Passenger context model

1. Overview

Manages passenger cancellations, class changes, flight changes, and amount tracking in the flight recovery scheduling system, registering passenger-related constraints and objectives into the column generation model.

1. Dependent Contexts

1. task (Flight Task)
2. bunch_compilation (Bunch Compilation)

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2. Concepts / Entities

1. Passenger

A passenger with an amount and a multi-leg flight list, each leg assigned a passenger class.

${\text{id}}_p$ : Unique identifier of passenger $p$.

${\text{amount}}_p$ : Amount of passenger $p$ (greater than 1 for group passengers).

${\text{flights}}_p$ : Leg list of passenger $p$, each entry is a (flight task, class) pair.

${\text{route}}_p$ : Airport route of passenger $p$.

2. Flight Passenger (FlightPassenger)

An association linking a passenger to a specific flight with an optional previous leg.

${\text{flight}}_{fp}$ : Associated flight task.

${\text{passenger}}_{fp}$ : Associated passenger.

${\text{prev}}_{fp}$ : Previous leg's flight passenger association (optional).

${\text{cls}}_{fp}$ : Passenger's class on this flight.

${\text{amount}}_{fp}$ : Passenger amount.

3. Passenger Cancel (PassengerCancel)

Tracks passenger cancellation decision variables in the column generation formulation.

${\text{passengerCancel}}_{fp}$ : Cancellation variable for flight passenger $fp$.

4. Passenger Change (PassengerChange)

Tracks passenger class change and flight change decision variables in the column generation formulation.

${\text{passengerClassChange}}_{fp,cls}$ : Variable for flight passenger $fp$ changing to class $cls$.

${\text{passengerFlightChange}}_{fp,f^{\prime },cls}$ : Variable for flight passenger $fp$ changing to flight $f^{\prime }$ and class $cls$.

5. Passenger Amount (PassengerAmount)

Computes passenger amount expressions per flight and class, accounting for cancellations and changes.

${\text{passengerAmount}}_{f,cls}$ : Passenger amount expression for flight $f$ at class $cls$.

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3. Variables

1. Decision Variables

$c_{fp}$ : Cancellation amount for flight passenger $fp$, dimensionless, domain $[0,{\text{amount}}_{fp}]$, integer, represents the number of cancelled passengers, $\mathrm{\forall }fp\in FP$.

$s_{fp,cls}$ : Class change amount for flight passenger $fp$ to class $cls$, dimensionless, domain $[0,{\text{amount}}_{fp}]$, integer, $\mathrm{\forall }fp\in FP,\mathrm{\forall }cls\in CLS\setminus \{fp.cls\}$.

$r_{fp,f^{\prime },cls}$ : Flight change amount for flight passenger $fp$ to flight $f^{\prime }$ and class $cls$, dimensionless, domain $[0,{\text{amount}}_{fp}]$, integer, $\mathrm{\forall }fp\in FP,\mathrm{\forall }{f}^{\prime }\in {\text{toFlights}}_{fp.flight},\mathrm{\forall }cls\in CLS$.

2. Auxiliary Variables

No additional auxiliary variables.

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4. Predicates

1. Passenger Status

isCancelled : Flight passenger $fp$ is cancelled ($c_{fp}>0$).

isClassChanged : Flight passenger $fp$ has a class change.

isFlightChanged : Flight passenger $fp$ has a flight change.

isTransfer : Passenger $p$ is a transfer passenger (route contains more than 2 airports).

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5. Sets

1. Flight Passengers

$FP$ : Universal set of all flight passenger associations.

$F{P}_f$ : Subset of flight passengers on flight $f$, $\mathrm{\forall }f\in F$.

$F{P}_p$ : Subset of flight passengers for passenger $p$, $\mathrm{\forall }p\in P$.

2. Flights

$F$ : Universal set of all flight tasks.

$F_{fp}$ : Subset of alternative flights for flight passenger $fp$ (same origin and destination).

3. Classes

$CLS$ : Universal set of all passenger classes (PassengerClass enum).

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6. Intermediate Values

1. Passenger Amount Expression

Description: Net passenger amount for flight $f$ at class $cls$, accounting for cancellations, class changes, and flight changes.

$${\text{passengerAmount}}_{f,cls}=\sum _{fp\in F{P}_f}(\mathbb{1}[fp.cls=cls]\cdot {\text{amount}}_{fp}-c_{fp}-\mathbb{1}[fp.cls=cls]\cdot \sum _{cl{s}^{\prime }\in CLS}{s}_{fp,cl{s}^{\prime }}-\mathbb{1}[fp.cls=cls]\cdot \sum _{f^{\prime },cl{s}^{\prime }}{r}_{fp,f^{\prime },cl{s}^{\prime }}+\sum _{cl{s}^{\prime }}{s}_{fp,cls}+\sum _{f{p}^{\prime }\in FP:f\in F_{f{p}^{\prime }}}{r}_{f{p}^{\prime },f,cls})$$

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7. Assertions

1. Passenger Route Continuity

Description: In a passenger's leg list, the arrival airport of a consecutive leg must match the departure airport of the next leg.

$$\mathrm{\forall }p\in P,\mathrm{\forall }k\in [1,|{\text{flights}}_p|)({\text{flights}}_p[k-1].arr={\text{flights}}_p[k].dep)$$

2. Flight Type Consistency

Description: All legs of a passenger must be flight types.

$$\mathrm{\forall }p\in P,\mathrm{\forall }(f,cls)\in {\text{flights}}_p(f.\text{isFlight})$$

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8. Constraints

1. Passenger Cancel Minimization

[CN]: 乘客取消最小化

Description: Minimize the total number of cancelled passengers (objective function term).

$$min\sum _{fp\in FP}{w}_{fp}\cdot c_{fp}$$

2. Passenger Class Change Minimization

[CN]: 乘客舱位变更最小化

Description: Minimize the total number of class-changed passengers (objective function term).

$$min\sum _{fp\in FP}\sum _{cls\in CLS\setminus \{fp.cls\}}{w}_{fp}\cdot s_{fp,cls}$$

3. Passenger Flight Change Minimization

[CN]: 乘客航班变更最小化

Description: Minimize the total number of flight-changed passengers (objective function term).

$$min\sum _{fp\in FP}\sum _{f^{\prime }\in F_{fp}}\sum _{cls\in CLS}{w}_{fp}\cdot r_{fp,f^{\prime },cls}$$

4. Passenger Flight Capacity Constraint

[CN]: 航班乘客容量约束

Description: The passenger amount per flight per class must not exceed available capacity.

$$s.t.{\text{passengerAmount}}_{f,cls}\le {\text{capacity}}_{f,cls},\mathrm{\forall }f\in F,\mathrm{\forall }cls\in CLS$$

5. Passenger Route Cancel Constraint

[CN]: 路线取消约束

Description: If any leg of a passenger is cancelled, all legs of the entire route are cancelled.

$$s.t.c_{fp}=c_{f{p}^{\prime }},\mathrm{\forall }p\in P,\mathrm{\forall }fp,f{p}^{\prime }\in F{P}_p$$

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9. Objective Function (if applicable)

Description: Minimize the weighted sum of passenger cancellations, class changes, and flight changes.

$$min\sum _{fp\in FP}(w_{fp}^{cancel}\cdot c_{fp}+\sum _{cls}{w}_{fp}^{class}\cdot s_{fp,cls}+\sum _{f^{\prime },cls}{w}_{fp}^{flight}\cdot r_{fp,f^{\prime },cls})$$

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10. Algorithm References

No independent algorithm references in this context.

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11. Ubiquitous Language

Term	Symbol	Definition
Passenger	$P$	A traveler with amount and multi-leg flight list
Flight Passenger	$FP$	Association between a passenger and a specific flight
Cancel	$c$	Number of cancelled passengers
Class Change	$s$	Number of passengers changing class
Flight Change	$r$	Number of passengers changing flight
Route	route	Sequence of airports visited by a passenger

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12. Design Decisions

Decision	Alternatives	Rationale	Date
Separate cancel/change modeling	Unified recovery variable	Different business semantics and penalty weights	-
Route-level cancel linkage	Independent per-leg cancellation	Passenger experience: partial cancellation is meaningless	-

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13. Change Log

Version	Change	Reason
v1	Initial implementation	Basic passenger domain modeling