Agent skill

linear-programming-solver

Linear programming skill for resource allocation, scheduling, and optimization problems

View SKILL.md on GitHub Repository
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Install this agent skill to your Project

npx add-skill https://github.com/a5c-ai/babysitter/tree/main/library/specializations/domains/business/decision-intelligence/skills/linear-programming-solver

Metadata

Additional technical details for this skill

domain
business
category
optimization
priority
medium
specialization
decision-intelligence
tools libraries 
[
    "pulp",
    "ortools",
    "pyomo",
    "cvxpy"
]
shared candidate
YES

SKILL.md

Linear Programming Solver

Overview

The Linear Programming Solver skill provides comprehensive capabilities for formulating and solving linear optimization problems. It supports resource allocation, production planning, scheduling, and other business optimization challenges through efficient solver integration and solution analysis.

Capabilities

  • LP model formulation assistance
  • Solver integration (GLPK, CBC, CPLEX, Gurobi)
  • Sensitivity analysis (shadow prices, reduced costs)
  • Infeasibility diagnosis
  • Unboundedness detection
  • Integer programming support
  • Multi-objective LP (goal programming)
  • Solution interpretation

Used By Processes

  • Prescriptive Analytics and Optimization
  • Resource Allocation
  • Supply Chain Optimization

Usage

Problem Formulation

python
# Define LP problem
lp_problem = {
    "name": "Production Planning",
    "sense": "maximize",  # or "minimize"
    "decision_variables": {
        "product_A": {"type": "continuous", "lower_bound": 0, "upper_bound": 1000},
        "product_B": {"type": "continuous", "lower_bound": 0, "upper_bound": 800},
        "product_C": {"type": "integer", "lower_bound": 0}  # integer variable
    },
    "objective": {
        "expression": "50*product_A + 40*product_B + 60*product_C",
        "description": "Maximize total profit"
    },
    "constraints": [
        {
            "name": "labor_hours",
            "expression": "2*product_A + 3*product_B + 4*product_C <= 2400",
            "description": "Total labor hours available"
        },
        {
            "name": "machine_time",
            "expression": "3*product_A + 2*product_B + 3*product_C <= 2000",
            "description": "Machine time capacity"
        },
        {
            "name": "raw_material",
            "expression": "product_A + product_B + product_C <= 1200",
            "description": "Raw material availability"
        },
        {
            "name": "demand_A",
            "expression": "product_A >= 100",
            "description": "Minimum demand for product A"
        }
    ]
}

Solver Configuration

python
# Solver settings
solver_config = {
    "solver": "CBC",  # or "GLPK", "CPLEX", "GUROBI"
    "time_limit": 300,  # seconds
    "mip_gap": 0.01,  # 1% optimality gap for MIP
    "threads": 4,
    "presolve": True,
    "cuts": "automatic"
}

Sensitivity Analysis

python
# Request sensitivity information
sensitivity_config = {
    "shadow_prices": True,
    "reduced_costs": True,
    "allowable_ranges": True,
    "what_if": [
        {"constraint": "labor_hours", "change": 100},
        {"objective_coeff": "product_A", "change": 5}
    ]
}

Common LP Problem Types

Problem Type Objective Key Constraints
Production Planning Maximize profit Capacity, demand
Transportation Minimize cost Supply, demand
Assignment Minimize cost/time One-to-one matching
Blending Minimize cost Quality specs, availability
Network Flow Min cost/max flow Flow balance, capacity
Portfolio Maximize return Risk, budget, diversification

Input Schema

json
{
  "problem_definition": {
    "name": "string",
    "sense": "maximize|minimize",
    "decision_variables": "object",
    "objective": {
      "expression": "string",
      "description": "string"
    },
    "constraints": ["object"]
  },
  "solver_config": {
    "solver": "string",
    "time_limit": "number",
    "mip_gap": "number"
  },
  "analysis_options": {
    "sensitivity": "boolean",
    "what_if": ["object"],
    "report_format": "string"
  }
}

Output Schema

json
{
  "status": "Optimal|Infeasible|Unbounded|TimeLimit",
  "objective_value": "number",
  "solution": {
    "variable_name": "number"
  },
  "sensitivity": {
    "shadow_prices": {
      "constraint_name": {
        "value": "number",
        "allowable_increase": "number",
        "allowable_decrease": "number"
      }
    },
    "reduced_costs": {
      "variable_name": {
        "value": "number",
        "allowable_increase": "number",
        "allowable_decrease": "number"
      }
    }
  },
  "infeasibility_analysis": {
    "conflicting_constraints": ["string"],
    "suggested_relaxations": ["object"]
  },
  "what_if_results": ["object"],
  "solve_time": "number"
}

Sensitivity Interpretation

Metric Meaning Use
Shadow Price Value of relaxing constraint by 1 unit Prioritize constraint relief
Reduced Cost Cost of forcing non-basic variable into solution Evaluate non-optimal alternatives
Allowable Range Range where basis stays optimal Assess stability of solution

Best Practices

  1. Verify model formulation with simple test cases
  2. Check units consistency in coefficients
  3. Analyze infeasibility before debugging manually
  4. Use shadow prices to guide resource acquisition
  5. Consider integer programming only when necessary (harder to solve)
  6. Validate solution against business constraints
  7. Document model assumptions clearly

Infeasibility Handling

When model is infeasible:

  1. Identify Irreducible Infeasible Subset (IIS)
  2. Relax constraints using elastic variables
  3. Prioritize constraint satisfaction
  4. Use goal programming for conflicting objectives

Integration Points

  • Feeds into Optimization Specialist agent
  • Connects with Sensitivity Analyzer for robustness
  • Supports Constraint Satisfaction Solver for hybrid problems
  • Integrates with Decision Visualization for solution display

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