القائمة
Linear programming skill for resource allocation, scheduling, and optimization problems
يُحدَّد Prompt الذي يراجع المصدر أولًا بشكل افتراضي. يمكنك التبديل إلى أمر مباشر أو تنزيل نسخة محلية.
اقرأ SKILL.md وأي ملفات مرافقة يعرضها SkillsMP قبل أن تقرر التثبيت.
التثبيت باستخدام Codex أو Claude انسخ هذا Prompt والصقه في Codex أو Claude أو مساعد آخر ليراجع صفحة Skill ويثبّتها لك.
يتجاوز الأمر المباشر Prompt المخصّص للمراجعة. افحص المصدر قبل تشغيله.
npx skills add https://github.com/a5c-ai/babysitter --skill linear-programming-solverيبقى الأمر في سطر واحد. مرّر أفقيًا لمراجعته كاملًا قبل النسخ.
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عرض SKILL.md
استنادا إلى تصنيف SOC المهني
| name | linear-programming-solver |
| description | Linear programming skill for resource allocation, scheduling, and optimization problems |
| allowed-tools | ["Read","Write","Glob","Grep","Bash"] |
| metadata | {"specialization":"decision-intelligence","domain":"business","category":"optimization","priority":"medium","shared-candidate":true,"tools-libraries":["pulp","ortools","pyomo","cvxpy"]} |
| graph | {"domains":["domain:business-intelligence"],"skillAreas":["skill-area:quantitative-modeling","skill-area:strategic-analysis","skill-area:data-analysis"],"roles":["role:data-scientist","role:quantitative-analyst","role:operations-analyst"]} |
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.
# 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 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"
}
# 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}
]
}
| 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 |
{
"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"
}
}
{
"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"
}
| 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 |
When model is infeasible: