Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:30:28

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: city_record

```sql
CREATE TABLE city (
  City_ID NUMBER,
  City TEXT,
  Hanzi TEXT,
  Hanyu_Pinyin TEXT,
  Regional_Population NUMBER,
  GDP NUMBER
);
```

```sql
CREATE TABLE match (
  Match_ID NUMBER,
  Date TEXT,
  Venue TEXT,
  Score TEXT,
  Result TEXT,
  Competition TEXT
);
```

```sql
CREATE TABLE temperature (
  City_ID NUMBER,
  Jan NUMBER,
  Feb NUMBER,
  Mar NUMBER,
  Apr NUMBER,
  Jun NUMBER,
  Jul NUMBER,
  Aug NUMBER,
  Sep NUMBER,
  Oct NUMBER,
  Nov NUMBER,
  Dec NUMBER
);
```

```sql
CREATE TABLE hosting_city (
  Year NUMBER,
  Match_ID NUMBER,
  Host_City TEXT
);
```



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": "city_record",
  "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": "city_record",
  "iteration": 0,
  "business_context": "A sports organization wants to optimize the selection of host cities for matches in a given year, considering factors like regional population, GDP, and average temperature during the match month.",
  "optimization_problem_description": "The goal is to maximize the overall benefit of selecting host cities for matches, where the benefit is a weighted sum of regional population, GDP, and average temperature during the match month. The selection must respect constraints such as the maximum number of matches per city and the total budget allocated for hosting.",
  "optimization_formulation": {
    "objective": "maximize \u2211(w1 * Population_i + w2 * GDP_i + w3 * Temperature_i) * x_i",
    "decision_variables": "x_i: binary variable indicating whether city i is selected as a host city",
    "constraints": [
      "\u2211(x_i) \u2264 Total_Matches: Total number of matches to be hosted",
      "\u2211(Cost_i * x_i) \u2264 Total_Budget: Total budget constraint for hosting",
      "x_i \u2264 Max_Matches_Per_City: Maximum number of matches per city",
      "x_i \u2208 {0, 1}: Binary decision variable"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Weight for regional population in the objective function"
      },
      "w2": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Weight for GDP in the objective function"
      },
      "w3": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Weight for average temperature in the objective function"
      }
    },
    "constraint_bounds": {
      "Total_Matches": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total number of matches to be hosted"
      },
      "Total_Budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total budget constraint for hosting"
      },
      "Max_Matches_Per_City": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of matches per city"
      }
    },
    "decision_variables": {
      "x_i": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary decision variable indicating whether city i is selected as a host city",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "Weights for the objective function (w1, w2, w3)",
    "Total number of matches to be hosted (Total_Matches)",
    "Total budget for hosting (Total_Budget)",
    "Maximum number of matches per city (Max_Matches_Per_City)",
    "Cost of hosting per city (Cost_i)"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "low",
    "next_focus": "Define the weights for the objective function and gather data for the constraints (Total_Matches, Total_Budget, Max_Matches_Per_City, Cost_i)."
  }
}
