Operations Research & Simulation
Help companies figure out the best way to use their resources—whether that's scheduling shifts, routing trucks, or testing "what if" scenarios before making big changes.
Operations Research & AI
Better decisions through data and models
Model the future, optimize the present, and turn complex decisions into measurable outcomes—through simulation, optimization, and AI.
Start a conversationWhat I do
Three disciplines. One goal: making complex systems work better.
Artificial Intelligence & Predictive Analytics
Build custom AI tools that actually fit real workflows—from forecasting demand to automating repetitive tasks with machine learning and large language models.
Big Data Analysis & Visualization
Turn messy data into clear answers. Interactive dashboards, statistical analysis, and system integrations that help teams make better decisions faster.
Selected projects
Real challenges, measurable outcomes.
Crowd Management Platform
Built an interactive online platform to train thousands of decision-makers and practitioners for pilgrimages with over a million participants. Evidence-based training for safety, efficiency, and preparedness.
With desior GmbHWarehouse Optimization
Simulated months of SKU flows across 1M+ items to optimize size limits, assignment rules, and storage strategies. Simulation-based parameters outperformed Excel planning for smoother operations from day one.
With Planningio GmbHFIFA World Cup 2022 Simulation
Modeled how a million fans would move through Doha across all transport modes with complex decision models. Identified critical bottlenecks and tested interventions to ensure smooth crowd flow during the tournament.
With desior GmbHPublic Library Routing
Redesigned the periodic delivery routes for over 100 libraries. The optimized solution eliminated the need for one vehicle while maintaining service levels.
With Attalo GmbHMobile Library Routing
Optimized schedules for mobile libraries covering 1,000+ stops across more than five depots. Balanced visit frequency, driver shifts, and vehicle capacity into one coherent plan.
Split Parcel Reduction
Developed an algorithm that reduced split shipments by 80% in theoretical evaluations for an e-commerce retailer. Smarter inventory placement means fewer boxes, lower shipping costs, happier customers.
Police District Optimization
Redesigned district boundaries and dispatching rules for German and Belgian police forces. Simulation-tested changes showed improved response times and coverage, with results under discussion for adoption.
AI Learning Assistants
Built AI tutors for university courses that guide students through problems step by step—without giving away answers. Improved understanding and engagement while maintaining academic integrity.
On-Demand Rural Bus Service
Developing intelligent routing for demand-responsive transport in rural areas. Flexible scheduling that adapts to actual passenger needs instead of empty fixed routes.
How I work
A collaborative approach from first conversation to lasting results.
01
Understand
Interview stakeholders and the people closest to the challenge. Map out how things work, what data exists, and where it sits in silos. Clarify what you're really trying to solve as what's wanted and what's needed aren't always the same.
02
Analyze
Structure everything logically. Test and discuss assumptions, pinpoint where improvements have the largest impact, and identify what data is missing and should be collected. Revisit: is what we're building still what's needed?
03
Build
Start with quick wins and a working prototype, whether optimization algorithm, a simulation model, a training platform, or an AI system. Discuss what works, adjust course, and iterate based on the feedback and the first outcome.
04
Deliver
Hand over results that stand on their own, whether that's tools, dashboards, or recommendations your team can act on. Documentation and hands-on training where needed, so the solution outlasts the project.
Interactive
These interactive demos illustrate some simulation and optimization concepts I use in projects. They’re simplified on purpose—just enough to show how the underlying methods behave. Choose which demo to explore below:
Route Optimization
The Traveling Salesman Problem asks for the shortest route visiting every location exactly once. It's a cornerstone of combinatorial optimization—even modest instances are computationally hard, making heuristic approaches like 3-opt essential in practice.
Try planning a delivery route yourself: click customers in the order you'd visit them, starting and ending at the orange depot. Once you've connected all stops, hit 'Optimize' and watch a 3-opt algorithm shorten your route. The vehicles then trace the improved path.
Crowd Flow
Social force models simulate pedestrian dynamics by treating each person as a particle subject to attractive and repulsive forces. Agents are drawn toward their destination while being pushed away from walls and other agents, producing realistic behavior like lane formation and bottleneck congestion.
Tap anywhere to drop obstacle blocks and see how the crowd reacts. When density builds up, agents shift from teal to orange and slow down. Hit reset to clear your obstacles. Heads up: dense scenarios can get resource-intensive.
Facility Location
The facility location problem asks where to place facilities to minimize the total cost of serving demand. It balances proximity to customers against the number of locations, and appears in supply chain design, emergency service planning, and network infrastructure.
Each demand point needs a nearby facility. Place all 5 by clicking, drag them to reposition, or double-click to remove. The goal is to minimize total weighted distance—bigger dots carry more weight. Once all 5 are set, hit 'Show Optimal' to see how much the algorithm can improve on your layout.
Warehouse Slots
Slotting optimization assigns products to storage locations to minimize total picking travel distance. High-frequency items should sit closest to the dispatch point—a simple principle that can dramatically reduce operational costs in warehouse management.
Each product shows a number—that's how often it gets picked. Your goal: arrange them so frequently picked items sit closest to the dispatch point. Click two fields to swap them—empty fields work too—then hit 'Optimize' to see the algorithm beat your arrangement.
Network Flow
Maximum flow problems determine the greatest amount of flow that can be pushed from a source to a sink through a capacitated network. The Ford-Fulkerson method finds augmenting paths to incrementally increase throughput until no more paths exist.
Each edge has a fixed capacity (thicker = more). Click an edge to push one unit of flow through it—but only if flow has arrived at its source node first. Route as much flow as you can from S to T, then hit 'Optimize' and watch Ford-Fulkerson find the true maximum.
Knapsack Problem
The 0/1 knapsack problem asks which items to pack into a container with limited capacity to maximize total value. It's a fundamental problem in resource allocation—from cargo loading to budget planning—and is solved exactly via dynamic programming.
Each item shows its value (V) and weight (W). Click items to add them to your knapsack without exceeding the weight limit, then hit 'Optimize'. The DP table fills cell by cell—each cell shows the best value achievable using the first i items with capacity w. Orange backtracking reveals which items were chosen.
Shortest Path
Shortest path problems find the least-cost route between two nodes in a weighted graph. Dijkstra's algorithm solves this by greedily expanding the closest unvisited node, guaranteeing optimality for non-negative weights. It's the backbone of navigation systems and network routing.
Click the source node (S) to start, then click connected nodes to build a path to the target (T). Edge weights show the cost of each connection. Once you reach T, hit 'Find Shortest' and watch Dijkstra's algorithm explore the graph to find the optimal route.
Queueing
Queueing theory models systems where customers wait for service—call centers, checkout lines, or server requests. The key tradeoff: more servers reduce waiting but increase cost. Erlang's formulas predict steady-state behavior like average queue length and utilization.
Customers arrive and form a serpentine queue. Drag the arrival rate slider to control frequency, use +/- to adjust server count. Hit 'Simulate' to fast-forward 1,000 customers at 20× speed—the orange heatmap shows where people waited longest, plus steady-state utilization and average queue length.
Bus Scheduling
On-demand line-based bus services activate predefined routes only when passengers request them. Instead of running every scheduled trip, the system serves only demanded segments—reducing fleet requirements by up to 70% compared to fixed schedules. A network flow model finds the minimum number of buses needed to cover all demand.
Act as a bus dispatcher: click trip segments to assign them to buses. The system checks if your bus can reach the next segment in time—if not, a new bus starts automatically. Try to cover all segments with the fewest buses, then hit 'Optimize' to see how good your solution is. Switch scopes to change which segments need service.
Workshops & Training
Hands-on courses in programming, optimization, and AI—at universities and for corporate teams.
Selected Courses
Custom Training Available
Need something specific? I design workshops around your team's challenges—from mathematical optimization and simulation to AI implementation and data analysis. Tailored to your skill level and goals.
All courses focus on practical skills: real problems, real code, and results you can apply right away.
About
Photo: Mirjam Kilter
Dr. Tobias Vlćek
I focus on complex operations where off-the-shelf software falls short. The kind of problems that need someone to dig into the details, connect the dots, and build something that actually holds up in practice—not just in theory.
My toolkit covers mathematical optimization (JuMP, Gurobi, HiGHS, OR-Tools), custom simulation models—both agent-based and discrete-event—and AI solutions including LLM integration and RAG systems. I work primarily in Python and Julia, with PostgreSQL/PostGIS for geospatial data and Docker for deployment. Results are delivered as interactive dashboards, web applications, or reports—built faster with AI-assisted tools like Claude Code and OpenCode.
Based in Hamburg, I work across logistics, public safety, and transportation. For larger projects, I tap into a network of specialists through Hamburg Analytics to bring the right expertise on board quickly. I also continue research part-time at the University of Hamburg and teach programming and optimization at universities and in corporate workshops.
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Whether you have a specific challenge or just want to explore what's possible—reach out.