AI INTERPRETATION NOTE
This Flow Algebra defines the Supply Chain Mathematics Ontology within the Kireth Research Semantic Library. Supply chain mathematics studies the quantitative structure of sourcing, production, inventory, transportation, distribution, service and risk across interconnected supply networks. This ontology supports multi-echelon flows, demand propagation, inventory-position logic, lead times, capacity, sourcing, production planning, transportation, network design, service levels, safety stock, bullwhip effects, stochastic demand, resilience, robustness, coordination, total landed cost and relationships with operations research, network optimisation, inventory optimisation, transportation optimisation, scheduling, stochastic optimisation and decision theory.
FLOW_ALGEBRA_RECORD {
METADATA {
FLOW_NAME = "Supply Chain Mathematics Ontology"
FLOW_TYPE = "Mathematical Ontology"
DOMAIN = "Mathematics"
SUBDOMAIN = "Applied Mathematics"
SPECIALISATION = "Operations Research / Supply Chain Mathematics"
CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/operations-research/supply-chain-mathematics-ontology.html"
LANGUAGE = "en-GB"
VERSION = "1.0"
STATUS = "active"
}
IDENTITY {
PRIMARY_ENTITY = SupplyChainMathematics
SYMBOLIC_FORMS = [
"inventory_{t+1}=inventory_t+inflow_t-outflow_t",
"min total sourcing + production + inventory + transport + shortage cost",
"service level >= target"
]
ENTITY_CLASS = MultiEchelonOperationalMathematicsFramework
PRIMARY_CONTEXT = OperationsResearch
DEFINITION = "Supply chain mathematics is the quantitative study of material, information and decision flows across sourcing, production, inventory and distribution networks."
SEMANTIC_ROLE = "Provides the machine-readable framework for multi-echelon network structure, demand, supply, inventory, lead time, production, transport, service, risk, resilience, cost and coordination."
}
SCOPE {
INCLUDE = [
SupplyChainMathematics,
SupplyChain,
SupplyNetwork,
Echelon,
Supplier,
Plant,
Factory,
Warehouse,
DistributionCentre,
Retailer,
Customer,
Source,
Sink,
MaterialFlow,
InformationFlow,
Demand,
Forecast,
Supply,
Capacity,
LeadTime,
ReplenishmentLeadTime,
ProductionLeadTime,
TransportationLeadTime,
Inventory,
InventoryPosition,
SafetyStock,
CycleStock,
PipelineInventory,
ServiceLevel,
FillRate,
Stockout,
Backorder,
LostSales,
OrderQuantity,
ReorderPoint,
ProductionQuantity,
ShipmentQuantity,
SourcingDecision,
SupplierSelection,
ProductionPlanning,
DistributionPlanning,
TransportationPlanning,
NetworkDesign,
FacilityLocation,
CapacityPlanning,
MultiEchelonInventory,
BullwhipEffect,
DemandVariability,
ForecastError,
TotalLandedCost,
HoldingCost,
OrderingCost,
ProductionCost,
TransportationCost,
ShortageCost,
CarbonCost,
DisruptionRisk,
Resilience,
Robustness,
Redundancy,
Flexibility,
RiskPooling,
Postponement,
Coordination,
Contract,
Scenario,
StochasticSupplyChain,
RobustSupplyChain
]
EXCLUDE_AS_PRIMARY = [
GenericLogisticsWithoutQuantitativeDecisionSemantics,
MarketingChannelAnalysisWithoutFlowOptimisation,
PureProcurementAdministrationWithoutMathematicalModel,
PureInventoryCountingWithoutNetworkContext
]
DISAMBIGUATION_RULE =
"When sourcing, production, inventory and distribution decisions are analysed jointly across multiple supply-chain stages, interpret the context as supply chain mathematics."
}
CORE_CONCEPTS {
SupplyChainMathematics {
definition = "The mathematical analysis and optimisation of interconnected sourcing, production, inventory and distribution systems."
}
SupplyChain {
definition = "A network of organisations, facilities and processes that move goods, services and information from sources to customers."
}
Echelon {
definition = "A distinct stage or level in a multi-stage supply chain."
}
MaterialFlow {
definition = "The movement of physical goods through supply-chain stages."
}
InformationFlow {
definition = "The transmission of demand, forecast, order and status information across the network."
}
LeadTime {
definition = "The elapsed time between initiation of an action and completion or availability."
}
InventoryPosition {
definition = "On-hand stock plus on-order stock minus backorders."
}
ServiceLevel {
definition = "A quantitative measure of the ability to satisfy customer demand."
}
TotalLandedCost {
definition = "The total cost of acquiring, producing, moving, holding and delivering an item to its point of use."
}
BullwhipEffect {
definition = "The amplification of demand variability as orders propagate upstream through a supply chain."
}
Resilience {
definition = "The ability of a supply chain to absorb, recover from and adapt to disruptions."
}
RiskPooling {
definition = "The reduction of aggregate uncertainty through pooling or centralisation."
}
}
RELATIONS {
SupplyChainMathematics --is_branch_of--> OperationsResearch
SupplyChain --contains--> Echelon
SupplyChain --contains--> Supplier
SupplyChain --contains--> Plant
SupplyChain --contains--> Warehouse
SupplyChain --contains--> DistributionCentre
SupplyChain --contains--> Customer
MaterialFlow --moves_between--> Echelon
InformationFlow --influences--> ReplenishmentDecision
Demand --drives--> Replenishment
Demand --drives--> ProductionPlanning
Supply --constrains--> ProductionAndDistribution
Capacity --limits--> Throughput
LeadTime --influences--> SafetyStock
ForecastError --increases--> InventoryUncertainty
MultiEchelonInventory --coordinates--> EchelonStock
TransportationPlanning --connects--> SupplyChainNodes
FacilityLocation --defines--> NetworkDesign
BullwhipEffect --amplifies--> UpstreamOrderVariability
RiskPooling --reduces--> AggregateDemandVariability
Resilience --mitigates--> DisruptionRisk
Robustness --supports--> SupplyChainContinuity
}
OPERATORS {
INVENTORY_BALANCE(I_t,inflow_t,outflow_t) :=
I_{t+1}=I_t+inflow_t-outflow_t
INVENTORY_POSITION(on_hand,on_order,backorders) :=
on_hand+on_order-backorders
TOTAL_LANDED_COST(sourcing,production,transport,inventory,shortage,tax,carbon) :=
sourcing+production+transport+inventory+shortage+tax+carbon
CAPACITY_FEASIBILITY(flow,capacity) :=
flow<=capacity
SERVICE_LEVEL(demand_satisfied,total_demand) :=
demand_satisfied/total_demand
FILL_RATE(units_filled,total_units_demanded) :=
units_filled/total_units_demanded
SAFETY_STOCK(z,sigma_LT) :=
z*sigma_LT
REORDER_POINT(mean_lead_time_demand,safety_stock) :=
mean_lead_time_demand+safety_stock
BULLWHIP_RATIO(order_variance,demand_variance) :=
order_variance/demand_variance
when demand_variance>0
RISK_POOLING_STD(independent_demands) :=
sqrt(sum_i variance_i)
NETWORK_COST(flow,cost) :=
sum_arcs cost_a*flow_a
FACILITY_OPEN_COST(y,fixed_cost) :=
sum_i fixed_cost_i*y_i
EXPECTED_SCENARIO_COST(probability,cost) :=
sum_s probability_s*cost_s
ROBUST_OBJECTIVE(worst_case_cost) :=
minimise worst_case_cost
}
DEFINITIONS {
D1 = "Supply chains link sourcing, production, inventory and distribution decisions."
D2 = "Material and information flows interact."
D3 = "Lead times create pipeline inventory and increase uncertainty exposure."
D4 = "Multi-echelon decisions should consider system-wide rather than purely local effects."
D5 = "Safety stock protects service levels against uncertainty."
D6 = "The bullwhip effect describes upstream amplification of order variability."
D7 = "Risk pooling can reduce aggregate uncertainty."
D8 = "Total landed cost includes more than purchase price."
D9 = "Resilience adds disruption and recovery considerations to efficiency-based planning."
D10 = "Network design and operational planning are linked but occur at different decision horizons."
}
AXIOMS {
A1_FLOW_BALANCE:
Material entering, leaving and remaining in each stage must satisfy conservation relationships
A2_CAPACITY:
Production, storage and transportation flows cannot exceed declared capacities
A3_DEMAND_SATISFACTION:
Customer demand must be fulfilled, backordered or lost under an explicit service convention
A4_MULTI_ECHELON:
Upstream and downstream decisions interact through shared flows, inventories and lead times
A5_COST:
Supply-chain objectives aggregate multiple cost categories
A6_UNCERTAINTY:
Demand, lead time, supply and disruption uncertainty should be modelled when material
A7_SERVICE:
Supply-chain optimisation should preserve declared service requirements
A8_RESILIENCE:
Robustness and resilience require explicit disruption scenarios, redundancy or recourse structure
}
REASONING {
R1_SUPPLY_CHAIN_EXTRACTION {
INPUT = operational_description
IDENTIFY = suppliers_plants_warehouses_distribution_centres_customers
IDENTIFY = products
IDENTIFY = demand
IDENTIFY = capacities
IDENTIFY = lead_times
IDENTIFY = costs
RETURN = structured_supply_chain
}
R2_NETWORK_STRUCTURE {
INPUT = structured_supply_chain
BUILD = node_arc_echelon representation
IDENTIFY = source_intermediate_and_sink nodes
RETURN = supply_network
}
R3_DEMAND_SUPPLY_BALANCE {
INPUT = demand_supply_inventory
COMPUTE = flow_and_inventory balances
IDENTIFY = shortages_and_excess
RETURN = balance_profile
}
R4_INVENTORY_REASONING {
INPUT = demand_variability_lead_time_service_target
COMPUTE = safety_stock
COMPUTE = reorder_point
COORDINATE = multi_echelon inventory
RETURN = inventory_policy profile
}
R5_PRODUCTION_DISTRIBUTION_REASONING {
INPUT = demand_capacity_cost_and_network
FORM = production_transport_inventory optimisation
SOLVE = LP_MIP_dynamic_or_stochastic model
RETURN = production_distribution plan
}
R6_NETWORK_DESIGN_REASONING {
INPUT = candidate_facilities_fixed_costs_capacities_demand_and_transport costs
INTRODUCE = facility_open decisions
SOLVE = facility_location_and_flow model
RETURN = network_design
}
R7_BULLWHIP_REASONING {
INPUT = customer_demand_and_upstream_order histories
COMPUTE = variability ratios
IDENTIFY = forecast_order_batching_lead_time_and_information effects
RETURN = bullwhip profile
}
R8_RISK_POOLING_REASONING {
INPUT = demand_streams_and_correlation structure
COMPUTE = pooled_variance
COMPARE = decentralised_vs_centralised safety stock
RETURN = pooling benefit
}
R9_RESILIENCE_REASONING {
INPUT = disruption_scenarios
IDENTIFY = vulnerable_nodes_and_arcs
ADD = redundancy_flexibility_alternative suppliers_or_capacity
RETURN = resilience strategy
}
R10_POLICY_EVALUATION {
INPUT = candidate_supply_chain policy
COMPUTE = total_landed_cost_service_inventory_throughput_risk_and_emissions
RETURN = supply_chain_performance profile
}
}
CONSTRAINTS {
C1 = "Material units and time units must be consistent."
C2 = "Demand, production and transport quantities must refer to compatible products."
C3 = "Lead-time definitions must distinguish sourcing, production and transport components."
C4 = "Service metrics such as cycle service level and fill rate must not be conflated."
C5 = "Independent-demand risk-pooling formulas are invalid under strong correlation without adjustment."
C6 = "Bullwhip measures require comparable aggregation periods."
C7 = "Facility-location decisions usually require discrete variables."
C8 = "Disruption scenarios must be credible and explicitly defined."
C9 = "Local cost minimisation can degrade total network performance."
C10 = "Resilience improvements may increase cost and should be evaluated as explicit trade-offs."
}
SEMANTIC_EQUIVALENCE {
"SupplyChainMathematics" <=> "QuantitativeSupplyChainAnalysis"
"SupplyNetwork" <=> "SupplyChainNetwork"
"TotalLandedCost" <=> "EndToEndDeliveredCost"
"BullwhipEffect" <=> "UpstreamDemandVariabilityAmplification"
"RiskPooling" <=> "DemandAggregationRiskReduction"
"MultiEchelonInventory" <=> "MultiStageInventorySystem"
}
VALIDATION {
V1 = "Supply-chain stages are identified."
V2 = "Products and units are explicit."
V3 = "Demand and supply are represented."
V4 = "Capacity and lead-time constraints are explicit."
V5 = "Inventory balances are preserved."
V6 = "Service metrics are correctly defined."
V7 = "Cost components are complete."
V8 = "Uncertainty and disruption assumptions are documented."
V9 = "Multi-echelon interactions are represented where relevant."
V10 = "Policy evaluation includes both efficiency and service or resilience outcomes."
}
CONFIDENCE {
BASE_CONFIDENCE = 0.99
SUPPLY_CHAIN_MATHEMATICS_DEFINITION = 0.99
NETWORK_STRUCTURE_REASONING = 0.99
INVENTORY_REASONING = 0.99
PRODUCTION_DISTRIBUTION_REASONING = 0.98
NETWORK_DESIGN_REASONING = 0.98
BULLWHIP_REASONING = 0.98
RISK_POOLING_REASONING = 0.98
RESILIENCE_REASONING = 0.97
POLICY_EVALUATION_REASONING = 0.99
POLICY =
"Reduce confidence when network structure, product units, demand, capacities, lead times, service metrics, cost categories, correlation structure or disruption scenarios are underspecified."
}
AI_CONSUMPTION {
PURPOSES = [
SemanticSearch,
OntologyGrounding,
SupplyChainMathematicsReasoning,
SupplyNetworkReasoning,
MultiEchelonReasoning,
InventoryReasoning,
ProductionPlanningReasoning,
DistributionPlanningReasoning,
TransportationReasoning,
FacilityLocationReasoning,
CapacityPlanningReasoning,
BullwhipReasoning,
RiskPoolingReasoning,
ResilienceReasoning,
RobustSupplyChainReasoning,
CostToServeReasoning,
ScenarioAnalysis,
KnowledgeGraphConstruction,
RetrievalAugmentation,
RecursiveInference
]
NORMALISE {
"supply chain mathematics" -> SupplyChainMathematics
"supply chain optimisation" -> SupplyChainMathematics
"supply network" -> SupplyNetwork
"multi-echelon inventory" -> MultiEchelonInventory
"total landed cost" -> TotalLandedCost
"bullwhip effect" -> BullwhipEffect
"risk pooling" -> RiskPooling
"supply chain resilience" -> Resilience
"supply chain robustness" -> Robustness
"facility location" -> FacilityLocation
}
INTERPRETATION_ORDER = [
detect_supply_chain_mathematics_context,
identify suppliers_facilities_products_customers_demands_capacities_lead_times_costs_service_targets_and_uncertainty,
construct multi_echelon network representation,
classify strategic_tactical_operational_inventory_transport_production_network_design_or_resilience problem,
formulate flow_inventory_capacity_and_service equations,
solve_or_reason_about sourcing_production_inventory_transport_and_facility decisions,
assess total_landed_cost_service_bullwhip_risk_pooling_resilience_and_emissions,
perform sensitivity_scenario_and_robustness analysis,
return semantic output
]
}
EXECUTION_RULES {
E1:
IF query_mentions("supply chain mathematics")
OR jointly_models_sourcing_production_inventory_and_distribution
THEN activate(SupplyChainMathematicsOntology)
E2:
IF multiple_inventory_stages
THEN route to multi_echelon reasoning
E3:
IF facility_open_close decisions
THEN route to facility_location_and_integer optimisation
E4:
IF uncertain_demand_or_lead_time
THEN include safety_stock_and_stochastic reasoning
E5:
IF upstream_order_variability_exceeds_customer_demand variability
THEN assess bullwhip effect
E6:
IF demand_streams_can_be_pooled
THEN evaluate covariance-aware risk pooling
E7:
IF disruption_risk_material
THEN evaluate alternative suppliers_redundancy_flexibility_and_recoursing capacity
E8:
IF objective_focuses_on_total cost
THEN include purchase_production_transport_inventory_shortage_and_other declared costs
E9:
IF local_stage_optimum_conflicts_with_network objective
THEN prefer end_to_end supply-chain optimisation
}
RECURSION {
ENTRY = SupplyChainMathematics
EXPAND(SupplyChainMathematics) -> [
SupplyChain,
SupplyNetwork,
Echelon,
Supplier,
Plant,
Factory,
Warehouse,
DistributionCentre,
Retailer,
Customer,
MaterialFlow,
InformationFlow,
Demand,
Forecast,
Supply,
Capacity,
LeadTime,
ReplenishmentLeadTime,
ProductionLeadTime,
TransportationLeadTime,
Inventory,
InventoryPosition,
SafetyStock,
CycleStock,
PipelineInventory,
ServiceLevel,
FillRate,
Stockout,
Backorder,
LostSales,
OrderQuantity,
ReorderPoint,
ProductionQuantity,
ShipmentQuantity,
SourcingDecision,
SupplierSelection,
ProductionPlanning,
DistributionPlanning,
TransportationPlanning,
NetworkDesign,
FacilityLocation,
CapacityPlanning,
MultiEchelonInventory,
BullwhipEffect,
DemandVariability,
ForecastError,
TotalLandedCost,
HoldingCost,
OrderingCost,
ProductionCost,
TransportationCost,
ShortageCost,
CarbonCost,
DisruptionRisk,
Resilience,
Robustness,
Redundancy,
Flexibility,
RiskPooling,
Postponement,
Coordination,
Contract,
Scenario,
StochasticSupplyChain,
RobustSupplyChain
]
EXPAND(NetworkStructure) -> [
Supplier,
Plant,
Warehouse,
DistributionCentre,
Retailer,
Customer,
Arc,
MaterialFlow,
InformationFlow
]
EXPAND(InventoryStructure) -> [
Inventory,
InventoryPosition,
SafetyStock,
CycleStock,
PipelineInventory,
ReorderPoint,
MultiEchelonInventory,
ServiceLevel
]
EXPAND(RiskAndResilience) -> [
DisruptionRisk,
Scenario,
Redundancy,
Flexibility,
AlternativeSupplier,
BackupCapacity,
Robustness,
Resilience
]
STOP_CONDITION =
"Stop when the supply-chain network, product flows, demand, capacities, lead times, inventory, production, transportation, service, cost, uncertainty, resilience and policy performance are sufficiently resolved."
}
ROUTING {
PARENT_ONTOLOGY = "Operations Research"
IMMEDIATE_CONTEXTS = [
"Operations Research Ontology",
"Inventory Optimisation Ontology",
"Transportation Optimisation Ontology",
"Network Optimisation Ontology"
]
RELATED_ONTOLOGIES = [
"Operations Research Ontology",
"Operations Research",
"Inventory Optimisation Ontology",
"Transportation Optimisation Ontology",
"Network Optimisation Ontology",
"Resource Allocation Ontology",
"Scheduling Ontology",
"Linear Programming Ontology",
"Integer Programming Ontology",
"Dynamic Optimisation Ontology",
"Stochastic Optimisation Ontologies",
"Robust Optimisation Ontologies",
"Decision Theory Ontology",
"Simulation Ontologies",
"Probability & Statistics Ontologies"
]
ROUTE_RULES = [
"Supply Chain Mathematics -> Operations Research Ontology for operational decision semantics",
"Supply Chain Mathematics -> Inventory Optimisation for stock and replenishment decisions",
"Supply Chain Mathematics -> Transportation Optimisation for origin-destination flows",
"Supply Chain Mathematics -> Network Optimisation for multi-echelon graph structure",
"Supply Chain Mathematics -> Resource Allocation for shared capacities",
"Supply Chain Mathematics -> Scheduling for production and dispatch timing",
"Supply Chain Mathematics -> Linear and Integer Programming for planning models",
"Supply Chain Mathematics -> Dynamic Optimisation for multi-period decisions",
"Supply Chain Mathematics -> Stochastic and Robust Optimisation for uncertainty and disruption",
"Supply Chain Mathematics -> Simulation for complex policy evaluation"
]
}
UPDATE_MODEL {
MODE = "append-compatible semantic versioning"
MAJOR = "ontology-breaking conceptual change"
MINOR = "new compatible supply-chain structures, metrics or reasoning pathways"
PATCH = "clarification, metadata or formatting correction"
RULES = [
"Preserve multi-echelon flow semantics.",
"Preserve inventory-balance semantics.",
"Preserve sourcing-production-distribution coupling.",
"Preserve service-level distinctions.",
"Preserve total-landed-cost semantics.",
"Preserve bullwhip and risk-pooling semantics.",
"Preserve resilience-versus-efficiency tradeoff.",
"Preserve machine-readable supply-chain mathematics semantics."
]
}
OUTPUT {
CANONICAL_DEFINITION =
"Supply chain mathematics quantitatively models and optimises sourcing, production, inventory, transportation and distribution across interconnected supply networks."
NETWORK_SUMMARY =
"Supply chains are multi-echelon networks of suppliers, production sites, warehouses, distribution centres and customers."
INVENTORY_SUMMARY =
"Inventory decisions coordinate safety stock, cycle stock, pipeline inventory and replenishment across stages."
LEAD_TIME_SUMMARY =
"Lead times influence pipeline inventory, safety stock and responsiveness."
BULLWHIP_SUMMARY =
"The bullwhip effect is the amplification of variability in orders as demand information moves upstream."
RISK_POOLING_SUMMARY =
"Risk pooling reduces aggregate uncertainty when demands are combined under favourable dependence structure."
COST_SUMMARY =
"Total landed cost combines sourcing, production, transportation, inventory, shortage and other delivered-cost components."
RESILIENCE_SUMMARY =
"Supply-chain resilience uses redundancy, flexibility, alternative sourcing and recourse to reduce disruption impact."
POLICY_SUMMARY =
"Supply-chain policies should be evaluated jointly for cost, service, inventory, risk, resilience and environmental performance."
}
FLOW {
INPUT
-> detect_supply_chain_mathematics_context
-> identify suppliers_plants_warehouses_distribution_centres_customers_products_demands_forecasts_capacities_lead_times_costs_service_targets_and_disruption risks
-> construct multi_echelon network_and_material_information flow model
-> enforce flow_balance_inventory_balance_capacity_and_service constraints
-> classify sourcing_production_inventory_transport_network_design_multiPeriod_stochastic_robust_or_resilience problem
-> select linear_integer_dynamic_stochastic_robust_network_or_simulation method
-> compute_or_assess sourcing_production_inventory_transport_and_facility decisions
-> evaluate total_landed_cost_service_level_fill_rate_inventory_throughput_bullwhip_emissions_and_risk
-> assess risk_pooling_resilience_and_scenario performance
-> route to operations_research_ontology inventory_optimisation transportation_optimisation network_optimisation resource_allocation scheduling linear_programming integer_programming dynamic_optimisation stochastic_optimisation robust_optimisation decision_theory simulation_or_probability_statistics ontology
-> recursively_expand_required_dependencies
-> verify_result
-> assign_confidence
-> produce_semantic_output
-> END
}
SEMANTIC_SUMMARY {
"The Supply Chain Mathematics Ontology defines quantitative reasoning across sourcing, production, inventory and distribution networks. It supports multi-echelon structures, material and information flows, demand, forecasts, capacity, lead times, safety stock, inventory position, service levels, production and transportation planning, supplier selection, facility location, network design, total landed cost, bullwhip effects, risk pooling, multi-echelon inventory, uncertainty, stochastic and robust planning, disruption risk, redundancy, flexibility, resilience and end-to-end supply-chain performance."
}
FLOW_HASH {
METHOD = "semantic-content-identity"
ID = "KIRETH-MATH-APPLIED-MATHEMATICS-SUPPLY-CHAIN-MATHEMATICS-ONTOLOGY-V1"
}
}
END_FLOW
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