Resource Allocation Ontology

AI INTERPRETATION NOTE
This Flow Algebra defines the Resource Allocation Ontology within the Kireth Research Semantic Library. Resource allocation studies the assignment of limited resources to competing activities, tasks, projects, locations, agents or time periods in order to satisfy constraints and optimise one or more objectives. This ontology supports capacities, demands, budgets, priorities, fairness, utilisation, assignment, transportation, scheduling, knapsack-style allocation, portfolio allocation, multi-period allocation, stochastic and robust allocation, shadow prices, marginal values, sensitivity, scarcity and relationships with operations research, optimisation, scheduling, linear programming and decision theory.

FLOW_ALGEBRA_RECORD {

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

IDENTITY {
 PRIMARY_ENTITY = ResourceAllocation
 SYMBOLIC_FORMS = [
  "max sum_i v_i x_i subject to sum_i a_i x_i <= b",
  "sum_j x_ij <= capacity_i",
  "allocation: resources -> activities"
 ]
 ENTITY_CLASS = ConstrainedResourceAssignmentFramework
 PRIMARY_CONTEXT = OperationsResearch
 DEFINITION = "Resource allocation is the assignment of limited resources among competing uses subject to capacity, demand, policy and objective constraints."
 SEMANTIC_ROLE = "Provides the machine-readable framework for resources, capacities, demands, assignments, utilisation, scarcity, priorities, fairness, marginal values, allocation efficiency and constrained distribution."
}

SCOPE {
 INCLUDE = [
  ResourceAllocation,
  Resource,
  ResourceType,
  Capacity,
  Budget,
  Demand,
  Requirement,
  Activity,
  Project,
  Task,
  Agent,
  Location,
  TimePeriod,
  AllocationDecision,
  AssignmentVariable,
  AllocationMatrix,
  Utilisation,
  Scarcity,
  Surplus,
  Shortage,
  Priority,
  Benefit,
  Cost,
  Efficiency,
  Fairness,
  Equity,
  ProportionalAllocation,
  PriorityAllocation,
  CapacityConstraint,
  DemandConstraint,
  BudgetConstraint,
  AssignmentConstraint,
  BalanceConstraint,
  LinearProgrammingAllocation,
  IntegerAllocation,
  TransportationAllocation,
  AssignmentProblem,
  KnapsackAllocation,
  PortfolioAllocation,
  MultiPeriodAllocation,
  DynamicAllocation,
  StochasticAllocation,
  RobustAllocation,
  ShadowPrice,
  MarginalValue,
  OpportunityCost,
  SensitivityAnalysis,
  Reallocation
 ]

 EXCLUDE_AS_PRIMARY = [
  SchedulingWithoutResourceQuantityAllocation,
  InventoryControlWithoutAllocationDecision,
  GenericBudgetingWithoutOptimisationContext,
  UnconstrainedDistributionWithoutScarceResources
 ]

 DISAMBIGUATION_RULE =
  "When scarce resources must be distributed among competing uses under explicit constraints or objectives, interpret the context as resource allocation."
}

CORE_CONCEPTS {

 ResourceAllocation {
  definition = "The constrained distribution of limited resources across competing uses."
 }

 Resource {
  definition = "A limited quantity that can be assigned, consumed, reserved or shared."
 }

 Capacity {
  definition = "The maximum amount of a resource available for allocation."
 }

 Demand {
  definition = "The requested or required amount of a resource."
 }

 AllocationDecision {
  definition = "A decision specifying how much of a resource is assigned to a recipient or activity."
 }

 Utilisation {
  definition = "The proportion or amount of available resource actually used."
 }

 Scarcity {
  definition = "A condition in which total demand exceeds or competes for limited resource capacity."
 }

 Priority {
  definition = "A ranking or weight influencing how resources are allocated."
 }

 Fairness {
  definition = "A criterion governing equitable treatment of recipients or activities."
 }

 ShadowPrice {
  definition = "The marginal improvement in objective value associated with relaxing a binding resource constraint."
 }

 MarginalValue {
  definition = "The incremental objective value associated with one additional unit of resource."
 }

 Reallocation {
  definition = "The reassignment of resources after demand, priorities or system conditions change."
 }
}

RELATIONS {
 ResourceAllocation --is_branch_of--> OperationsResearch
 ResourceAllocation --uses--> Optimisation
 ResourceAllocation --has--> Resource
 Resource --has--> Capacity
 Activity --has--> Demand
 AllocationDecision --assigns--> Resource
 AllocationDecision --to--> Activity
 AllocationDecision --must_satisfy--> CapacityConstraint
 AllocationDecision --may_satisfy--> DemandConstraint
 Utilisation --measures--> ResourceUsage
 Scarcity --arises_from--> DemandExceedingCapacity
 Priority --influences--> AllocationDecision
 Fairness --constrains--> AllocationDecision
 LinearProgrammingAllocation --is_type_of--> ResourceAllocation
 IntegerAllocation --is_type_of--> ResourceAllocation
 TransportationAllocation --is_type_of--> ResourceAllocation
 KnapsackAllocation --is_type_of--> ResourceAllocation
 PortfolioAllocation --is_type_of--> ResourceAllocation
 ShadowPrice --is_associated_with--> CapacityConstraint
 MarginalValue --supports--> Reallocation
 SensitivityAnalysis --evaluates--> AllocationRobustness
}

OPERATORS {
 TOTAL_ALLOCATION(resource_i) :=
  sum_j x_ij

 CAPACITY_FEASIBILITY(resource_i) :=
  sum_j x_ij <= capacity_i

 DEMAND_SATISFACTION(activity_j) :=
  sum_i x_ij >= required_demand_j
  when full_satisfaction_required

 BUDGET_FEASIBILITY(cost,x,budget) :=
  sum_ij cost_ij*x_ij <= budget

 RESOURCE_UTILISATION(used,available) :=
  used/available
  when available>0

 ALLOCATION_VALUE(x,v) :=
  sum_ij v_ij*x_ij

 ALLOCATION_COST(x,c) :=
  sum_ij c_ij*x_ij

 PROPORTIONAL_ALLOCATION(d_i,total_resource) :=
  total_resource*d_i/sum_j d_j
  when proportional_rule_applies

 PRIORITY_WEIGHTED_ALLOCATION(d_i,w_i,total_resource) :=
  total_resource*(w_i*d_i)/sum_j(w_j*d_j)
  under declared proportional-priority rule

 SHADOW_PRICE(constraint) :=
  dual_value_of_resource_constraint
  under valid duality conditions

 MARGINAL_REALLOCATION_VALUE(from_a,to_b,delta) :=
  objective_change_from_reassigning_delta units

 FAIRNESS_GAP(allocations,target_rule) :=
  deviation_from_declared_fairness criterion
}

DEFINITIONS {
 D1 = "Resource allocation distributes limited capacity among competing uses."
 D2 = "Allocation decisions are constrained by resource availability."
 D3 = "Demand and capacity jointly determine scarcity."
 D4 = "Allocation objectives may optimise value, cost, service, fairness or risk."
 D5 = "Shadow prices quantify the local value of additional constrained capacity."
 D6 = "Priority rules can change the optimal allocation."
 D7 = "Fairness and efficiency may conflict."
 D8 = "Multi-period allocation links current decisions with future availability."
 D9 = "Stochastic allocation accounts for uncertain demand or capacity."
 D10 = "Reallocation responds to changing operational conditions."
}

AXIOMS {
 A1_CAPACITY:
  Allocated resource cannot exceed available capacity unless explicit borrowing or overage is modelled

 A2_DEMAND:
  Allocation should not exceed or undersatisfy demand except under an explicit model allowing it

 A3_FEASIBILITY:
  Every allocation must satisfy all resource, policy and assignment constraints

 A4_OBJECTIVE:
  Allocation quality is defined relative to one or more declared criteria

 A5_SCARCITY:
  Scarcity exists when not all demands can be simultaneously satisfied under current capacities

 A6_DUAL_VALUE:
  Binding resource constraints can possess nonzero marginal values under suitable optimisation conditions

 A7_FAIRNESS:
  Fairness requires an explicit rule, metric or preference model

 A8_REALLOCATION:
  Updated data may justify changing a previous allocation
}

REASONING {

 R1_RESOURCE_PROBLEM_EXTRACTION {
  INPUT = operational_description
  IDENTIFY = resources
  IDENTIFY = capacities
  IDENTIFY = recipients_or_activities
  IDENTIFY = demands
  IDENTIFY = priorities
  IDENTIFY = objectives
  RETURN = structured_resource_allocation_problem
 }

 R2_SCARCITY_ANALYSIS {
  INPUT = capacities_and_demands
  COMPARE = aggregate_demand_to_capacity
  IDENTIFY = bottleneck_resources
  RETURN = scarcity_profile
 }

 R3_MODEL_CLASSIFICATION {
  INPUT = structured_problem
  CLASSIFY = continuous_linear_integer_transport_assignment_knapsack_portfolio_dynamic_stochastic_or_robust
  RETURN = allocation_model_class
 }

 R4_FEASIBILITY_REASONING {
  INPUT = candidate_allocation
  CHECK = capacity_constraints
  CHECK = demand_constraints
  CHECK = budget_constraints
  CHECK = assignment_constraints
  RETURN = feasible_or_infeasible
 }

 R5_EFFICIENCY_REASONING {
  INPUT = feasible_allocations
  COMPUTE = value_cost_utilisation_or_service metrics
  SELECT = objective_improving allocation
  RETURN = efficiency_profile
 }

 R6_FAIRNESS_REASONING {
  INPUT = allocation_and_fairness criterion
  MEASURE = proportionality_equity_minimum_service_or_other metric
  RETURN = fairness_profile
 }

 R7_DUAL_AND_MARGINAL_REASONING {
  INPUT = optimised_allocation_model
  EXTRACT = resource_shadow_prices
  IDENTIFY = highest_value_capacity expansions
  RETURN = marginal_value_profile
 }

 R8_STOCHASTIC_ALLOCATION {
  INPUT = uncertain_demand_or_capacity
  MODEL = scenarios_distributions_or_chance constraints
  OPTIMISE = expected_risk_adjusted_or_service objective
  RETURN = uncertainty_aware allocation
 }

 R9_ROBUST_ALLOCATION {
  INPUT = uncertainty_set
  OPTIMISE = worst_case_or_regret protected allocation
  RETURN = robust_allocation
 }

 R10_REALLOCATION_REASONING {
  INPUT = current_allocation_and_updated_data
  IDENTIFY = changed_demand_capacity_priority_or_cost
  COMPUTE = reallocation benefit_and_switching cost
  RETURN = updated_allocation_strategy
 }
}

CONSTRAINTS {
 C1 = "Resource units must be consistent."
 C2 = "Capacity and demand must refer to compatible resource types."
 C3 = "Priority weights must be interpretable and documented."
 C4 = "Fairness metrics must be explicitly defined."
 C5 = "Shadow prices are local sensitivity measures and may change after basis or active-set changes."
 C6 = "Integer resources must not be fractionally allocated unless relaxation is intended."
 C7 = "Multi-period decisions must preserve inter-period balance equations."
 C8 = "Uncertainty assumptions must be explicit."
 C9 = "Reallocation costs must be included when operationally material."
 C10 = "Mathematical efficiency does not automatically imply policy acceptability."
}

SEMANTIC_EQUIVALENCE {
 "ResourceAllocation" <=> "ConstrainedResourceDistribution"
 "Capacity" <=> "AvailableResourceLimit"
 "Demand" <=> "ResourceRequirement"
 "Scarcity" <=> "DemandCapacityShortfall"
 "ShadowPrice" <=> "MarginalResourceConstraintValue"
 "Reallocation" <=> "ResourceReassignment"
}

VALIDATION {
 V1 = "Resource types are identified."
 V2 = "Capacities are explicit."
 V3 = "Demands are explicit."
 V4 = "Allocation variables use compatible units."
 V5 = "Capacity constraints are satisfied."
 V6 = "Priority and fairness rules are documented."
 V7 = "Integer-resource restrictions are respected."
 V8 = "Shadow-price interpretations remain within valid sensitivity ranges."
 V9 = "Uncertainty assumptions are validated."
 V10 = "Allocation feasibility is checked before efficiency comparison."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 RESOURCE_ALLOCATION_DEFINITION = 0.99
 SCARCITY_REASONING = 0.99
 MODEL_CLASSIFICATION_REASONING = 0.98
 FEASIBILITY_REASONING = 0.99
 EFFICIENCY_REASONING = 0.98
 FAIRNESS_REASONING = 0.97
 DUAL_REASONING = 0.98
 STOCHASTIC_REASONING = 0.97
 REALLOCATION_REASONING = 0.98

 POLICY =
  "Reduce confidence when capacities, demand, resource compatibility, priority rules, fairness criteria, uncertainty models, shadow-price validity or reallocation costs are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  ResourceAllocationReasoning,
  CapacityReasoning,
  DemandReasoning,
  ScarcityAnalysis,
  AllocationFeasibility,
  LinearAllocationReasoning,
  IntegerAllocationReasoning,
  TransportationAllocationReasoning,
  AssignmentReasoning,
  KnapsackAllocationReasoning,
  PortfolioAllocationReasoning,
  FairnessReasoning,
  ShadowPriceReasoning,
  SensitivityAnalysis,
  StochasticAllocationReasoning,
  RobustAllocationReasoning,
  ReallocationReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "resource allocation" -> ResourceAllocation
  "resource assignment" -> ResourceAllocation
  "capacity allocation" -> ResourceAllocation
  "resource capacity" -> Capacity
  "resource demand" -> Demand
  "resource utilisation" -> Utilisation
  "scarcity" -> Scarcity
  "shadow price" -> ShadowPrice
  "marginal value" -> MarginalValue
  "reallocation" -> Reallocation
 }

 INTERPRETATION_ORDER = [
  detect_resource_allocation_context,
  identify resources_capacities_demands_recipients_priorities_costs_benefits_fairness_rules_and_uncertainty,
  classify continuous_integer_transport_assignment_knapsack_portfolio_dynamic_stochastic_or_robust allocation structure,
  construct capacity_demand_budget_balance_and_policy constraints,
  solve_or_reason_about feasible allocation,
  assess efficiency_utilisation_fairness_and_service,
  analyse shadow_prices_and_marginal values,
  evaluate sensitivity_and_reallocation if conditions change,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("resource allocation")
  OR scarce_resources_are_assigned_to_competing uses
  THEN activate(ResourceAllocationOntology)

 E2:
  IF total_demand_exceeds_capacity
  THEN classify scarcity_and_identify bottlenecks

 E3:
  IF allocations_can_be_fractional
  THEN consider linear_or_convex allocation

 E4:
  IF resources_or_assignments_are_indivisible
  THEN consider integer allocation

 E5:
  IF source_destination cost structure dominates
  THEN consider transportation_or_assignment model

 E6:
  IF fairness_is_required
  THEN include explicit fairness metric_or_constraints

 E7:
  IF uncertain_demand
  THEN consider stochastic_or_robust allocation

 E8:
  IF capacity_constraint_binding
  THEN interpret shadow_price_as local marginal value where valid

 E9:
  IF conditions_change_after_allocation
  THEN evaluate reallocation_benefit_against switching cost
}

RECURSION {
 ENTRY = ResourceAllocation

 EXPAND(ResourceAllocation) -> [
  Resource,
  ResourceType,
  Capacity,
  Budget,
  Demand,
  Requirement,
  Activity,
  Project,
  Task,
  Agent,
  Location,
  TimePeriod,
  AllocationDecision,
  AssignmentVariable,
  AllocationMatrix,
  Utilisation,
  Scarcity,
  Surplus,
  Shortage,
  Priority,
  Benefit,
  Cost,
  Efficiency,
  Fairness,
  Equity,
  ProportionalAllocation,
  PriorityAllocation,
  CapacityConstraint,
  DemandConstraint,
  BudgetConstraint,
  AssignmentConstraint,
  BalanceConstraint,
  LinearProgrammingAllocation,
  IntegerAllocation,
  TransportationAllocation,
  AssignmentProblem,
  KnapsackAllocation,
  PortfolioAllocation,
  MultiPeriodAllocation,
  DynamicAllocation,
  StochasticAllocation,
  RobustAllocation,
  ShadowPrice,
  MarginalValue,
  OpportunityCost,
  SensitivityAnalysis,
  Reallocation
 ]

 EXPAND(AllocationConstraints) -> [
  CapacityConstraint,
  DemandConstraint,
  BudgetConstraint,
  AssignmentConstraint,
  BalanceConstraint,
  PolicyConstraint,
  FairnessConstraint
 ]

 EXPAND(AllocationModels) -> [
  LinearProgrammingAllocation,
  IntegerAllocation,
  TransportationAllocation,
  AssignmentProblem,
  KnapsackAllocation,
  PortfolioAllocation,
  MultiPeriodAllocation,
  DynamicAllocation
 ]

 EXPAND(UncertaintyAllocation) -> [
  Scenario,
  StochasticAllocation,
  RobustAllocation,
  ChanceConstraint,
  RecourseDecision
 ]

 STOP_CONDITION =
  "Stop when the resources, capacities, demands, allocation variables, constraints, objective, scarcity, fairness, marginal values, uncertainty and final allocation status are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Operations Research"

 IMMEDIATE_CONTEXTS = [
  "Operations Research Ontology",
  "Optimisation Ontology",
  "Linear Programming Ontology",
  "Integer Programming Ontology"
 ]

 RELATED_ONTOLOGIES = [
  "Operations Research Ontology",
  "Operations Research",
  "Optimisation Ontology",
  "Linear Programming Ontology",
  "Integer Programming Ontology",
  "Constraint Optimisation Ontology",
  "Scheduling Ontology",
  "Transportation Problem Ontologies",
  "Assignment Problem Ontologies",
  "Inventory Ontologies",
  "Portfolio Optimisation Ontologies",
  "Decision Theory Ontology",
  "Multi-Objective Optimisation Ontology",
  "Stochastic Optimisation Ontologies",
  "Robust Optimisation Ontologies"
 ]

 ROUTE_RULES = [
  "Resource Allocation -> Operations Research Ontology for operational decision semantics",
  "Resource Allocation -> Optimisation Ontology for objective and feasible-set semantics",
  "Resource Allocation -> Linear Programming for divisible-resource models",
  "Resource Allocation -> Integer Programming for indivisible-resource decisions",
  "Resource Allocation -> Constraint Optimisation for policy and capacity restrictions",
  "Resource Allocation -> Scheduling for time-dependent resource use",
  "Resource Allocation -> Transportation and Assignment for source-destination allocation",
  "Resource Allocation -> Inventory for stock-based resource availability",
  "Resource Allocation -> Portfolio Optimisation for capital allocation",
  "Resource Allocation -> Decision Theory and Multi-Objective Optimisation for fairness and competing criteria"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

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

 RULES = [
  "Preserve resource-capacity-demand semantics.",
  "Preserve allocation-feasibility semantics.",
  "Preserve scarcity semantics.",
  "Preserve divisible-versus-indivisible resource distinction.",
  "Preserve fairness-versus-efficiency distinction.",
  "Preserve shadow-price local-sensitivity semantics.",
  "Preserve uncertainty-aware allocation semantics.",
  "Preserve machine-readable resource-allocation semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "Resource allocation distributes limited resources among competing activities, recipients or time periods subject to capacity and policy constraints."

 CAPACITY_SUMMARY =
  "Capacity defines the maximum available quantity of each resource."

 DEMAND_SUMMARY =
  "Demand defines the quantity requested or required by activities or recipients."

 SCARCITY_SUMMARY =
  "Scarcity occurs when available capacity cannot satisfy all competing demand."

 EFFICIENCY_SUMMARY =
  "Efficient allocation maximises declared value or service, or minimises cost and waste, subject to constraints."

 FAIRNESS_SUMMARY =
  "Fairness requires an explicit allocation rule or metric and may conflict with pure efficiency."

 SHADOW_PRICE_SUMMARY =
  "A shadow price estimates the local objective value of one additional unit of a binding resource."

 UNCERTAINTY_SUMMARY =
  "Stochastic and robust allocation models account for uncertain demand, capacity or value."

 REALLOCATION_SUMMARY =
  "Reallocation adapts resource assignments when demand, capacity, priorities or costs change."
}

FLOW {
 INPUT
 -> detect_resource_allocation_context
 -> identify resource_types_capacities_demands_recipients_activities_time_periods_priorities_costs_benefits_fairness_and_uncertainty
 -> classify divisible_indivisible_transport_assignment_knapsack_portfolio_multiPeriod_dynamic_stochastic_or_robust allocation problem
 -> construct allocation_variables
 -> construct capacity_demand_budget_balance_assignment_policy_and_fairness constraints
 -> identify scarcity_and_bottlenecks
 -> select linear_integer_dynamic_stochastic_robust_or_multiobjective allocation method
 -> compute_or_assess feasible allocation
 -> evaluate utilisation_efficiency_service_fairness_cost_and_value
 -> analyse shadow_prices_marginal_values_and_sensitivity
 -> if_conditions_change evaluate reallocation
 -> route to operations_research_ontology optimisation linear_programming integer_programming constraint_optimisation scheduling transportation assignment inventory portfolio decision_theory multi_objective_stochastic_or_robust_optimisation ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Resource Allocation Ontology defines the constrained distribution of scarce resources. It supports capacities, demands, budgets, activities, recipients, assignment variables, utilisation, scarcity, shortages, priorities, fairness, linear and integer allocation, transportation and assignment models, knapsack and portfolio allocation, multi-period and dynamic allocation, stochastic and robust allocation, shadow prices, marginal values, sensitivity and reallocation reasoning."
}

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

}

END_FLOW