ULSAlgorithms · C# / .NET · Operations Research

Find an algorithm. Understand it. Use it.

A simpler documentation experience for deterministic Uncapacitated Lot-Sizing: one card per algorithm, one consistent page per method, and one common API pattern.

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Version 1.1.0-g3e5595996d · commit 3e5595996d
Minimal usageIUlsSolver
var problem = new UlsProblem(
    demands,
    setupCosts,
    productionCosts,
    holdingCosts);

IUlsSolver solver =
    new WagnerWhitinSolver();

var result = solver.Solve(problem);
Explain each line →
42public strategies
17direct exact
4formulations
2cutting-plane
19heuristics
Choose by method family

Four clear entry points

No release packs, no duplicated catalog pages, no need to understand the source tree before choosing a method.

All public methods

Choose an algorithm

Click a card for a dedicated page with description, specifications, operation, minimal code and API links.

42 algorithms
Exact algorithms

Direct methods

Self-contained exact implementations: dynamic programming, networks and combinatorial approaches.

Exact algorithmAdaptive exact strategy selection

Adaptive exact selection

AdaptiveExactUlsSolver

Selects the linear Wagner-Whitin specialization when applicable; otherwise uses a configurable O(T log T) general exact fallback

O(T) in the NSM case; O(T log T) in the general caseOpen →
Exact algorithmWagner–Whitin DP

Wagner–Whitin classical

WagnerWhitinClassicalSolver

Classical dynamic program

O(T²)Open →
Exact algorithmWagner–Whitin DP

Wagner–Whitin / Evans

WagnerWhitinEvansSolver

Low-storage forward DP

O(T²)Open →
Exact algorithmGeometric DP

Wagner–Whitin linear

WagnerWhitinSolver

Linear convex-hull specialization

O(T)Open →
Exact algorithmGeometric DP

Wagelmans general

WagelmansGeneralSolver

General geometric dynamic program

O(T log T)Open →
Exact algorithmGeometric DP

Federgruen–Tzur general

FedergruenTzurSolver

Forward tree-accelerated DP

O(T log T)Open →
Exact algorithmGeometric DP

Federgruen–Tzur linear (NSM)

FedergruenTzurNoSpeculativeMotiveSolver

Linear specialization

O(T)Open →
Exact algorithmGeometric DP

Federgruen–Tzur linear (setup)

FedergruenTzurNondecreasingSetupSolver

Linear restricted specialization

O(T)Open →
Exact algorithmMonge / geometric DP

Aggarwal–Park

AggarwalParkSolver

CDQ + implicit Monge/SMAWK architecture

O(T log T)Open →
Exact algorithmPlanning-horizon DP

Bahl–Taj planning horizon

BahlTajPlanningHorizonSolver

Data-dependent planning-horizon pruning

O(T²) worst caseOpen →
Exact algorithmPlanning-horizon DP

Heady–Zhu

HeadyZhuEconomicPartPeriodSolver

Planning horizon + economic-part-period pruning

O(T²) worst caseOpen →
Exact algorithmLinear Wagner–Whitin

Chowdhury–Baki–Azab

ChowdhuryBakiAzabSolver

Published O(T) active-diagonal algorithm

O(T)Open →
Exact algorithmPlanning-horizon DP

Sadjadi–Aryanezhad–Sadeghi

SadjadiAryanezhadSadeghiSolver

Incremental pruning + planning horizon

O(T²) worst caseOpen →
Exact algorithmParallel DP

Lyu–Lee parallel

LyuLeeParallelSolver

Modern shared-memory reconstruction

O(T²) work; O(T²/p) ideal parallel candidate spanOpen →
Exact algorithmWagner–Whitin DP

Saydam–McKnew

SaydamMcKnewFastWagnerWhitinSolver

Modern contiguous triangular-cost reconstruction

O(T²)Open →
Exact algorithmBranch and bound

Jacobs–Khumawala

JacobsKhumawalaBranchAndBoundSolver

Modern branch/subproblem reconstruction

O(T²)Open →
Exact algorithmNetwork / shortest path

Zangwill network

ZangwillNetworkSolver

Backward DAG shortest path

O(T²)Open →
Mathematical optimization

Solver-backed formulations

Exact mathematical models with automatic optimization-engine discovery.

Mathematical optimizationSolver-backed mathematical formulation

Aggregate inventory formulation

AggregateInventoryFormulationSolver

Aggregate x/y/I MILP with automatic solver selection

Solver-dependentOpen →
Mathematical optimizationSolver-backed mathematical formulation

Facility-location formulation

FacilityLocationFormulationSolver

Disaggregated q[t,k]/y formulation

Solver-dependentOpen →
Mathematical optimizationSolver-backed network formulation

Shortest-path formulation

ShortestPathFormulationSolver

Continuous network-flow formulation with path reconstruction

Solver-dependentOpen →
Mathematical optimizationSolver-backed mathematical formulation

Inventory-eliminated formulation

InventoryEliminatedFormulationSolver

Aggregate x/y formulation with inventory algebraically eliminated

Solver-dependentOpen →
Polyhedral methods

Cutting planes

Exact root strengthening using classical (l,S) inequalities.

Cutting-plane methodCutting planes / convex hull

General (l,S) cutting-plane

GeneralLsCuttingPlaneSolver

Exact general (l,S) separation + strengthened final MILP

O(T²) separation per root iteration + solverOpen →
Cutting-plane methodCutting planes / Wagner–Whitin

Wagner–Whitin (l,S) cutting-plane

WagnerWhitinLsCuttingPlaneSolver

O(T²) prefix-S Wagner–Whitin separation + strengthened final MILP

O(T²) separation per root iteration + solverOpen →
Fast construction rules

Heuristics

Practical feasible plans with a common strategy contract and no false optimality claim.

HeuristicBaseline

Lot-for-Lot

LotForLotSolver

One replenishment per positive-demand period

O(T)Open →
HeuristicAverage-cost

Silver–Meal

SilverMealSolver

Least cost per covered period

O(T)Open →
HeuristicAverage-cost

Least Unit Cost

LeastUnitCostSolver

Least relevant cost per unit

O(T)Open →
HeuristicPart-period

Part-Period Balancing

PartPeriodBalancingSolver

Closest balance to economic part period

O(T)Open →
HeuristicMarginal-cost

Groff

GroffSolver

Marginal setup/holding criterion

O(T)Open →
HeuristicFixed-cycle

Periodic Order Quantity

PeriodicOrderQuantitySolver

EOQ-derived replenishment interval

O(T)Open →
HeuristicMarginal-cost

Freeland–Colley

FreelandColleySolver

Local incremental carrying-cost criterion

O(T)Open →
HeuristicPart-period

Patterson–LaForge IPPA

PattersonLaForgeIncrementalPartPeriodSolver

Incremental part-period stopping rule

O(T)Open →
HeuristicPart-period

Wemmerlöv corrected PPB

WemmerlovModifiedPartPeriodBalancingSolver

Corrected PPB with ν = 0.5

O(T)Open →
HeuristicLook-ahead / look-back

Wemmerlöv PPB + LALB

WemmerlovPpbLookAheadLookBackSolver

PPB with local LALB adjustment

O(T)Open →
HeuristicLook-ahead / look-back

Wemmerlöv corrected PPB + LALB

WemmerlovModifiedPpbLookAheadLookBackSolver

Corrected PPB + LALB

O(T)Open →
HeuristicPart-period

Part-Period Simplified

PartPeriodSimplifiedSolver

No-overshoot EPP / Part-Period Simplified rule

O(T)Open →
HeuristicAverage-cost

Segerstedt reformulated Silver-Meal

SegerstedtReformulatedSilverMealSolver

Reformulated Silver-Meal over non-zero demand events

O(T)Open →
HeuristicAverage-cost / post-processing

Chiu modified Least Unit Cost

ChiuModifiedLeastUnitCostSolver

Classical LUC plus cost-beneficial final-lot merge

O(T)Open →
HeuristicPart-period / post-processing

Chiu-Ting modified Part-Period Balancing

ChiuTingModifiedPartPeriodBalancingSolver

Nearest-EPP PPB plus cost-beneficial final-lot merge

O(T)Open →
HeuristicAverage-cost / net period

Ho-Chang-Solis net Least Period Cost

HoChangSolisNetLeastPeriodCostSolver

Incremental O(T) evaluation of the published nAPC stopping rule; zero-demand periods are excluded from the average denominator

O(T)Open →
HeuristicAverage-cost / net period

Ho-Chang-Solis improved nLPC(i)

HoChangSolisImprovedNetLeastPeriodCostSolver

Incremental nAPC rule with the published improved tie-breaking stop condition

O(T)Open →
HeuristicPart-period / EOQ hybrid

McLaren Order Moment

McLarenOrderMomentSolver

EOQ-derived Order Moment Target with part-period accumulation and a final marginal holding/setup test

O(T)Open →
HeuristicGlobal part-period merge

Karni Maximum Part-Period Gain

KarniMaximumPartPeriodGainSolver

Priority-queue acceleration of the published non-forward global smallest-part-period merge rule

O(T log T)Open →
StartGetting Started

Input arrays → algorithm → solution.

 UseSimple API

The four types most users need.

 ChooseComplexity & assumptions

Know when a restricted method applies.

 TrustValidation & benchmarks

Tests, exact oracles and performance evidence.