constraints.

5. DRL-4: CVaR Optimization #

5.1 Trigger Condition #

DRL-4 applies when 0.60 ≤ DRI < 0.80. At this level, risk distributions are estimable with meaningful accuracy, supporting risk-aware optimization through Conditional Value at Risk (CVaR) minimization.

5.2 Mathematical Formulation #

where:

with being the loss under scenario , the confidence level (default 0.95), a risk aversion parameter, and the expected return.

Scenarios are generated from the historical demand distribution, augmented with stress scenarios corresponding to observed risk events in R3.

5.3 Data Requirements #

DRL-4 requires:

• Demand distributions (not just point estimates)
• Risk scenario catalog with occurrence probabilities
• Covariance structure of returns across portfolio segments

5.4 Practical Advantage #

CVaR optimization is particularly valuable when tail risks are material. A pharmaceutical portfolio exposed to supply concentration risk (few suppliers) or demand concentration risk (few therapeutic categories) has fat-tailed loss distributions that mean-variance approaches systematically underestimate. CVaR explicitly optimizes the tail, making it appropriate for pharmaceutical portfolios with structural fragility.

5.5 Example #

A specialty pharmaceutical portfolio has DRI = 0.71. Risk scenarios have been constructed from observed supply disruptions and demand shocks over the past three years. CVaR optimization at α = 0.95 identifies an allocation that reduces the expected shortfall in the worst 5% of scenarios by 23% while maintaining 97% of the expected return achievable with LP.

6. DRL-5: Multi-Objective AI Optimization #

6.1 Trigger Condition #

DRL-5 applies when DRI ≥ 0.80. At this level, information quality is sufficient to support multi-objective optimization with AI-generated preference models.

6.2 Mathematical Formulation #

DRL-5 employs a multi-objective evolutionary algorithm (MOEA) to generate the Pareto-optimal frontier across multiple objectives:

where objectives may include:

• Expected portfolio return
• Portfolio CVaR (tail risk)
• Supply chain resilience score
• Regulatory compliance buffer
• Strategic diversity index

The MOEA generates a set of Pareto-optimal solutions, which are then ranked using a learned preference model (trained on historical decision-maker choices) to select a preferred solution.

6.3 AI Integration #

At DRL-5, machine learning models contribute in three ways:

1. Demand forecasting: Deep learning models (LSTM or Transformer-based) provide distribution forecasts with uncertainty quantification.
2. Risk modeling: Anomaly detection and causal inference identify emerging risks before they manifest in standard metrics.
3. Preference learning: Inverse reinforcement learning infers decision-maker preferences from historical choices, enabling preference-aware Pareto solution selection.

6.4 Example #

A major portfolio segment covering high-volume chronic disease medications has DRI = 0.87 following a stable 18-month post-disruption period. DRL-5 optimization generates 2,400 Pareto-optimal solutions across four objectives. The preference learning model identifies a solution that achieves 94% of maximum expected return, 89% of minimum CVaR, and maximizes supply resilience — a combination that matches the decision-maker’s revealed preferences from the past 24 months.

graph LR
    subgraph DRL-1["DRL-1 (DRI < 0.20)"]
        A1[No optimization
Freeze status quo]
    end
    subgraph DRL2["DRL-2 (0.20–0.40)"]
        A2[Proportional
Rebalancing]
    end
    subgraph DRL3["DRL-3 (0.40–0.60)"]
        A3[Linear
Programming LP]
    end
    subgraph DRL4["DRL-4 (0.60–0.80)"]
        A4[CVaR Stochastic
Optimization]
    end
    subgraph DRL5["DRL-5 (DRI ≥ 0.80)"]
        A5[NSGA-II Multi-
Objective AI]
    end
    DRL-1 -->DRI improves| DRL2
    DRL2 -->DRI improves| DRL3
    DRL3 -->DRI improves| DRL4
    DRL4 -->DRI improves| DRL5
    DRL5 -->DRI drops| DRL4

7. Strategy Comparison and Selection Guidance #

Factor	DRL-1	DRL-2	DRL-3	DRL-4	DRL-5
Min DRI	—	0.20	0.40	0.60	0.80
Data requirement	None	Ordinal rankings	Point estimates	Distributions	Full uncertainty quant.
Computation time	Trivial	Seconds	Minutes	Hours	Hours–Days
Expected improvement	0%	3–8%	8–15%	12–22%	18–30%
Risk of backfiring	N/A	Low	Medium	Low (explicit risk)	Low (explicit risk)

Expected improvement figures are illustrative estimates from HPF-P pilot deployments and should be validated in specific organizational contexts.

xychart-beta
    title "Expected Portfolio Improvement by DRL Level"
    x-axis ["DRL-1", "DRL-2", "DRL-3", "DRL-4", "DRL-5"]
    y-axis "Expected Improvement (%)" 0 --> 35
    bar [0, 5.5, 11.5, 17, 24]
    line [0, 5.5, 11.5, 17, 24]

8. Conclusion #

The five-level DRL framework provides a complete and principled taxonomy for pharmaceutical portfolio optimization strategy selection. By mapping information quality (DRI) to optimization method (DRL), the framework ensures that decision-making resources are allocated appropriately: conservative approaches where information is limited, sophisticated AI methods where information quality justifies them.

The key insight is that optimization method selection should be a function of information availability, not of organizational preference or algorithmic fashion. DRL operationalises this principle in a form that is quantitative, auditable, and directly implementable in the HPF-P platform.