Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:35:08

Prompt:
You are an Operations Research (OR) expert in iteration 2 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 1):
{
  "iteration": 2,
  "converged": false,
  "business_context": "A movie streaming platform aims to maximize viewer satisfaction by recommending movies based on ratings. The platform needs to allocate a limited number of recommendations to movies such that the total satisfaction (sum of stars) is maximized, while ensuring that no movie is recommended more than a certain number of times and no reviewer is overloaded with recommendations.",
  "optimization_problem": "The platform needs to decide how many times each movie should be recommended to maximize the total satisfaction (sum of stars) from the ratings. Constraints include limiting the number of recommendations per movie and ensuring that no reviewer receives too many recommendations.",
  "objective": "maximize \u2211(stars[i,j] * x[i,j]) where x[i,j] is the number of times movie j is recommended to reviewer i",
  "table_count": 1,
  "key_changes": [
    "Added a new table for star ratings to address missing objective coefficients, updated business configuration logic, and ensured all mappings are complete."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the missing objective coefficients for stars[i,j]",
  "mapping_adequacy_summary": "partially_adequate"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added a new table for star ratings to address missing objective coefficients, updated business configuration logic, and ensured all mappings are complete.

CREATE TABLE MovieRecommendationLimits (
  movie_id INTEGER,
  max_recommendations INTEGER
);

CREATE TABLE ReviewerRecommendationLimits (
  reviewer_id INTEGER,
  max_recommendations INTEGER
);

CREATE TABLE RecommendationAssignments (
  reviewer_id INTEGER,
  movie_id INTEGER,
  recommendation_count INTEGER
);

CREATE TABLE MovieRatings (
  reviewer_id INTEGER,
  movie_id INTEGER,
  star_rating INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "MovieRecommendationLimits": {
      "business_purpose": "Maximum number of recommendations allowed for each movie",
      "optimization_role": "constraint_bounds",
      "columns": {
        "movie_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the movie",
          "optimization_purpose": "Identifies the movie for which the recommendation limit applies",
          "sample_values": "1, 2, 3"
        },
        "max_recommendations": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of recommendations allowed for the movie",
          "optimization_purpose": "Constraint bound for movie recommendations",
          "sample_values": "5, 5, 5"
        }
      }
    },
    "ReviewerRecommendationLimits": {
      "business_purpose": "Maximum number of recommendations allowed for each reviewer",
      "optimization_role": "constraint_bounds",
      "columns": {
        "reviewer_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the reviewer",
          "optimization_purpose": "Identifies the reviewer for which the recommendation limit applies",
          "sample_values": "1, 2, 3"
        },
        "max_recommendations": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of recommendations allowed for the reviewer",
          "optimization_purpose": "Constraint bound for reviewer recommendations",
          "sample_values": "3, 3, 3"
        }
      }
    },
    "RecommendationAssignments": {
      "business_purpose": "Number of times each movie is recommended to each reviewer",
      "optimization_role": "decision_variables",
      "columns": {
        "reviewer_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the reviewer",
          "optimization_purpose": "Identifies the reviewer receiving the recommendation",
          "sample_values": "1, 2, 3"
        },
        "movie_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the movie",
          "optimization_purpose": "Identifies the movie being recommended",
          "sample_values": "1, 2, 3"
        },
        "recommendation_count": {
          "data_type": "INTEGER",
          "business_meaning": "Number of times the movie is recommended to the reviewer",
          "optimization_purpose": "Decision variable for recommendation assignments",
          "sample_values": "1, 2, 3"
        }
      }
    },
    "MovieRatings": {
      "business_purpose": "Star ratings given by reviewers to movies",
      "optimization_role": "objective_coefficients",
      "columns": {
        "reviewer_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the reviewer",
          "optimization_purpose": "Identifies the reviewer providing the rating",
          "sample_values": "1, 2, 3"
        },
        "movie_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for the movie",
          "optimization_purpose": "Identifies the movie being rated",
          "sample_values": "1, 2, 3"
        },
        "star_rating": {
          "data_type": "INTEGER",
          "business_meaning": "Star rating given by the reviewer to the movie",
          "optimization_purpose": "Objective coefficient for recommendation optimization",
          "sample_values": "4, 5, 3"
        }
      }
    }
  }
}



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": 2,
  "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": 2,
  "business_context": "A movie streaming platform aims to maximize viewer satisfaction by recommending movies based on ratings. The platform needs to allocate a limited number of recommendations to movies such that the total satisfaction (sum of stars) is maximized, while ensuring that no movie is recommended more than a certain number of times and no reviewer is overloaded with recommendations.",
  "optimization_problem_description": "The platform needs to decide how many times each movie should be recommended to maximize the total satisfaction (sum of stars) from the ratings. Constraints include limiting the number of recommendations per movie and ensuring that no reviewer receives too many recommendations.",
  "optimization_formulation": {
    "objective": "maximize \u2211(stars[i,j] * x[i,j]) where x[i,j] is the number of times movie j is recommended to reviewer i",
    "decision_variables": "x[i,j] = number of times movie j is recommended to reviewer i (integer)",
    "constraints": [
      "\u2211(x[i,j]) \u2264 max_recommendations[j] for each movie j",
      "\u2211(x[i,j]) \u2264 max_recommendations[i] for each reviewer i",
      "x[i,j] \u2265 0 for all i, j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "stars[i,j]": {
        "currently_mapped_to": "MovieRatings.star_rating",
        "mapping_adequacy": "good",
        "description": "Star rating given by reviewer i to movie j"
      }
    },
    "constraint_bounds": {
      "max_recommendations[j]": {
        "currently_mapped_to": "MovieRecommendationLimits.max_recommendations",
        "mapping_adequacy": "good",
        "description": "Maximum number of recommendations allowed for movie j"
      },
      "max_recommendations[i]": {
        "currently_mapped_to": "ReviewerRecommendationLimits.max_recommendations",
        "mapping_adequacy": "good",
        "description": "Maximum number of recommendations allowed for reviewer i"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "RecommendationAssignments.recommendation_count",
        "mapping_adequacy": "good",
        "description": "Number of times movie j is recommended to reviewer i",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
