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Operations Research and Management Science
Operations Research Calculators: Linear Programming, Queuing, Transportation and Decision Analysis
Every core operations research and management science calculator an engineer needs to optimize an allocation, size a waiting line, model a stochastic system, and choose well under uncertainty. Free, no sign-up, and your numbers stay in your browser.
Which operations research calculator do you need?
Tools are grouped by the kind of decision they support. Each one launches with a sourced method, worked examples, and a chart.
Match the question to the tool
| What you want to figure out | Start with this tool | Also check |
|---|---|---|
| Get the best mix of products under limited resources | Linear Programming | Transportation Problem |
| Ship from plants to warehouses at least total cost | Transportation Problem | Linear Programming |
| Match people or machines to jobs one-to-one | Assignment Problem | Transportation Problem |
| Size a service line or decide how many servers | Queuing Theory | Markov Chains |
| Estimate how long customers or jobs will wait | Queuing Theory | Decision Analysis |
| Model a system that drifts between states over time | Markov Chains | Queuing Theory |
| Choose an option when you have no probabilities | Decision Analysis | Linear Programming |
| Value information before you decide (EVPI) | Decision Analysis | Markov Chains |
Built to outrun the generic OR solvers
Real algorithms
Simplex for linear programming, the Hungarian method for assignment, exact queuing formulas, not rounded approximations or black boxes.
Shows the working
Optimal values come with the detail that matters: shadow prices, the distribution plan, steady-state vector, or the criterion-by-criterion choice.
Runs in your browser
All math is client-side. The numbers you enter are never sent to a server, stored, or sold.
Export and share
Download a clean PDF or share a result, so a model travels from a homework set or a planning meeting intact.
Sensible defaults
Each tool opens with a worked example already filled in, so you see a correct result before touching a number.
Kept current
Methods and references are reviewed as textbooks and standard practice evolve.
Optimization: turning a goal and constraints into the best decision
The optimization cluster is the heart of operations research: you state an objective to maximize or minimize, list the constraints that limit you, and the model returns the decision that does best within those limits. Linear programming is the general form, and the simplex method solves it by walking the corners of the feasible region to the optimum, reporting not just the answer but the shadow prices that say how much one more unit of a scarce resource would be worth. The transportation and assignment problems are structured special cases, shipping from sources to destinations and matching one set to another, and their dedicated algorithms solve them faster than the general simplex. Together they answer the everyday industrial question of how to allocate limited people, machines, material, and money to get the most out of them.
Waiting lines: why queues form even below full utilization
Queuing theory explains something every operations manager has seen: lines and delays appear long before a system is fully loaded, because arrivals and service times vary. Using Kendall notation like M/M/1 and M/M/c, the models take an arrival rate and a service rate and return utilization, the average number waiting and in the system, and the average wait, revealing the sharp non-linear climb in delay as utilization approaches one. That curve is why a server run at ninety percent utilization has far more than nine times the wait of one at fifty percent, and why the right number of servers, not the fewest, is often the cheaper choice once the cost of waiting is counted.
Markov chains: modeling systems that drift between states
A Markov chain models a system that moves among a finite set of states where the next state depends only on the current one. Feed the calculator a transition matrix and it returns the probabilities after any number of steps and, more usefully, the steady-state distribution, the long-run fraction of time the system spends in each state. Engineers use this for machine condition, where states might be running, degraded, and failed, for reliability and maintenance planning, and for anything from customer retention to inventory position that can be framed as jumps between states. The steady-state vector is frequently the number that drives a capacity or staffing decision.
Decision analysis: choosing well when the future is uncertain
Decision analysis structures a choice among options whose payoff depends on which future state occurs. Laid out as a payoff table, the same problem is read differently depending on what you know. Under risk, with probabilities in hand, expected monetary value ranks the options and the expected value of perfect information puts a price on resolving the uncertainty. Under pure uncertainty, without probabilities, the choice reflects your risk attitude through criteria such as maximax, maximin, minimax regret, Hurwicz, and Laplace. The calculator applies all of them to one table, so you can see how much the recommended action depends on the decision rule you adopt.
Operations research calculator FAQs
What is operations research?
Operations research, also called operational research or management science, is the discipline of using mathematical models to make better decisions about how to run a system. It grew out of military logistics in the Second World War and now underpins scheduling, routing, inventory, staffing, and capacity decisions across industry. The common thread is turning a real decision into a model with an objective to optimize and constraints to respect, then solving it. These calculators cover the classic models an industrial engineer meets first: linear programming, transportation and assignment, queuing, Markov chains, and decision analysis.
Which operations research calculator should I start with?
Start with linear programming if your problem is to get the most or least of something (profit, cost, time) subject to limited resources; it is the workhorse of the field. Use the transportation or assignment calculators when the structure is specifically about shipping between sources and destinations or matching one set to another. Reach for queuing theory when the question is about waiting lines and service capacity, Markov chains when a system moves between states over time, and decision analysis when you must choose among options under uncertainty.
What is the difference between linear programming and the transportation and assignment problems?
The transportation and assignment problems are special cases of linear programming with a particular structure. Linear programming is general: any linear objective and any linear constraints. The transportation problem is the narrower case of shipping units from supply points to demand points at minimum cost, and the assignment problem is a further special case where each source is matched to exactly one destination one-to-one. Because they are structured, they have faster dedicated algorithms (the transportation and Hungarian methods) than the general simplex, which is why they get their own calculators.
What do M/M/1 and M/M/c mean in queuing theory?
They are Kendall notation for queuing models. The first letter is the arrival process, the second is the service-time distribution, and the number is how many servers there are. M stands for Markovian, meaning arrivals follow a Poisson process and service times are exponential. So M/M/1 is one server with Poisson arrivals and exponential service, M/M/c is the same with c parallel servers, and M/M/1/K adds a maximum system capacity of K. The queuing calculator computes utilization, average number in the queue and system, and average waiting time for each.
When should I use a Markov chain?
Use a Markov chain when a system moves among a finite set of states over time and the probability of the next state depends only on the current one, not the full history. Classic uses include machine condition (running, degraded, failed), customer or brand switching, credit-rating migration, and weather. From the transition matrix, the calculator finds the n-step probabilities and the steady-state distribution, the long-run fraction of time spent in each state, which is often the number you actually want for capacity or reliability planning.
What is the difference between decision-making under uncertainty and under risk?
Under risk you know the probabilities of the possible future states, so you can compute an expected monetary value (EMV) for each option and pick the highest, and you can value information with EVPI. Under uncertainty you do not have probabilities, so you fall back on criteria that reflect your risk attitude: maximax for an optimist, maximin for a pessimist, minimax regret to limit hindsight regret, Hurwicz to blend optimism and pessimism, and Laplace to assume all states equally likely. The decision analysis calculator applies all of these to a single payoff table.
Do these calculators store the numbers I enter?
No. Every calculator runs entirely in your browser. The values you enter are never sent to our servers, stored, or shared. See our Privacy Policy.
Are the calculators free and do they need an account?
Yes, every tool is free and no account or sign-up is required. There is no paywall and no limit on how many times you can run a calculation.
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