Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:35:08

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either 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
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

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

Database: movie_1

```sql
CREATE TABLE Movie (
  mID NUMBER,
  title TEXT,
  year NUMBER,
  director TEXT
);
```

```sql
CREATE TABLE Reviewer (
  rID NUMBER,
  name TEXT
);
```

```sql
CREATE TABLE Rating (
  rID NUMBER,
  mID NUMBER,
  stars NUMBER,
  ratingDate TIME
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "movie_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 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 needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "movie_1",
  "iteration": 0,
  "business_context": "A movie streaming platform wants to maximize viewer satisfaction by recommending movies based on ratings. The platform aims 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_per_movie[j] for each movie j",
      "\u2211(x[i,j]) \u2264 max_recommendations_per_reviewer[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": "Rating.stars",
        "mapping_adequacy": "good",
        "description": "The rating stars given by reviewer i to movie j"
      }
    },
    "constraint_bounds": {
      "max_recommendations_per_movie[j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of recommendations allowed for movie j"
      },
      "max_recommendations_per_reviewer[i]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of recommendations allowed for reviewer i"
      }
    },
    "decision_variables": {
      "x[i,j]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Number of times movie j is recommended to reviewer i",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "max_recommendations_per_movie[j]",
    "max_recommendations_per_reviewer[i]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Define and map the missing constraint bounds for max_recommendations_per_movie and max_recommendations_per_reviewer"
  }
}
