Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:47:19

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: party_host

```sql
CREATE TABLE party (
  Party_ID NUMBER,
  Party_Theme TEXT,
  Location TEXT,
  First_year TEXT,
  Last_year TEXT,
  Number_of_hosts NUMBER
);
```

```sql
CREATE TABLE host (
  Host_ID NUMBER,
  Name TEXT,
  Nationality TEXT,
  Age TEXT
);
```

```sql
CREATE TABLE party_host (
  Party_ID NUMBER,
  Host_ID NUMBER,
  Is_Main_in_Charge OTHERS
);
```



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": "party_host",
  "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": "party_host",
  "iteration": 0,
  "business_context": "A party hosting company wants to minimize the total cost of hosting parties while ensuring that each party has a sufficient number of hosts and that hosts are assigned based on their availability and expertise.",
  "optimization_problem_description": "The company needs to minimize the total cost of hosting parties by assigning hosts to parties in a way that respects the constraints on the number of hosts per party, the availability of hosts, and the expertise required for each party theme.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_host[Host_ID] \u00d7 assign[Party_ID, Host_ID])",
    "decision_variables": "assign[Party_ID, Host_ID] (binary: 1 if host is assigned to party, 0 otherwise)",
    "constraints": [
      "\u2211(assign[Party_ID, Host_ID]) \u2265 min_hosts[Party_ID] for each Party_ID",
      "\u2211(assign[Party_ID, Host_ID]) \u2264 max_hosts[Party_ID] for each Party_ID",
      "\u2211(assign[Party_ID, Host_ID]) \u2264 1 for each Host_ID",
      "assign[Party_ID, Host_ID] \u2264 expertise_match[Party_ID, Host_ID] for each Party_ID, Host_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_host[Host_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Cost associated with each host"
      }
    },
    "constraint_bounds": {
      "min_hosts[Party_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Minimum number of hosts required for each party"
      },
      "max_hosts[Party_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum number of hosts allowed for each party"
      },
      "expertise_match[Party_ID, Host_ID]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Binary indicator if host's expertise matches party theme"
      }
    },
    "decision_variables": {
      "assign[Party_ID, Host_ID]": {
        "currently_mapped_to": "party_host.Party_ID, party_host.Host_ID",
        "mapping_adequacy": "partial",
        "description": "Assignment of hosts to parties",
        "variable_type": "binary"
      }
    }
  },
  "missing_optimization_requirements": [
    "cost_per_host[Host_ID]",
    "min_hosts[Party_ID]",
    "max_hosts[Party_ID]",
    "expertise_match[Party_ID, Host_ID]"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Identify and map missing data/parameters for complete linear optimization model"
  }
}
