Transportation Optimisation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Transportation Optimisation Ontology within the Kireth Research Semantic Library. Transportation optimisation studies the movement of goods, people or resources between origins and destinations while minimising cost, time, distance, emissions or other objectives subject to supply, demand, capacity, route and policy constraints. This ontology supports classical transportation problems, balanced and unbalanced models, transshipment, capacitated transportation, multi-period and multi-commodity transport, assignment, network flow, route cost, supply-demand balance, degeneracy, initial basic feasible solutions, transportation simplex methods, MODI and stepping-stone methods, integer and mixed-integer extensions, stochastic and robust transportation and relationships with operations research, network optimisation, resource allocation, logistics and supply-chain modelling.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Transportation Optimisation Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Operations Research / Transportation Optimisation"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/operations-research/transportation-optimisation-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = TransportationOptimisation
 SYMBOLIC_FORMS = [
  "min sum_i sum_j c_ij x_ij",
  "sum_j x_ij = s_i",
  "sum_i x_ij = d_j",
  "x_ij >= 0"
 ]
 ENTITY_CLASS = OriginDestinationFlowOptimisationFramework
 PRIMARY_CONTEXT = OperationsResearch
 DEFINITION = "Transportation optimisation is the optimisation of flows from origins to destinations subject to supply, demand, capacity and network constraints."
 SEMANTIC_ROLE = "Provides the machine-readable framework for origins, destinations, supply, demand, shipment quantities, unit transport costs, balanced and unbalanced transportation models, transshipment, capacitated flow and transportation-specific solution methods."
}

SCOPE {
 INCLUDE = [
  TransportationOptimisation,
  TransportationProblem,
  Origin,
  Destination,
  Supply,
  Demand,
  Shipment,
  ShipmentQuantity,
  TransportationCost,
  UnitTransportationCost,
  TransportationMatrix,
  CostMatrix,
  SupplyConstraint,
  DemandConstraint,
  CapacityConstraint,
  BalancedTransportationProblem,
  UnbalancedTransportationProblem,
  DummyOrigin,
  DummyDestination,
  FeasibleTransportationPlan,
  BasicFeasibleSolution,
  Degeneracy,
  TransportationSimplex,
  MODIMethod,
  UVMMethod,
  SteppingStoneMethod,
  NorthwestCornerMethod,
  LeastCostMethod,
  VogelApproximationMethod,
  OpportunityCost,
  ReducedCost,
  LoopAdjustment,
  TransshipmentProblem,
  CapacitatedTransportation,
  MultiCommodityTransportation,
  MultiPeriodTransportation,
  FixedChargeTransportation,
  IntegerTransportation,
  MixedIntegerTransportation,
  StochasticTransportation,
  RobustTransportation,
  AssignmentProblem,
  NetworkFlow,
  LogisticsCost,
  RouteConstraint,
  EmissionsCost,
  ServiceLevel
 ]

 EXCLUDE_AS_PRIMARY = [
  VehicleRoutingWithoutOriginDestinationSupplyDemandStructure,
  GenericNetworkFlowWithoutTransportationSemantics,
  SchedulingWithoutShipmentFlows,
  InventoryOptimisationWithoutMovementDecision
 ]

 DISAMBIGUATION_RULE =
  "When quantities must be shipped from supply origins to demand destinations under transport costs and capacity constraints, interpret the context as transportation optimisation."
}

CORE_CONCEPTS {

 TransportationOptimisation {
  definition = "Optimisation of origin-to-destination flows under supply, demand and cost constraints."
 }

 TransportationProblem {
  definition = "A structured flow problem assigning shipment quantities from multiple origins to multiple destinations."
 }

 Origin {
  definition = "A source location with available supply."
 }

 Destination {
  definition = "A receiving location with demand."
 }

 Supply {
  definition = "The amount available for shipment from an origin."
 }

 Demand {
  definition = "The amount required at a destination."
 }

 ShipmentQuantity {
  definition = "The decision variable specifying how much is transported from an origin to a destination."
 }

 UnitTransportationCost {
  definition = "The cost per unit shipped on a specified origin-destination lane."
 }

 BalancedTransportationProblem {
  definition = "A transportation problem in which total supply equals total demand."
 }

 UnbalancedTransportationProblem {
  definition = "A transportation problem in which total supply differs from total demand."
 }

 BasicFeasibleSolution {
  definition = "A feasible transportation plan represented by a basis of shipment cells."
 }

 Degeneracy {
  definition = "A transportation basis with fewer than m+n-1 positive or basic allocations under classical assumptions."
 }
}

RELATIONS {
 TransportationOptimisation --is_branch_of--> OperationsResearch
 TransportationOptimisation --is_special_case_of--> NetworkOptimisation
 TransportationProblem --has--> Origin
 TransportationProblem --has--> Destination
 Origin --has--> Supply
 Destination --has--> Demand
 ShipmentQuantity --connects--> Origin
 ShipmentQuantity --connects--> Destination
 ShipmentQuantity --incurs--> TransportationCost
 SupplyConstraint --limits--> OriginShipment
 DemandConstraint --requires--> DestinationReceipt
 BalancedTransportationProblem --is_type_of--> TransportationProblem
 UnbalancedTransportationProblem --is_type_of--> TransportationProblem
 DummyOrigin --balances--> ExcessDemand
 DummyDestination --balances--> ExcessSupply
 NorthwestCornerMethod --generates--> BasicFeasibleSolution
 LeastCostMethod --generates--> BasicFeasibleSolution
 VogelApproximationMethod --generates--> BasicFeasibleSolution
 MODIMethod --tests--> TransportationOptimality
 SteppingStoneMethod --tests--> TransportationOptimality
 TransshipmentProblem --generalises--> TransportationProblem
 AssignmentProblem --is_special_case_of--> TransportationProblem
}

OPERATORS {
 TOTAL_TRANSPORT_COST(x,c) :=
  sum_i sum_j c_ij*x_ij

 SUPPLY_BALANCE(i,x,s) :=
  sum_j x_ij = s_i
  for balanced fully-used supply convention

 DEMAND_BALANCE(j,x,d) :=
  sum_i x_ij = d_j

 NONNEGATIVITY(x_ij) :=
  x_ij>=0

 TOTAL_SUPPLY(s) :=
  sum_i s_i

 TOTAL_DEMAND(d) :=
  sum_j d_j

 BALANCE_TEST(s,d) :=
  TOTAL_SUPPLY(s)=TOTAL_DEMAND(d)

 ADD_DUMMY_DESTINATION(excess_supply) :=
  destination_with_demand_equal_excess_supply

 ADD_DUMMY_ORIGIN(excess_demand) :=
  origin_with_supply_equal_excess_demand

 MODI_REDUCED_COST(c_ij,u_i,v_j) :=
  c_ij-(u_i+v_j)

 OPPORTUNITY_COST(c_ij,u_i,v_j) :=
  c_ij-u_i-v_j

 LOOP_ADJUSTMENT(loop,theta) :=
  alternately_add_and_subtract_theta_along_closed transportation loop

 TRANSPORTATION_BASIS_SIZE(m,n) :=
  m+n-1
  under nondegenerate classical formulation
}

DEFINITIONS {
 D1 = "Transportation optimisation moves quantities from origins to destinations."
 D2 = "The classical transportation objective minimises total shipment cost."
 D3 = "Balanced problems have equal total supply and total demand."
 D4 = "Unbalanced problems can be balanced using dummy origins or destinations."
 D5 = "Classical transportation models are linear programmes with special network structure."
 D6 = "A nondegenerate basic feasible solution has m+n-1 basic cells."
 D7 = "MODI and stepping-stone methods evaluate nonbasic cells for potential cost improvement."
 D8 = "Transshipment allows flow through intermediate nodes."
 D9 = "Fixed charges and discrete shipment decisions require integer or mixed-integer extensions."
 D10 = "Transportation objectives may include time, emissions, reliability or service in addition to monetary cost."
}

AXIOMS {
 A1_ORIGIN_SUPPLY:
  Shipments from an origin cannot exceed or must equal available supply under the declared model

 A2_DESTINATION_DEMAND:
  Shipments into a destination must satisfy declared demand requirements

 A3_NONNEGATIVITY:
  Shipment quantities are nonnegative unless reverse flows are explicitly represented

 A4_BALANCE:
  Classical balanced transportation requires total supply equal total demand

 A5_COST:
  Total transportation cost aggregates lane-level shipment quantities times unit costs

 A6_FEASIBILITY:
  A transportation plan is feasible only if all supply, demand, capacity and policy constraints are satisfied

 A7_SPECIAL_LP_STRUCTURE:
  Classical transportation problems form a structured linear-programming class

 A8_OPTIMALITY:
  A feasible transportation plan is optimal when no admissible shipment reallocation can improve the objective
}

REASONING {

 R1_TRANSPORTATION_PROBLEM_EXTRACTION {
  INPUT = operational_description
  IDENTIFY = origins
  IDENTIFY = destinations
  IDENTIFY = supplies
  IDENTIFY = demands
  IDENTIFY = transport_costs
  IDENTIFY = capacities_and_route restrictions
  RETURN = structured_transportation_problem
 }

 R2_BALANCE_ANALYSIS {
  INPUT = supplies_and_demands
  COMPUTE = total_supply_and_total_demand
  IF equal
   CLASSIFY = balanced
  ELSE IF supply>demand
   ADD = dummy_destination
  ELSE
   ADD = dummy_origin
  RETURN = balanced_equivalent_model
 }

 R3_INITIAL_SOLUTION_NORTHWEST {
  INPUT = balanced_transportation_matrix
  ALLOCATE = min(current_origin_supply,current_destination_demand)
  ADVANCE = exhausted_row_or_column
  RETURN = initial_basic_feasible_solution
 }

 R4_INITIAL_SOLUTION_LEAST_COST {
  INPUT = balanced_transportation_matrix
  SELECT = lowest_cost_available_cell
  ALLOCATE = maximum_feasible quantity
  UPDATE = residual_supply_and_demand
  RETURN = initial_basic_feasible_solution
 }

 R5_VOGEL_APPROXIMATION {
  INPUT = cost_matrix
  COMPUTE = row_and_column penalties
  SELECT = largest_penalty
  ALLOCATE = to_lowest_cost_cell_in_selected row_or_column
  REPEAT = until all supply_and_demand satisfied
  RETURN = high_quality_initial_solution
 }

 R6_MODI_OPTIMALITY {
  INPUT = current_basic_solution
  SOLVE = u_i+v_j=c_ij for basic cells
  COMPUTE = reduced_costs_for_nonbasic cells
  IF all_reduced_costs>=0_under_minimisation
   RETURN = optimal
  ELSE
   SELECT = most_negative entering cell
   BUILD = closed_loop
   ADJUST = allocations
  RETURN = improved_transportation_plan
 }

 R7_STEPPING_STONE {
  INPUT = nonbasic_cell_and_current_basis
  BUILD = alternating_closed_path
  COMPUTE = net_cost_change_per_unit
  IF negative
   ADJUST = flow_along_loop
  RETURN = improved_plan_or_optimality assessment
 }

 R8_CAPACITATED_TRANSPORTATION {
  INPUT = lane_capacities
  ADD = x_ij<=u_ij
  SOLVE = LP_or_network_flow model
  RETURN = capacitated_transport plan
 }

 R9_TRANSSHIPMENT_REASONING {
  INPUT = origins_intermediate_nodes_destinations
  ENFORCE = flow_balance_at_transshipment nodes
  SOLVE = minimum_cost_flow
  RETURN = transshipment plan
 }

 R10_ROBUSTNESS_AND_SENSITIVITY {
  INPUT = optimal_transport plan
  PERTURB = costs_supplies_demands_capacities
  IDENTIFY = binding lanes_and_constraints
  RETURN = transportation_sensitivity profile
 }
}

CONSTRAINTS {
 C1 = "Supply and demand units must be compatible."
 C2 = "Transportation costs must use a consistent unit basis."
 C3 = "Dummy-origin or dummy-destination costs must represent intended semantics."
 C4 = "Blocked or prohibited routes must not receive shipment."
 C5 = "Classical MODI reasoning assumes a valid transportation basis."
 C6 = "Degeneracy must be handled without violating basis structure."
 C7 = "Fixed-charge transport requires integer activation variables."
 C8 = "Multi-commodity transportation shares capacities across commodities where declared."
 C9 = "Uncertain demand or cost should use stochastic or robust formulations when material."
 C10 = "A low-cost plan is invalid if service, capacity or policy constraints are violated."
}

SEMANTIC_EQUIVALENCE {
 "TransportationOptimisation" <=> "TransportationOptimization"
 "TransportationProblem" <=> "OriginDestinationAllocationProblem"
 "ShipmentQuantity" <=> "TransportationFlowDecision"
 "UnitTransportationCost" <=> "LaneUnitCost"
 "MODIMethod" <=> "UVMethod"
 "VogelApproximationMethod" <=> "VAM"
}

VALIDATION {
 V1 = "Origins and destinations are complete."
 V2 = "Supply and demand values are explicit."
 V3 = "Cost matrix dimensions match origin-destination structure."
 V4 = "Balance condition is checked."
 V5 = "Dummy nodes are added consistently when required."
 V6 = "Shipment plan satisfies all supply and demand constraints."
 V7 = "Prohibited routes receive no flow."
 V8 = "Degeneracy is handled correctly."
 V9 = "Optimality test uses correct reduced-cost sign convention."
 V10 = "Cost, service and feasibility status are reported separately."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 TRANSPORTATION_OPTIMISATION_DEFINITION = 0.99
 BALANCE_REASONING = 0.99
 INITIAL_SOLUTION_REASONING = 0.98
 VOGEL_REASONING = 0.98
 MODI_REASONING = 0.99
 STEPPING_STONE_REASONING = 0.99
 CAPACITATED_REASONING = 0.98
 TRANSSHIPMENT_REASONING = 0.99
 SENSITIVITY_REASONING = 0.98

 POLICY =
  "Reduce confidence when supply, demand, lane costs, route restrictions, dummy-node semantics, degeneracy, capacities, commodity structure or uncertainty assumptions are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  TransportationOptimisationReasoning,
  TransportationProblemExtraction,
  SupplyDemandBalanceReasoning,
  NorthwestCornerReasoning,
  LeastCostReasoning,
  VogelApproximationReasoning,
  MODIReasoning,
  SteppingStoneReasoning,
  CapacitatedTransportationReasoning,
  TransshipmentReasoning,
  MultiCommodityTransportationReasoning,
  FixedChargeTransportationReasoning,
  RobustTransportationReasoning,
  SensitivityAnalysis,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "transportation optimisation" -> TransportationOptimisation
  "transportation optimization" -> TransportationOptimisation
  "transportation problem" -> TransportationProblem
  "transport problem" -> TransportationProblem
  "northwest corner method" -> NorthwestCornerMethod
  "least cost method" -> LeastCostMethod
  "Vogel approximation method" -> VogelApproximationMethod
  "VAM" -> VogelApproximationMethod
  "MODI method" -> MODIMethod
  "stepping-stone method" -> SteppingStoneMethod
 }

 INTERPRETATION_ORDER = [
  detect_transportation_optimisation_context,
  identify origins_destinations_supplies_demands_lane_costs_capacities_route_restrictions_time_emissions_and_service criteria,
  test balance_and_add dummy nodes_if_required,
  classify classical_capacitated_transshipment_multiCommodity_multiPeriod_fixedCharge_integer_stochastic_or_robust problem,
  generate initial feasible solution_or_form LP_network model,
  improve_solution_via MODI_steppingStone_network_simplex_or_general optimiser,
  verify supply_demand_capacity_route_and_policy feasibility,
  assess total_cost_service_emissions_and_sensitivity,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("transportation optimisation")
  OR asks_how_much_to_ship_from_origins_to_destinations
  THEN activate(TransportationOptimisationOntology)

 E2:
  IF total_supply_equals_total_demand
  THEN classify balanced transportation problem

 E3:
  IF total_supply_exceeds_total_demand
  THEN add dummy_destination_when balancing is appropriate

 E4:
  IF total_demand_exceeds_total_supply
  THEN add dummy_origin_when balancing is appropriate

 E5:
  IF classical_balanced_linear_transportation
  THEN use transportation-specific initialisation_and_optimality methods where useful

 E6:
  IF lane_capacity_constraints
  THEN route to capacitated transportation_or_min_cost flow

 E7:
  IF intermediate transfer_nodes exist
  THEN classify as transshipment

 E8:
  IF fixed_route_activation costs
  THEN route to mixed_integer transportation

 E9:
  IF uncertain_supply_demand_or_costs
  THEN route to stochastic_or_robust transportation
}

RECURSION {
 ENTRY = TransportationOptimisation

 EXPAND(TransportationOptimisation) -> [
  TransportationProblem,
  Origin,
  Destination,
  Supply,
  Demand,
  Shipment,
  ShipmentQuantity,
  TransportationCost,
  UnitTransportationCost,
  TransportationMatrix,
  CostMatrix,
  SupplyConstraint,
  DemandConstraint,
  CapacityConstraint,
  BalancedTransportationProblem,
  UnbalancedTransportationProblem,
  DummyOrigin,
  DummyDestination,
  FeasibleTransportationPlan,
  BasicFeasibleSolution,
  Degeneracy,
  TransportationSimplex,
  MODIMethod,
  UVMMethod,
  SteppingStoneMethod,
  NorthwestCornerMethod,
  LeastCostMethod,
  VogelApproximationMethod,
  OpportunityCost,
  ReducedCost,
  LoopAdjustment,
  TransshipmentProblem,
  CapacitatedTransportation,
  MultiCommodityTransportation,
  MultiPeriodTransportation,
  FixedChargeTransportation,
  IntegerTransportation,
  MixedIntegerTransportation,
  StochasticTransportation,
  RobustTransportation,
  AssignmentProblem,
  NetworkFlow,
  LogisticsCost,
  RouteConstraint,
  EmissionsCost,
  ServiceLevel
 ]

 EXPAND(InitialSolutionMethods) -> [
  NorthwestCornerMethod,
  LeastCostMethod,
  VogelApproximationMethod
 ]

 EXPAND(OptimalityMethods) -> [
  MODIMethod,
  UVMMethod,
  SteppingStoneMethod,
  TransportationSimplex,
  NetworkSimplex
 ]

 EXPAND(ExtendedTransportationModels) -> [
  CapacitatedTransportation,
  TransshipmentProblem,
  MultiCommodityTransportation,
  MultiPeriodTransportation,
  FixedChargeTransportation,
  IntegerTransportation,
  StochasticTransportation,
  RobustTransportation
 ]

 STOP_CONDITION =
  "Stop when origins, destinations, supplies, demands, shipment variables, costs, balance, capacities, initial feasible plan, optimality test, extended-model structure and sensitivity are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Operations Research"

 IMMEDIATE_CONTEXTS = [
  "Operations Research Ontology",
  "Network Optimisation Ontology",
  "Resource Allocation Ontology",
  "Linear Programming Ontology"
 ]

 RELATED_ONTOLOGIES = [
  "Operations Research Ontology",
  "Operations Research",
  "Network Optimisation Ontology",
  "Resource Allocation Ontology",
  "Linear Programming Ontology",
  "Integer Programming Ontology",
  "Constraint Optimisation Ontology",
  "Scheduling Ontology",
  "Inventory Optimisation Ontology",
  "Assignment Problem Ontologies",
  "Supply Chain Ontologies",
  "Logistics Ontologies",
  "Stochastic Optimisation Ontologies",
  "Robust Optimisation Ontologies"
 ]

 ROUTE_RULES = [
  "Transportation Optimisation -> Operations Research Ontology for operational decision semantics",
  "Transportation Optimisation -> Network Optimisation for min-cost flow and transshipment",
  "Transportation Optimisation -> Resource Allocation for scarce origin capacity",
  "Transportation Optimisation -> Linear Programming for classical continuous models",
  "Transportation Optimisation -> Integer Programming for fixed-charge or indivisible shipment decisions",
  "Transportation Optimisation -> Constraint Optimisation for route and service restrictions",
  "Transportation Optimisation -> Scheduling for time-dependent shipment movement",
  "Transportation Optimisation -> Inventory Optimisation for stock-flow coordination",
  "Transportation Optimisation -> Supply Chain and Logistics for multi-stage distribution systems",
  "Transportation Optimisation -> Stochastic and Robust Optimisation for uncertain supply, demand and costs"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible transportation models, algorithms or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"

 RULES = [
  "Preserve origin-destination flow semantics.",
  "Preserve supply-demand balance semantics.",
  "Preserve balanced-versus-unbalanced distinction.",
  "Preserve classical transportation basis semantics.",
  "Preserve dummy-node semantics.",
  "Preserve transportation-specific optimality semantics.",
  "Preserve transshipment and capacity distinctions.",
  "Preserve machine-readable transportation-optimisation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "Transportation optimisation determines how much to ship from origins to destinations while satisfying supply, demand and capacity constraints and optimising transport performance."

 BALANCE_SUMMARY =
  "A balanced transportation problem has total supply equal to total demand."

 UNBALANCED_SUMMARY =
  "An unbalanced problem can often be converted to balanced form using a dummy origin or destination."

 INITIAL_SOLUTION_SUMMARY =
  "Northwest-corner, least-cost and Vogel methods generate initial basic feasible transportation plans."

 MODI_SUMMARY =
  "MODI uses row and column potentials to calculate reduced costs and identify improving nonbasic shipment cells."

 STEPPING_STONE_SUMMARY =
  "The stepping-stone method evaluates closed shipment loops to estimate the cost effect of introducing a nonbasic route."

 TRANSSHIPMENT_SUMMARY =
  "Transshipment models permit movement through intermediate nodes."

 EXTENSION_SUMMARY =
  "Capacitated, fixed-charge, multi-commodity, multi-period, stochastic and robust transportation models extend the classical structure."

 STATUS_SUMMARY =
  "Transportation outputs should distinguish feasible, degenerate, improved, optimal and uncertainty-dependent solutions."
}

FLOW {
 INPUT
 -> detect_transportation_optimisation_context
 -> identify origins_destinations_supply_demand_shipment_costs_lane_capacities_route_restrictions_time_service_emissions_and_uncertainty
 -> test total_supply_vs_total_demand
 -> if_unbalanced add dummy_origin_or_destination with declared semantics
 -> classify classical_capacitated_transshipment_multiCommodity_multiPeriod_fixedCharge_integer_stochastic_or_robust transportation problem
 -> generate feasible_start_using northwestCorner_leastCost_Vogel_or_general LP method
 -> improve using MODI_steppingStone_transportationSimplex_networkSimplex_or_general optimiser
 -> verify supply_demand_nonnegativity_capacity_route_and_policy constraints
 -> compute total_transport_cost_service_time_emissions_and_other objectives
 -> analyse reduced_costs_shadow_values_and_sensitivity
 -> route to operations_research_ontology network_optimisation resource_allocation linear_programming integer_programming constraint_optimisation scheduling inventory_optimisation assignment supply_chain logistics stochastic_optimisation_or_robust_optimisation ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Transportation Optimisation Ontology defines origin-to-destination shipment optimisation. It supports supplies, demands, shipment quantities, unit costs, balanced and unbalanced problems, dummy nodes, initial basic feasible solutions, northwest-corner, least-cost and Vogel approximation methods, MODI and stepping-stone optimality improvement, degeneracy, transshipment, capacitated transport, multi-commodity and multi-period models, fixed-charge and integer transportation, stochastic and robust transport, assignment and network-flow relationships."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-TRANSPORTATION-OPTIMISATION-ONTOLOGY-V1"
}

}

END_FLOW