Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-27 22:50:07

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: museum_visit

```sql
CREATE TABLE museum (
  Museum_ID NUMBER,
  Name TEXT,
  Num_of_Staff NUMBER,
  Open_Year TEXT
);
```

```sql
CREATE TABLE visitor (
  ID NUMBER,
  Name TEXT,
  Level_of_membership NUMBER,
  Age NUMBER
);
```

```sql
CREATE TABLE visit (
  Museum_ID NUMBER,
  visitor_ID TEXT,
  Num_of_Ticket NUMBER,
  Total_spent NUMBER
);
```



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": "museum_visit",
  "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": "museum_visit",
  "iteration": 0,
  "business_context": "A museum wants to optimize the allocation of its staff across different museums to maximize visitor satisfaction while minimizing operational costs. The number of staff allocated to each museum affects the visitor experience and the operational cost.",
  "optimization_problem_description": "The goal is to determine the optimal number of staff to allocate to each museum to maximize visitor satisfaction, which is assumed to be proportional to the number of staff, while minimizing the total operational cost. The operational cost is a linear function of the number of staff allocated.",
  "optimization_formulation": {
    "objective": "maximize total_visitor_satisfaction = \u2211(satisfaction_coefficient[m] * staff_allocated[m]) - \u2211(cost_coefficient[m] * staff_allocated[m])",
    "decision_variables": "staff_allocated[m] for each museum m, which is an integer representing the number of staff allocated to museum m",
    "constraints": [
      "\u2211(staff_allocated[m]) <= total_available_staff",
      "staff_allocated[m] >= minimum_staff_required[m] for each museum m",
      "staff_allocated[m] <= maximum_staff_capacity[m] for each museum m"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "satisfaction_coefficient[m]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the increase in visitor satisfaction per additional staff member at museum m"
      },
      "cost_coefficient[m]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "represents the operational cost per staff member at museum m"
      }
    },
    "constraint_bounds": {
      "total_available_staff": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "total number of staff available for allocation across all museums"
      },
      "minimum_staff_required[m]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "minimum number of staff required to operate museum m"
      },
      "maximum_staff_capacity[m]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "maximum number of staff that can be accommodated at museum m"
      }
    },
    "decision_variables": {
      "staff_allocated[m]": {
        "currently_mapped_to": "museum.Num_of_Staff",
        "mapping_adequacy": "partial",
        "description": "number of staff allocated to museum m",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [
    "satisfaction_coefficient for each museum",
    "cost_coefficient for each museum",
    "total_available_staff",
    "minimum_staff_required for each museum",
    "maximum_staff_capacity for each museum"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Gather missing data for coefficients and constraints to complete the optimization model"
  }
}
