Iteration 2 - OR_EXPERT_REFINEMENT
Sequence: 5
Timestamp: 2025-07-25 22:31:11

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 university aims to optimize the allocation of pet care resources to students based on their pets' needs and the students' demographics. The goal is to minimize the total cost of pet care while ensuring that each pet receives adequate care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "optimization_problem": "The optimization problem aims to minimize the total cost of pet care by allocating resources efficiently. The decision variables represent the amount of resources allocated to each pet. Constraints ensure that each pet receives a minimum level of care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "objective": "minimize \u2211(cost_per_pet_type[PetType] \u00d7 resource_allocation[PetID])",
  "table_count": 1,
  "key_changes": [
    "Added resource_allocation table to map decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings align with OR expert's requirements."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Define and map the decision variables to the schema or business configuration logic.",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Added resource_allocation table to map decision variables, updated business configuration logic with new scalar parameters, and ensured all mappings align with OR expert's requirements.

CREATE TABLE pet_type_costs (
  pet_type STRING,
  cost FLOAT
);

CREATE TABLE pet_care_requirements (
  pet_type STRING,
  min_care FLOAT,
  max_care FLOAT
);

CREATE TABLE resource_allocation (
  pet_id STRING,
  amount FLOAT
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "pet_type_costs": {
      "business_purpose": "Cost associated with caring for each pet type",
      "optimization_role": "objective_coefficients",
      "columns": {
        "pet_type": {
          "data_type": "STRING",
          "business_meaning": "Type of pet",
          "optimization_purpose": "Index for cost coefficient",
          "sample_values": [
            "dog",
            "cat",
            "bird"
          ]
        },
        "cost": {
          "data_type": "FLOAT",
          "business_meaning": "Cost per pet type",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": [
            50.0,
            30.0,
            20.0
          ]
        }
      }
    },
    "pet_care_requirements": {
      "business_purpose": "Minimum and maximum care requirements for each pet type",
      "optimization_role": "constraint_bounds",
      "columns": {
        "pet_type": {
          "data_type": "STRING",
          "business_meaning": "Type of pet",
          "optimization_purpose": "Index for care requirements",
          "sample_values": [
            "dog",
            "cat",
            "bird"
          ]
        },
        "min_care": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum care requirement",
          "optimization_purpose": "Lower bound in constraints",
          "sample_values": [
            10.0,
            5.0,
            3.0
          ]
        },
        "max_care": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum care requirement",
          "optimization_purpose": "Upper bound in constraints",
          "sample_values": [
            100.0,
            50.0,
            30.0
          ]
        }
      }
    },
    "resource_allocation": {
      "business_purpose": "Amount of resources allocated to each pet",
      "optimization_role": "decision_variables",
      "columns": {
        "pet_id": {
          "data_type": "STRING",
          "business_meaning": "Unique identifier for each pet",
          "optimization_purpose": "Index for decision variables",
          "sample_values": [
            "pet1",
            "pet2",
            "pet3"
          ]
        },
        "amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of resources allocated",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": [
            50.0,
            30.0,
            20.0
          ]
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "min_resource_allocation": {
    "sample_value": 0,
    "data_type": "FLOAT",
    "business_meaning": "Minimum resource allocation per pet",
    "optimization_role": "Lower bound for decision variables",
    "configuration_type": "scalar_parameter"
  },
  "max_resource_allocation": {
    "sample_value": 1000,
    "data_type": "FLOAT",
    "business_meaning": "Maximum resource allocation per pet",
    "optimization_role": "Upper bound for decision variables",
    "configuration_type": "scalar_parameter"
  }
}


TASK: Refine the optimization problem formulation by analyzing current data schema mapping and identifying requirements while maintaining LINEAR structure.

JSON STRUCTURE REQUIRED:

{
  "database_id": "pets_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": "pets_1",
  "iteration": 2,
  "business_context": "A university aims to optimize the allocation of pet care resources to students based on their pets' needs and the students' demographics. The goal is to minimize the total cost of pet care while ensuring that each pet receives adequate care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "optimization_problem_description": "The optimization problem aims to minimize the total cost of pet care by allocating resources efficiently. The decision variables represent the amount of resources allocated to each pet. Constraints ensure that each pet receives a minimum level of care based on its type, age, and weight, and that the total resources do not exceed the available budget and weight capacity.",
  "optimization_formulation": {
    "objective": "minimize \u2211(cost_per_pet_type[PetType] \u00d7 resource_allocation[PetID])",
    "decision_variables": "resource_allocation[PetID] (continuous)",
    "constraints": [
      "resource_allocation[PetID] \u2265 min_care[PetType]",
      "resource_allocation[PetID] \u2264 max_care[PetType]",
      "\u2211(resource_allocation[PetID]) \u2264 max_resource_allocation",
      "resource_allocation[PetID] \u2265 min_resource_allocation"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "cost_per_pet_type[PetType]": {
        "currently_mapped_to": "pet_type_costs.cost",
        "mapping_adequacy": "good",
        "description": "Cost associated with caring for each pet type"
      }
    },
    "constraint_bounds": {
      "min_care[PetType]": {
        "currently_mapped_to": "pet_care_requirements.min_care",
        "mapping_adequacy": "good",
        "description": "Minimum care requirement for each pet type"
      },
      "max_care[PetType]": {
        "currently_mapped_to": "pet_care_requirements.max_care",
        "mapping_adequacy": "good",
        "description": "Maximum care requirement for each pet type"
      },
      "max_resource_allocation": {
        "currently_mapped_to": "business_configuration_logic.max_resource_allocation",
        "mapping_adequacy": "good",
        "description": "Maximum total resource allocation"
      },
      "min_resource_allocation": {
        "currently_mapped_to": "business_configuration_logic.min_resource_allocation",
        "mapping_adequacy": "good",
        "description": "Minimum resource allocation per pet"
      }
    },
    "decision_variables": {
      "resource_allocation[PetID]": {
        "currently_mapped_to": "resource_allocation.amount",
        "mapping_adequacy": "good",
        "description": "Amount of resources allocated to each pet",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
