Operations Research

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76 domain-specific abstractions whose origin domain is Operations Research. They span 58 subdomains — sort by that column to group them, or click any subdomain to filter to it.

Abstraction	Subdomain	Description
1-Center Problem	Facility Location	A minimax location problem that places one center to minimize the largest distance or service cost to any demand point.
3-dimensional matching	Combinatorial Optimization	A matching in a tripartite 3-uniform hypergraph: a set of triples no two of which share any coordinate, with optimization and perfect-decision variants.
Assemble-to-order system	Inventory and Queueing Models	An assemble-to-order system holds components in inventory and assembles products only after orders arrive, coupling shared-part stocking with demand uncertainty.
Balanced matrix	Combinatorial Optimization	A binary matrix containing no odd-order square submatrix in which every row and column has exactly two ones.
Bayesian search theory	Search Theory	A probabilistic lost-object search using location beliefs, detection chances, and updates when results arrive.
BCMP network	Queueing TheoryMulticlass Product Form Networks	A class of queueing networks whose permitted node disciplines and routing assumptions yield a product-form equilibrium distribution.
Biconvex optimization	Mathematical OptimizationNonconvex Optimization	Biconvex optimization is a generalization of convex optimization where the objective function and the constraint set can be biconvex.
Bilinear program	Mathematical Optimization	A nonlinear optimization problem whose objective or constraints contain products that are linear in either variable block when the other is fixed.
Chance-Constrained Programming	Stochastic Optimization	An optimization framework that requires uncertain constraints to hold with at least a specified probability, trading nominal objective performance against a declared risk of infeasibility.
Circulation problem	Combinatorial Optimization	A network-flow feasibility or optimization problem assigning edge flows within lower and upper bounds while conserving flow at every vertex.
Closure problem	Combinatorial Optimization	The optimization problem of selecting a maximum-weight vertex set in a directed graph subject to the rule that selecting a vertex also selects every vertex reachable along its outgoing dependencies.
Complementarity theory	Mathematical Optimization	The theory of optimization and equilibrium problems seeking nonnegative vectors whose paired components have zero product, so each constraint and associated slack cannot both be positive.
Concurrent Estimation	Discrete Event SystemsSimulation Estimation	A discrete-event simulation method that maintains valid coupled alternative state histories within one nominal run to estimate performance under several parameter settings.
Covector mapping principle	Computational Optimal Control	A compatibility principle giving conditions under which discretizing an optimal-control problem and then dualizing yields covectors corresponding to a discretization of the continuous Pontryagin adjoint system.
Cutting Stock Problem	Cutting and Packing	An optimization problem that chooses feasible cutting patterns for available stock and their use counts to meet item demands while minimizing a declared stock-use, cost, or waste objective.
Decision Method	Decision AnalysisDecision Science	A decision method is a repeatable procedure that represents a decision frame, feasible alternatives, objectives or loss, evidence and uncertainty, preference or priority information, and an aggregation or search rule to recommend, rank, or adapt a course of action.
Decision Quality	Decision AnalysisDecision Process	Decision quality assesses a choice before its outcome through its frame, alternatives, information, values, reasoning, and commitment.
Discrete rate simulation	Industrial Simulation	A simulation method combining discrete events with continuous rate-based flows of material.
Discrete-Event Simulation	Discrete Event Systems	A simulation paradigm that represents system evolution as timestamped events that instantaneously change state, with no modeled state change between consecutive events.
Dual linear program	Duality	The linear program constructed from a specified primal by exchanging variables and constraints, transposing the coefficient matrix, reversing objective direction, and applying the corresponding sign and inequality rules.
G/G/1 Queue	Queueing Theory	A single-server queue model with general arrival and service behavior whose waiting results depend on declared sequencing and analysis assumptions.
Generalized Semi-Infinite Programming	Mathematical OptimizationSemi Infinite Programming	Optimize finitely many decision variables subject to infinitely many parameterized constraints whose index set itself depends on the decision, coupling outer feasibility to a moving lower-level feasible set.
Gittins index	Multi Armed Bandits and Optimal Stopping	Assign each state of an eligible discounted Markov reward arm the greatest reward rate attainable before an adapted stopping time, enabling an optimal classical bandit policy by selecting the arm with largest current index.
Goal programming	—	A multiobjective optimization method that assigns target levels to several objectives and minimizes weighted or prioritized deviations from those targets.
Gomory–Hu tree	Combinatorial Optimization	A weighted tree representing every pairwise minimum-cut value of an undirected capacitated graph through the minimum edge on the corresponding tree path.
Greedy Randomized Adaptive Search Procedure	MetaheuristicsCombinatorial Optimization	The greedy randomized adaptive search procedure (also known as GRASP) is a metaheuristic algorithm commonly applied to combinatorial optimization problems.
Guillotine cutting	Cutting and Packing Optimization	A rectangular stock-cutting constraint in which every cut must pass straight from one edge of the current rectangular piece to the opposite edge, recursively partitioning it into two rectangles.
Imperialist competitive algorithm	Metaheuristic Optimization	A population-based metaheuristic that groups candidate solutions into empires whose competition, assimilation and collapse search an optimization landscape.
Jackson's Theorem (Queueing Theory)	Queueing Theory	A queueing-network theorem giving a product-form stationary distribution for stable Markovian service nodes with suitable external arrivals and probabilistic routing.
Job-shop scheduling	Machine Scheduling	Order machine-specific operations for jobs with fixed technological precedences so shared machines never overlap and a declared schedule objective is optimized.
Kingman's Formula	Queueing Theory	In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue.
Lexicographic Optimization	Multiobjective Optimization	Lexicographic optimization is sometimes called preemptive optimization, since a small increase in one objective value preempts a much larger increase in less important objective values.
Lindley equation	Queueing TheoryWaiting Time Recursions	The reflected random-walk recursion W_(n+1)=max(0,W_n+X_n), canonically describing successive waiting times in a single-server queue.
Linear programming relaxation	Mathematical OptimizationInteger Programming	This relaxation technique transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.
Liner shipping network design and scheduling problem	—	A maritime-operations optimization problem jointly choosing liner services, schedules, vessel deployment, and container flows.
Local search (optimization)	Optimization	A heuristic optimization method that repeatedly moves to neighboring candidate solutions using local objective information.
Makespan	Scheduling Theory	The elapsed time from the start of the earliest scheduled operation to completion of the latest operation or job.
Markovian arrival process	Queueing TheoryStochastic Processes	A Markovian arrival process represents correlated event arrivals by transitions of a finite-state continuous-time Markov chain, separating transitions that generate arrivals from those that only change background state.
Matroid parity problem	Combinatorial Optimization	The optimization problem of selecting the largest collection of prescribed element pairs whose union is independent in a matroid.
Maximum satisfiability problem	Combinatorial Optimization	The optimization problem of assigning Boolean variables to maximize the number or total weight of satisfied clauses in a conjunctive normal form formula.
Minimum Relevant Variables in a Linear System	Mathematical OptimizationCardinality Minimization	Among all vectors satisfying a declared system of linear relations, select one with minimum support cardinality—the fewest nonzero variables—creating a generally NP-hard cardinality optimization rather than an ordinary continuous linear program.
Minimum-cost flow problem	Network Flow Optimization	The optimization problem of routing a required amount of flow through a capacitated network while satisfying conservation and minimizing total edge cost.
Multi-attribute utility	Decision Analysis	A utility representation assigning values to outcomes described by several attributes while encoding tradeoffs, interactions and uncertainty preferences.
Multi-commodity flow problem	Network Optimization	Route multiple source–sink commodities through one capacitated network while each commodity obeys flow conservation and all commodities jointly share edge capacities, optimizing congestion, cost, or satisfied demand.
Nesting (process)	Manufacturing Optimization	The computational layout of parts within one- to three-dimensional stock or build volume to reduce waste, motion or production time under manufacturing constraints.
Network Simplex Algorithm	Network Optimization	Solve a minimum-cost flow by maintaining a spanning-tree basis, pricing bound-fixed arcs with node-potential reduced costs, augmenting around an entering arc's fundamental cycle, and exchanging the limiting arc until dual signs certify optimality.
Nonlinear programming	Nonlinear Optimization	Optimization of an objective subject to constraints when the objective or at least one constraint is nonlinear in the decision variables.
Nurse scheduling problem	—	The constrained optimization problem of assigning qualified staff to shifts while satisfying coverage rules and balancing preferences, fairness and cost.
Offered load	Queueing TheoryTraffic Intensity Before Admission	Measure the average service work presented to a queue or telecommunications resource before blocking, loss, or carrying effects, conventionally as arrival rate times mean holding time.
Optimal Kidney Exchange	Kidney Exchange Optimization	Optimal kidney exchange selects compatible donation cycles or chains to optimize transplants among medically incompatible patient–donor pairs.
Optimistic knowledge gradient	Sequential Decision MakingCrowdsourced Label Allocation	A sequential sampling policy for costly crowdsourced labeling that scores an item by an optimistic estimate of how one more label could improve the final classification decision.
Pareto front	Multiobjective Optimization	The set of feasible objective vectors or solutions not dominated by any alternative in a multi-objective optimization problem.
Particle swarm optimization	Metaheuristic Optimization	A population-based optimization method in which candidate positions move through a search space using their own best experience and information from a neighborhood or global best.
Polling system	Queueing Theory	A queueing system in which one server visits multiple queues according to a routing rule and applies a declared service discipline at each visit.
Potentially all pairwise rankings of all possible alternatives	Multi Criteria Decision Analysis	Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA) is a method for multi-criteria decision making (MCDM) or conjoint analysis, as implemented by decision-making software and conjoint analysis products 1000minds and MeenyMo.
Quadratic knapsack problem	Combinatorial Optimization	A capacity-constrained item-selection optimization with pairwise and optional individual profits.
Quasi-bipartite graph	Combinatorial Optimization	A Steiner-tree instance in which the nonterminal vertices form an independent set, so every edge has at least one terminal endpoint.
Relaxation (approximation)	Mathematical Optimization	The replacement of a difficult optimization problem by an easier problem with weakened constraints or simplified structure whose solution bounds or informs the original.
Retrial Queue	Queueing Theory	A queueing model in which blocked requests enter an orbit and later retry admission to a finite-capacity service facility under an explicit retrial policy.
Ring star problem	Combinatorial OptimizationNetwork Design	The ring star problem (RSP) is a NP-hard problem in combinatorial optimization.
Set TSP problem	Combinatorial Optimization	A traveling-salesman generalization seeking a minimum-cost tour that visits at least one vertex from every specified group.
Sethi–Skiba Point	Optimal ControlMultiple Optimal Trajectories	An initial state or state-space locus from which distinct feasible optimal-control trajectories attain the same optimal value under one dynamic objective.
Simplex pivot rule	Linear ProgrammingNetwork Optimization	Choose among eligible simplex pivot moves by a specified entering or leaving rule, from ordinary LP variables to network-flow arcs.
Simulation	Simulation MethodologyComputational Modeling	The execution or enactment of a model through states, events, or responses so selected behavior of a real, possible, or hypothesized target can be explored under declared conditions.
Simulation-based optimization	Simulation Optimization	Optimization in which candidate decisions are evaluated by a computational simulation—often noisy, expensive and derivative-free—rather than a closed-form objective or constraint model.
Single-machine scheduling	—	The optimization of job order and timing on one capacity-one resource under declared release, precedence and objective rules.
Special Ordered Set	Mixed Integer and Global Optimization	A mixed-integer optimization constraint that orders a declared variable list and restricts its nonzero support to at most one member (SOS1) or at most two adjacent members (SOS2), exposing disjunctive structure for solver enforcement, branching, or reformulation.
Stacker Crane Problem	Pickup Delivery RoutingCombinatorial Optimization	A least-cost closed-tour problem for one unit-load carrier serving fixed directed pickup-to-delivery requests in an order it may choose.
Stochastic programming	Optimization Under Uncertainty	An optimization framework in which uncertain parameters are represented by probability distributions or scenarios and decisions are chosen across one or more information stages.
Stochastic Tunneling	Global OptimizationMonte Carlo Optimization	A Monte Carlo global-optimization method that transforms objective values relative to the best value found so higher wells flatten while minima locations remain fixed, permitting stochastic escape without a cooling schedule.
Strip packing problem	Packing ProblemsCombinatorial Optimization	The strip packing problem is a 2-dimensional geometric minimization problem.
Submodular flow	Combinatorial Optimization	A combinatorial optimization problem that minimizes linear flow cost subject to edge bounds and submodular constraints on net flow across every vertex subset.
Transport problem	Transportation ProblemLinear Programming	An optimization problem that allocates or couples supply at source locations with demand at destination locations while minimizing total transport cost under mass-balance or assignment constraints.
Uniform-machines scheduling	Scheduling Theory	In the specific variant called uniform machine scheduling, some machines are uniformly faster than others.
Wardrop Equilibrium	Traffic AssignmentNetwork Equilibrium	In game theory and operations research, a Wardrop equilibrium is a concept developed by John Glen Wardrop for the prediction of traffic patterns in transportation networks that are subject to congestion.
ÉLECTRE	Multicriteria Decision AidingOutranking Methods	A family of multicriteria decision-aiding methods that constructs credibility-qualified outranking relations between alternatives and exploits them to support choice, ranking, or sorting without forcing every criterion into full compensation.