Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:41:41

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 film studio aims to maximize its total gross revenue by strategically allocating its films to different markets based on estimated revenue ranges.",
  "optimization_problem": "The studio wants to decide how much to allocate each film to each market to maximize total gross revenue, considering the low and high revenue estimates for each film-market pair.",
  "objective": "maximize \u2211(Revenue_ij \u00d7 Allocation_ij) where Revenue_ij is the estimated revenue for film i in market j and Allocation_ij is the proportion of film i allocated to market j",
  "table_count": 2,
  "key_changes": [
    "Schema changes include creating tables for film-market allocations and revenue estimates, modifying existing tables to better map optimization requirements, and adding business configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine revenue estimation and allocation constraints",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for film-market allocations and revenue estimates, modifying existing tables to better map optimization requirements, and adding business configuration logic for scalar parameters and formulas.

CREATE TABLE film_market_allocation (
  allocation_proportion FLOAT
);

CREATE TABLE film_market_revenue_estimate (
  low_estimate FLOAT,
  high_estimate FLOAT,
  average_revenue FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "film_market_allocation": {
      "business_purpose": "Proportion of each film allocated to each market",
      "optimization_role": "decision_variables",
      "columns": {
        "allocation_proportion": {
          "data_type": "FLOAT",
          "business_meaning": "Proportion of film i allocated to market j",
          "optimization_purpose": "Decision variable in optimization formulation",
          "sample_values": "0.0 to 1.0"
        }
      }
    },
    "film_market_revenue_estimate": {
      "business_purpose": "Low and high revenue estimates for each film in each market",
      "optimization_role": "objective_coefficients",
      "columns": {
        "low_estimate": {
          "data_type": "FLOAT",
          "business_meaning": "Low revenue estimate for film i in market j",
          "optimization_purpose": "Used to calculate average revenue estimate",
          "sample_values": "100000.0 to 500000.0"
        },
        "high_estimate": {
          "data_type": "FLOAT",
          "business_meaning": "High revenue estimate for film i in market j",
          "optimization_purpose": "Used to calculate average revenue estimate",
          "sample_values": "500000.0 to 1000000.0"
        },
        "average_revenue": {
          "data_type": "FLOAT",
          "business_meaning": "Average revenue estimate for film i in market j",
          "optimization_purpose": "Objective coefficient in optimization formulation",
          "sample_values": "300000.0 to 750000.0"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "revenue_estimation_formula": {
    "formula_expression": "(Low_Estimate_ij + High_Estimate_ij) / 2",
    "data_type": "STRING",
    "business_meaning": "Average revenue estimate for film i in market j",
    "optimization_role": "Used to calculate objective coefficients",
    "configuration_type": "business_logic_formula"
  },
  "allocation_constraint_bound": {
    "sample_value": 1,
    "data_type": "FLOAT",
    "business_meaning": "Maximum proportion of a film that can be allocated to any market",
    "optimization_role": "Used to set constraint bounds",
    "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": "film_rank",
  "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": "film_rank",
  "iteration": 1,
  "business_context": "A film studio aims to maximize its total gross revenue by strategically allocating its films to different markets based on average revenue estimates.",
  "optimization_problem_description": "The studio wants to decide the proportion of each film to allocate to each market to maximize total gross revenue, using average revenue estimates for each film-market pair and ensuring that the total allocation for each film does not exceed 100%.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Average_Revenue_ij \u00d7 Allocation_ij) where Average_Revenue_ij is the average revenue estimate for film i in market j and Allocation_ij is the proportion of film i allocated to market j",
    "decision_variables": "Allocation_ij: continuous variable representing the proportion of film i allocated to market j",
    "constraints": "\u2211(Allocation_ij) \u2264 1 for each film i, Allocation_ij \u2265 0 for all i, j"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Average_Revenue_ij": {
        "currently_mapped_to": "film_market_revenue_estimate.average_revenue",
        "mapping_adequacy": "good",
        "description": "Average revenue estimate for film i in market j"
      }
    },
    "constraint_bounds": {
      "Allocation_Constraint_i": {
        "currently_mapped_to": "business_configuration_logic.allocation_constraint_bound",
        "mapping_adequacy": "good",
        "description": "Maximum proportion of a film that can be allocated to any market"
      }
    },
    "decision_variables": {
      "Allocation_ij": {
        "currently_mapped_to": "film_market_allocation.allocation_proportion",
        "mapping_adequacy": "good",
        "description": "Proportion of film i allocated to market j",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
