Iteration 1 - OR_EXPERT_REFINEMENT
Sequence: 3
Timestamp: 2025-07-27 23:52:22

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": "Optimize the allocation of bikes across stations to minimize the number of stations running out of bikes or docks at any given time.",
  "optimization_problem": "The goal is to determine the optimal number of bikes to allocate to each station at the start of the day to minimize the likelihood of stations running out of bikes or docks, considering current availability and expected demand.",
  "objective": "minimize \u2211(shortage_penalty[i] * shortage[i] + excess_penalty[i] * excess[i])",
  "table_count": 1,
  "key_changes": [
    "Schema changes include creating new tables for penalty costs and expected demand, modifying existing tables to include missing data, and updating configuration logic for scalar parameters and formulas."
  ],
  "math_consistency": "high",
  "next_iteration_focus": "Determine penalty costs and gather expected demand data for each station",
  "mapping_adequacy_summary": "needs_improvement"
}

CURRENT SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for penalty costs and expected demand, modifying existing tables to include missing data, and updating configuration logic for scalar parameters and formulas.

CREATE TABLE station (
  station_id INTEGER,
  dock_count INTEGER,
  shortage FLOAT,
  excess FLOAT
);

CREATE TABLE expected_demand (
  station_id INTEGER,
  expected_demand INTEGER
);


```

CURRENT DATA DICTIONARY:
{
  "tables": {
    "station": {
      "business_purpose": "Stores information about each bike station",
      "optimization_role": "decision_variables",
      "columns": {
        "station_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each station",
          "optimization_purpose": "Identifies stations in optimization",
          "sample_values": "1, 2, 3"
        },
        "dock_count": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum number of bikes that can be docked at the station",
          "optimization_purpose": "Constraint bound for bike allocation",
          "sample_values": "10, 15, 20"
        },
        "shortage": {
          "data_type": "FLOAT",
          "business_meaning": "Number of bikes short at the station",
          "optimization_purpose": "Decision variable for shortage",
          "sample_values": "0, 1, 2"
        },
        "excess": {
          "data_type": "FLOAT",
          "business_meaning": "Number of excess bikes at the station",
          "optimization_purpose": "Decision variable for excess",
          "sample_values": "0, 1, 2"
        }
      }
    },
    "expected_demand": {
      "business_purpose": "Stores expected demand for bikes at each station",
      "optimization_role": "business_data",
      "columns": {
        "station_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each station",
          "optimization_purpose": "Links demand data to stations",
          "sample_values": "1, 2, 3"
        },
        "expected_demand": {
          "data_type": "INTEGER",
          "business_meaning": "Expected number of bikes needed at the station",
          "optimization_purpose": "Used to forecast demand in optimization",
          "sample_values": "5, 10, 15"
        }
      }
    }
  }
}


CURRENT BUSINESS CONFIGURATION LOGIC:
{
  "shortage_penalty": {
    "sample_value": "10",
    "data_type": "FLOAT",
    "business_meaning": "Penalty cost for each bike shortage at a station",
    "optimization_role": "Used in the objective function to minimize shortage costs",
    "configuration_type": "scalar_parameter"
  },
  "excess_penalty": {
    "sample_value": "5",
    "data_type": "FLOAT",
    "business_meaning": "Penalty cost for each excess bike at a station",
    "optimization_role": "Used in the objective function to minimize excess costs",
    "configuration_type": "scalar_parameter"
  },
  "total_bikes": {
    "sample_value": "1000",
    "data_type": "INTEGER",
    "business_meaning": "Total number of bikes available in the system",
    "optimization_role": "Used as a constraint bound in the optimization model",
    "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": "bike_1",
  "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": "bike_1",
  "iteration": 1,
  "business_context": "Optimize the allocation of bikes across stations to minimize the number of stations running out of bikes or docks at any given time.",
  "optimization_problem_description": "Determine the optimal number of bikes to allocate to each station at the start of the day to minimize the likelihood of stations running out of bikes or docks, considering current availability and expected demand.",
  "optimization_formulation": {
    "objective": "minimize \u2211(shortage_penalty * shortage[i] + excess_penalty * excess[i])",
    "decision_variables": "shortage[i], excess[i] for each station i",
    "constraints": [
      "\u2211(shortage[i] + excess[i]) = total_bikes",
      "shortage[i] >= 0 for all i",
      "excess[i] >= 0 for all i",
      "shortage[i] + expected_demand[i] <= dock_count[i] for all i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "shortage_penalty": {
        "currently_mapped_to": "business_configuration_logic.shortage_penalty",
        "mapping_adequacy": "good",
        "description": "Penalty cost for each bike shortage at a station"
      },
      "excess_penalty": {
        "currently_mapped_to": "business_configuration_logic.excess_penalty",
        "mapping_adequacy": "good",
        "description": "Penalty cost for each excess bike at a station"
      }
    },
    "constraint_bounds": {
      "total_bikes": {
        "currently_mapped_to": "business_configuration_logic.total_bikes",
        "mapping_adequacy": "good",
        "description": "Total number of bikes available in the system"
      },
      "dock_count[i]": {
        "currently_mapped_to": "station.dock_count",
        "mapping_adequacy": "good",
        "description": "Maximum number of bikes that can be docked at the station"
      }
    },
    "decision_variables": {
      "shortage[i]": {
        "currently_mapped_to": "station.shortage",
        "mapping_adequacy": "good",
        "description": "Number of bikes short at the station",
        "variable_type": "continuous"
      },
      "excess[i]": {
        "currently_mapped_to": "station.excess",
        "mapping_adequacy": "good",
        "description": "Number of excess bikes at the station",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}
