01 · MATHEMATICAL OPTIMIZATION
Find the optimal solution.
Linear, integer, goal, and network optimization.
Formulate LP, MIP, and goal programming models with a live LaTeX preview. Solve network flows — shortest path, max flow, min-cost — on an interactive graph editor. No coding required.
Objective Function
Constraints
x₁, x₂, ... ≥ 0 assumed
Machine hours
Labor hours
Live Preview
Maximize Z = 5x₁ + 4x₂
6x₁ + 4x₂ ≤ 24 (Machine hours)
1x₁ + 2x₂ ≤ 6 (Labor hours)
x₁ ≥ 0, x₂ ≥ 0
Optimal solution
x₁*
3.0
x₂*
1.5
Z*
22.5
Status
Optimal
Network Optimization · Shortest Path
| Node | Dist from A | Previous |
|---|---|---|
| A | 0 | — |
| B | 3 | C |
| C | 2 | A |
| D | 8 | B |
| E | 12 | C |
| F | 10 | D |
02 · ASSIGNMENT & SCHEDULING
Assign the right resource at the right time.
Assignment problems, scheduling, and project management.
Solve assignment problems with the Hungarian algorithm. Build job-shop and shift schedules. Plan projects with CPM/PERT — critical path, slack, and Gantt chart included.
CPM · Critical Path
Assignment · Hungarian Method
Total Cost
13
Assigned
4/4
Utilization
100%
Avg Cost
3.25
Z* = c₁₂(1) + c₂₁(1) + c₃₃(1) + c₄₄(1) = 2+6+1+4 = 13
| # | Worker | Task | Cost |
|---|---|---|---|
| 1 | Worker 1 | Task B | 2 |
| 2 | Worker 2 | Task A | 6 |
| 3 | Worker 3 | Task C | 1 |
| 4 | Worker 4 | Task D | 4 |
| Total | 13 | ||
03 · INVENTORY & SUPPLY CHAIN
Optimize stock, flow, and facility placement.
Inventory models, supply chain optimization, facility location.
Calculate EOQ with a sawtooth timeline and cost tradeoff curves. Optimize multi-echelon supply chains with demand uncertainty. Solve facility location problems with coverage and p-median models.
EOQ Model · Inventory Policy
Q* = √(2DS/H) = √(2×1000×50/2) = 223.61
Optimal Q*
223.61
units
Total Cost TC*
$447.21
/year
Orders/Year
4.47
orders
Cycle Length
81.6
days
Inventory Timeline (Sawtooth)
Cost Tradeoff Curves
Ordering ↓ as Q↑ · Holding ↑ as Q↑ · Total minimized at Q*
04 · STOCHASTIC MODELS
Model uncertainty and randomness.
Markov chains, queueing theory, reliability analysis.
Build Markov chain models with state distribution evolution charts and transition matrices. Analyze M/M/1 queues with P(n) distributions, SLA analysis, and sensitivity curves. Estimate system reliability with MTBF/MTTR.
Markov Chain · State Distribution Evolution π⁽ᵗ⁾
Probability of being in each state at time t
M/M/1 · State Probability Distribution P(n)
Probability of n customers in system ρ = 0.80
05 · SIMULATION & RISK
Quantify uncertainty through simulation.
Monte Carlo, discrete event simulation, scenario analysis.
Run Monte Carlo simulations with output distribution histograms, VaR/CVaR risk analysis, and tornado sensitivity charts. Build discrete event models for process bottleneck detection.
Monte Carlo · Output Distribution (N=10,000)
Mean
12.5
Std Dev
2.49
VaR 95%
8.45
CVaR 95%
7.5
Formula: X + Y
Risk Analysis · VaR & CVaR
VaR 95% (P5)
8.45
CVaR 95%
7.5
P(X<0)
0%
Sensitivity Analysis — Tornado Chart
Variance contribution % of each variable
06 · DECISION ANALYTICS
Make better decisions under uncertainty.
Decision trees, AHP, and multi-criteria analysis.
Build decision trees with expected value calculations. Prioritize criteria with AHP — criteria weight bar charts and alternative performance spider charts. Rank options with TOPSIS, VIKOR, and ELECTRE.
AHP · Car Selection
Criteria Weights
Cost
55.8%
Safety
26.3%
Performance
5.7%
Comfort
12.2%
Alternative Performance by Criterion
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