mathematics

Operations Research & Optimization

The science of better decisions — linear programming feasibility regions, inventory cost optimization, job scheduling heuristics, Monte Carlo probability estimation, and Markov chain steady-state analysis.

operations researchlinear programmingoptimizationinventory managementschedulingMonte CarloMarkov chains

Operations research applies advanced analytical methods to help make better decisions. Born from military logistics in World War II, OR now drives supply chains, airline scheduling, financial portfolio optimization, and machine learning. Its core insight is that complex real-world problems can be modeled mathematically and solved — or at least bounded — with elegant algorithms.

These simulations let you explore linear programming feasible regions, minimize inventory holding and ordering costs, schedule jobs on machines, estimate probabilities with Monte Carlo sampling, and watch Markov chains converge to steady state — all with real-time interactive controls.

5 interactive simulations

simulator

Economic Order Quantity & Inventory Costs

Optimize inventory replenishment — explore how demand rate, ordering cost, and holding cost determine the economic order quantity and total cost

simulator

Linear Programming & Feasible Region

Visualize a 2D linear programming problem — adjust constraints and objective function to see the feasible region, corner points, and optimal solution

simulator

Markov Chain & Steady-State Analysis

Visualize a discrete Markov chain — adjust transition probabilities and watch the state distribution converge to its steady-state equilibrium

simulator

Monte Carlo Simulation & Probability Estimation

Estimate pi and other quantities using random sampling — watch Monte Carlo convergence in real time as sample size grows

simulator

Job Scheduling & Makespan Optimization

Schedule jobs on parallel machines — explore how job count, machine count, and heuristic choice affect makespan and load balance