Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:34:23

Prompt:
You are an Operations Research (OR) expert in iteration 1 of an alternating optimization process. The algorithm alternates between OR expert analysis and data engineering implementation until convergence.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST remain Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- If previous iteration introduced nonlinear elements, redesign as linear formulation
- Maintain between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and mapping analysis. Do NOT propose database changes.
ROW COUNT AWARENESS: Understand that data engineer applies 3-row minimum rule - insufficient table data gets moved to business_configuration_logic.json.


DATA AVAILABILITY CHECK: 
Before listing missing requirements, verify:
- Check current schema for required data columns
- Check business configuration logic for required parameters  
- Only list as "missing" if data is truly unavailable
- If all mappings are "good", missing_requirements should be []

CONSISTENCY RULES:
- IF all mapping_adequacy == "good" THEN missing_optimization_requirements = []
- IF missing_optimization_requirements = [] THEN complete CAN be true
- IF complete == true THEN confidence should be "high"

SELF-CHECK: Before responding, verify:
1. Does current schema contain the data I claim is missing?
2. Are my mapping assessments consistent with missing requirements?
3. Is my complete status consistent with missing requirements?

MAPPING COMPLETENESS CHECK: Ensure logical consistency between:
- All objective coefficients mapped with adequacy evaluation
- All constraint bounds mapped with adequacy evaluation  
- All decision variables mapped with adequacy evaluation
- Missing requirements list matches inadequate mappings only


CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.



CURRENT STATE (iteration 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A movie streaming service wants to optimize the allocation of promotional budget across different movies to maximize the average rating improvement, subject to budget constraints and minimum promotional requirements for each movie.",
  "optimization_problem": "The goal is to determine the optimal allocation of a fixed promotional budget to different movies to maximize the expected increase in their average ratings. Each movie has a different sensitivity to promotional spending, and there are minimum promotional requirements for each movie.",
  "objective": "maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating new tables for missing optimization data and updating business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Gathering data on promotion sensitivity and budget constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE promotion_sensitivity (
  mID INTEGER,
  sensitivity_value FLOAT
);

CREATE TABLE budget_allocation (
  mID INTEGER,
  amount FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "promotion_sensitivity": {
      "business_purpose": "represents the sensitivity of each movie's rating to promotional spending",
      "optimization_role": "objective_coefficients",
      "columns": {
        "mID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each movie",
          "optimization_purpose": "index for sensitivity values",
          "sample_values": "1, 2, 3"
        },
        "sensitivity_value": {
          "data_type": "FLOAT",
          "business_meaning": "sensitivity of the movie's rating to promotional spending",
          "optimization_purpose": "coefficient in the objective function",
          "sample_values": "0.1, 0.2, 0.3"
        }
      }
    },
    "budget_allocation": {
      "business_purpose": "represents the allocation of promotional budget to each movie",
      "optimization_role": "decision_variables",
      "columns": {
        "mID": {
          "data_type": "INTEGER",
          "business_meaning": "unique identifier for each movie",
          "optimization_purpose": "index for budget allocation",
          "sample_values": "1, 2, 3"
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "amount of budget allocated to the movie",
          "optimization_purpose": "decision variable in the optimization model",
          "sample_values": "10000, 15000, 20000"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "total_budget": {
    "sample_value": "100000",
    "data_type": "FLOAT",
    "business_meaning": "the total promotional budget available for allocation",
    "optimization_role": "used as an upper bound constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  },
  "min_promotion_requirement": {
    "sample_value": "5000",
    "data_type": "FLOAT",
    "business_meaning": "the minimum promotional budget that must be allocated to each movie",
    "optimization_role": "used as a lower bound constraint in the optimization model",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "movie_1",
  "iteration": 1,
  "business_context": "Updated realistic business scenario description that supports linear optimization",
  "optimization_problem_description": "Refined description of LINEAR optimization problem", 
  "optimization_formulation": {
    "objective": "refined linear minimize/maximize with mathematical precision (sum of weighted variables only)",
    "decision_variables": "clearly defined controllable linear variables (continuous or integer)",
    "constraints": "mathematically precise LINEAR constraint definitions (no variable products or divisions) - maintain 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are still needed for linear formulation (should be [] if all mappings are good)"
  ],
  
  "iteration_status": {
    "complete": true/false based on linear formulation completeness,
    "confidence": "updated confidence level",
    "next_focus": "What needs refinement for linear optimization OR 'Ready for convergence'"
  }
}

Response:
{
  "database_id": "movie_1",
  "iteration": 1,
  "business_context": "A movie streaming service aims to optimize the allocation of its promotional budget across various movies to maximize the expected improvement in their average ratings, considering budget constraints and minimum promotional requirements for each movie.",
  "optimization_problem_description": "Determine the optimal allocation of a fixed promotional budget to different movies to maximize the expected increase in their average ratings. Each movie has a different sensitivity to promotional spending, and there are minimum promotional requirements for each movie.",
  "optimization_formulation": {
    "objective": "maximize sum(promotion_sensitivity[mID] * budget_allocation[mID])",
    "decision_variables": "budget_allocation[mID] for each movie mID, continuous",
    "constraints": [
      "sum(budget_allocation[mID]) <= total_budget",
      "budget_allocation[mID] >= min_promotion_requirement for each movie mID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "promotion_sensitivity[mID]": {
        "currently_mapped_to": "promotion_sensitivity.sensitivity_value",
        "mapping_adequacy": "good",
        "description": "sensitivity of each movie's rating to promotional spending"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "business_configuration_logic.total_budget",
        "mapping_adequacy": "good",
        "description": "the total promotional budget available for allocation"
      },
      "min_promotion_requirement": {
        "currently_mapped_to": "business_configuration_logic.min_promotion_requirement",
        "mapping_adequacy": "good",
        "description": "the minimum promotional budget that must be allocated to each movie"
      }
    },
    "decision_variables": {
      "budget_allocation[mID]": {
        "currently_mapped_to": "budget_allocation.amount",
        "mapping_adequacy": "good",
        "description": "amount of budget allocated to each movie",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
