Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-25 22:28:55

Prompt:
You are an Operations Research (OR) expert in iteration 1 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 0):
{
  "iteration": 1,
  "converged": false,
  "business_context": "A phone distributor aims to optimize the allocation of phone stocks across different markets to maximize total revenue while respecting market capacities and minimizing stock shortages.",
  "optimization_problem": "The distributor needs to decide how many units of each phone model to allocate to each market to maximize total revenue, ensuring that the total stock allocated does not exceed the available stock for each phone model and that the total stock in each market does not exceed its capacity.",
  "objective": "maximize \u2211(Price[Phone_ID] \u00d7 Num_of_stock[Market_ID, Phone_ID])",
  "table_count": 2,
  "key_changes": [
    "Schema changes include adding tables for maximum market capacities and minimum stock requirements, and updating business configuration logic to include scalar parameters and formulas for optimization constraints."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Refine constraints to include minimum stock requirements and maximum market capacities",
  "mapping_adequacy_summary": "mostly_good"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include adding tables for maximum market capacities and minimum stock requirements, and updating business configuration logic to include scalar parameters and formulas for optimization constraints.

CREATE TABLE phone (
  Phone_ID INTEGER,
  Price FLOAT
);

CREATE TABLE market (
  Market_ID INTEGER,
  Num_of_shops INTEGER
);

CREATE TABLE phone_market (
  Market_ID INTEGER,
  Phone_ID INTEGER,
  Num_of_stock INTEGER
);

CREATE TABLE market_capacity (
  Market_ID INTEGER,
  Max_Capacity INTEGER
);

CREATE TABLE phone_min_stock (
  Market_ID INTEGER,
  Phone_ID INTEGER,
  Min_Stock INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "phone": {
      "business_purpose": "Stores information about each phone model",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Phone_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each phone model",
          "optimization_purpose": "Index for phone model in optimization",
          "sample_values": "1, 2, 3"
        },
        "Price": {
          "data_type": "FLOAT",
          "business_meaning": "Price of each phone model",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": "699.99, 899.99, 999.99"
        }
      }
    },
    "market": {
      "business_purpose": "Stores information about each market",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Market_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each market",
          "optimization_purpose": "Index for market in optimization",
          "sample_values": "1, 2, 3"
        },
        "Num_of_shops": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of shops in each market",
          "optimization_purpose": "Constraint bound for total stock in each market",
          "sample_values": "10, 15, 20"
        }
      }
    },
    "phone_market": {
      "business_purpose": "Stores stock allocation information for each phone model in each market",
      "optimization_role": "decision_variables",
      "columns": {
        "Market_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each market",
          "optimization_purpose": "Index for market in optimization",
          "sample_values": "1, 2, 3"
        },
        "Phone_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each phone model",
          "optimization_purpose": "Index for phone model in optimization",
          "sample_values": "1, 2, 3"
        },
        "Num_of_stock": {
          "data_type": "INTEGER",
          "business_meaning": "Number of units of each phone model allocated to each market",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "50, 100, 150"
        }
      }
    },
    "market_capacity": {
      "business_purpose": "Stores maximum stock capacity for each market",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Market_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each market",
          "optimization_purpose": "Index for market in optimization",
          "sample_values": "1, 2, 3"
        },
        "Max_Capacity": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum stock capacity for each market",
          "optimization_purpose": "Constraint bound for total stock in each market",
          "sample_values": "1000, 1500, 2000"
        }
      }
    },
    "phone_min_stock": {
      "business_purpose": "Stores minimum stock requirements for each phone model in each market",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Market_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each market",
          "optimization_purpose": "Index for market in optimization",
          "sample_values": "1, 2, 3"
        },
        "Phone_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each phone model",
          "optimization_purpose": "Index for phone model in optimization",
          "sample_values": "1, 2, 3"
        },
        "Min_Stock": {
          "data_type": "INTEGER",
          "business_meaning": "Minimum stock requirements for each phone model in each market",
          "optimization_purpose": "Constraint bound for minimum stock allocation",
          "sample_values": "50, 100, 150"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "max_market_capacity": {
    "sample_value": 1000,
    "data_type": "INTEGER",
    "business_meaning": "Maximum stock capacity for each market",
    "optimization_role": "Constraint bound for total stock in each market",
    "configuration_type": "scalar_parameter"
  },
  "min_stock_requirement": {
    "sample_value": 50,
    "data_type": "INTEGER",
    "business_meaning": "Minimum stock requirements for each phone model in each market",
    "optimization_role": "Constraint bound for minimum stock allocation",
    "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": "phone_market",
  "iteration": 1,
  "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": "phone_market",
  "iteration": 1,
  "business_context": "A phone distributor aims to optimize the allocation of phone stocks across different markets to maximize total revenue while respecting market capacities and ensuring minimum stock requirements are met.",
  "optimization_problem_description": "The distributor needs to decide how many units of each phone model to allocate to each market to maximize total revenue, ensuring that the total stock allocated does not exceed the available stock for each phone model, the total stock in each market does not exceed its capacity, and the minimum stock requirements for each phone model in each market are met.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Price[Phone_ID] \u00d7 Num_of_stock[Market_ID, Phone_ID])",
    "decision_variables": "Num_of_stock[Market_ID, Phone_ID] (integer)",
    "constraints": [
      "\u2211(Num_of_stock[Market_ID, Phone_ID]) \u2264 Max_Capacity[Market_ID] for each Market_ID",
      "Num_of_stock[Market_ID, Phone_ID] \u2265 Min_Stock[Market_ID, Phone_ID] for each Market_ID and Phone_ID"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Price[Phone_ID]": {
        "currently_mapped_to": "phone.Price",
        "mapping_adequacy": "good",
        "description": "Price of each phone model used as coefficient in the objective function"
      }
    },
    "constraint_bounds": {
      "Max_Capacity[Market_ID]": {
        "currently_mapped_to": "market_capacity.Max_Capacity",
        "mapping_adequacy": "good",
        "description": "Maximum stock capacity for each market"
      },
      "Min_Stock[Market_ID, Phone_ID]": {
        "currently_mapped_to": "phone_min_stock.Min_Stock",
        "mapping_adequacy": "good",
        "description": "Minimum stock requirements for each phone model in each market"
      }
    },
    "decision_variables": {
      "Num_of_stock[Market_ID, Phone_ID]": {
        "currently_mapped_to": "phone_market.Num_of_stock",
        "mapping_adequacy": "good",
        "description": "Number of units of each phone model allocated to each market",
        "variable_type": "integer"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
