Output-1: Operation Research Get link Facebook X Pinterest Email Other Apps March 25, 2026 <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Life Operating System</title> <script src="https://cdn.tailwindcss.com"></script> <script src="https://cdn.jsdelivr.net/npm/chart.js"></script> <link href="https://fonts.googleapis.com/css2?family=Fira+Code:wght@400;600&family=Inter:wght@300;400;600;800&display=swap" rel="stylesheet"> <style> body { font-family: 'Inter', sans-serif; background-color: #0f172a; color: #f8fafc; margin: 0; padding: 0; } .font-mono { font-family: 'Fira Code', monospace; } .glass-card { background: rgba(30, 41, 59, 0.7); backdrop-filter: blur(10px); border: 1px solid #334155; } .chart-container { position: relative; width: 100%; max-width: 600px; margin-left: auto; margin-right: auto; height: 320px; max-height: 400px; padding: 1rem; } @media (min-width: 768px) { .chart-container { height: 380px; } } .gradient-text { background-clip: text; -webkit-background-clip: text; -webkit-text-fill-color: transparent; } .gradient-cyan { background-image: linear-gradient(to right, #22d3ee, #3b82f6); } .gradient-pink { background-image: linear-gradient(to right, #f472b6, #db2777); } .gradient-amber { background-image: linear-gradient(to right, #fbbf24, #d97706); } .formula-box { background: #020617; border-left: 4px solid #3b82f6; } </style> </head> <body class="antialiased min-h-screen pb-20"> <header class="max-w-7xl mx-auto pt-10 pb-12 px-6"> <h1 class="text-4xl md:text-6xl font-extrabold tracking-tight mb-4"> <span class="gradient-text gradient-cyan">LOS v1.0</span> </h1> <p class="text-xl text-slate-400 font-light mb-8">Stochastic Optimization for the 36-Year-Old Statistician.</p> </header> <main class="max-w-7xl mx-auto px-6 grid grid-cols-1 xl:grid-cols-2 gap-10"> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-cyan-300 bg-cyan-900/50 rounded-full">Module 01</span> <h2 class="text-2xl font-bold mt-4 mb-2">Assignment Problem</h2> <p class="text-slate-400">Hungarian Method for Cognitive Allocation</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">min Σ C<sub>ij</sub> X<sub>ij</sub></p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <div class="chart-container"><canvas id="chart-assignment"></canvas></div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-pink-300 bg-pink-900/50 rounded-full">Module 02</span> <h2 class="text-2xl font-bold mt-4 mb-2">Decision Theory</h2> <p class="text-slate-400">Bayesian Belief Updating</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4" style="border-left-color: #f472b6;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">P(θ|y) ∝ P(y|θ)P(θ)</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <div class="chart-container"><canvas id="chart-bayesian"></canvas></div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl xl:col-span-2"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-amber-300 bg-amber-900/50 rounded-full">Module 03</span> <h2 class="text-2xl font-bold mt-4 mb-2">Inventory Control</h2> <p class="text-slate-400">Economic Order Quantity (EOQ)</p> </div> <div class="grid grid-cols-1 lg:grid-cols-2 gap-8"> <div class="formula-box p-4 rounded-r-lg" style="border-left-color: #fbbf24;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">Q<sup>*</sup> = √(2DS / H)</p> <p class="text-xs text-slate-400 mt-2">"Just In Time" processing beats hoarding data.</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4"> <div class="chart-container" style="max-width: 100%;"><canvas id="chart-eoq"></canvas></div> </div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-green-300 bg-green-900/50 rounded-full">Module 04</span> <h2 class="text-2xl font-bold mt-4 mb-2">Game Theory</h2> <p class="text-slate-400">Simultaneous Social Mechanics</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4" style="border-left-color: #4ade80;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">u<sub>i</sub>(s<sub>i</sub><sup>*</sup>, s<sub>-i</sub><sup>*</sup>) ≥ u<sub>i</sub>(s<sub>i</sub>, s<sub>-i</sub><sup>*</sup>)</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <table class="w-full text-sm text-center text-slate-300 border-collapse"> <thead><tr><th class="border border-slate-600 p-2"></th><th class="border border-slate-600 p-2 text-cyan-400">Share</th><th class="border border-slate-600 p-2 text-pink-400">Hoard</th></tr></thead> <tbody> <tr><th class="border border-slate-600 p-2 text-cyan-400">Share</th><td class="border border-slate-600 p-4 bg-slate-700/50">+10, +10</td><td class="border border-slate-600 p-4">-5, +15</td></tr> <tr><th class="border border-slate-600 p-2 text-pink-400">Hoard</th><td class="border border-slate-600 p-4">+15, -5</td><td class="border border-slate-600 p-4 bg-slate-800">0, 0</td></tr> </tbody> </table> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-purple-300 bg-purple-900/50 rounded-full">Module 05</span> <h2 class="text-2xl font-bold mt-4 mb-2">Project Mgmt</h2> <p class="text-slate-400">CPM/PERT for Exam Prep</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4" style="border-left-color: #a855f7;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">Slack = LS - ES</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <div class="chart-container"><canvas id="chart-cpm"></canvas></div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl xl:col-span-2"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-red-300 bg-red-900/50 rounded-full">Module 06</span> <h2 class="text-2xl font-bold mt-4 mb-2">Queueing Theory</h2> <p class="text-slate-400">M/M/1 Logic for Bottlenecks</p> </div> <div class="grid grid-cols-1 lg:grid-cols-2 gap-8"> <div class="formula-box p-4 rounded-r-lg" style="border-left-color: #ef4444;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">L<sub>q</sub> = ρ<sup>2</sup> / (1 - ρ)</p> <p class="text-xs text-slate-400 mt-2">Keep system utilization (ρ) below 80% or the queue explodes.</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4"> <div class="chart-container" style="max-width: 100%;"><canvas id="chart-queue"></canvas></div> </div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-indigo-300 bg-indigo-900/50 rounded-full">Module 07</span> <h2 class="text-2xl font-bold mt-4 mb-2">Replacement</h2> <p class="text-slate-400">Diminishing Returns</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4" style="border-left-color: #6366f1;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">min TC(t) = [C(t) + M(t)] / t</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <div class="chart-container"><canvas id="chart-replacement"></canvas></div> </div> </article> <article class="glass-card rounded-2xl p-6 flex flex-col shadow-2xl"> <div class="mb-6"> <span class="px-3 py-1 text-xs font-bold uppercase tracking-wider text-teal-300 bg-teal-900/50 rounded-full">Module 08</span> <h2 class="text-2xl font-bold mt-4 mb-2">Sequencing</h2> <p class="text-slate-400">Minimizing Makespan</p> </div> <div class="formula-box p-4 rounded-r-lg mb-4" style="border-left-color: #14b8a6;"> <h3 class="text-sm font-bold text-slate-500 uppercase tracking-widest mb-1">The Formula</h3> <p class="font-mono text-lg">min (max C<sub>j</sub>)</p> </div> <div class="w-full bg-slate-800/50 rounded-xl p-4 mt-auto"> <div class="chart-container"><canvas id="chart-sequencing"></canvas></div> </div> </article> </main> <script> function wr(t){ if(t.length<=16)return t; let w=t.split(' ');let l=[];let c=''; for(let i=0;i<w.length;i++){ if((c+' 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