Bunch generation context model

1. Overview

The bunch-generation context builds feasible flight-task columns per aircraft, including an initial pool and reduced-cost pricing. It returns domain objects to the selection algorithm; it does not register master variables.

1. Dependent Contexts

Task, rule, crew, cargo, aircraft, and the compilation shadow-price contract.

2. Concepts / Entities

1. Route graph

$G_{a} = (V_{a}, E_{a})$ is the aircraft-specific task transition graph;

$f e a s i b l e_{a} (e)$ is its rule/time/aircraft feasibility predicate.

2. Flight-task bunch

$B_{b}$ is an ordered task sequence for aircraft a; $c o s t_{b}$ is its total cost; $c o v e r (t, b)$ indicates task coverage.

3. Shadow-price map

$π_{t}$ and $μ_{a}$ are master dual values used to calculate reduced cost.

3. Variables

No solver decision variables are owned by this context. A generated bunch is an output object, not a binary variable until compilation inserts it.

4. Predicates

initial(b): bunch belongs to the seed pool. feasible(b): all task/rule, aircraft, time, lock, and cost checks pass. improving(b): reduced cost is below the configured tolerance.

5. Sets

$A$ : aircraft; $T$ : tasks; $G_{a}$ : graph for aircraft a; $B_{0}$ : initial bunches; $B_{t}^{p r i c e}$ : pricing output at iteration t; $Π$ : shadow-price maps.

6. Intermediate Values

For bunch b of aircraft a, the pricing reduced cost is:

r c (b) = c o s t_{b} - \sum_{t \in B_{b}} π_{t} - μ_{a}

The exact cost and dual normalization are supplied by the configured cost calculator and compilation policy.

7. Assertions

Every generated bunch has a known aircraft, a nonempty ordered task sequence, and passes the configured feasibility judger:

\forall b \in B_{t}^{p r i c e} : f e a s i b l e (b) = t r u e

8. Constraints

This context does not register solver rows. Generation enforces graph edges, locks, connection times, rule restrictions, and aircraft usability before a column is returned.

9. Objective Function (if applicable)

Pricing searches for rc(b)<0; this is a subproblem criterion, not an independent global objective registered by the context.

10. Algorithm References

Algorithm	Source role	Purpose
InitialFlightTaskBunchGenerator	initial pool	seed compilation
FlightTaskBunchGenerator	pricing	enumerate improving feasible bunches

11. Ubiquitous Language

Term	Symbol	Definition
route graph	`G_a`	aircraft-specific feasible transition graph
bunch/column	`b`	ordered task sequence returned to compilation
pricing	`rc(b)`	search for an improving column
shadow price	`π, μ`	dual values from the master

12. Design Decisions

Decision	Alternative	Rationale
keep generated columns outside the solver until insertion	preallocate all possible bunches	supports incremental column generation

13. Change Log

Version	Change	Reason
1.0	Documented initial/pricing output boundary	Distinguish pricing results from master variables

Bunch generation context model ​

1. Overview ​

1. Dependent Contexts ​

2. Concepts / Entities ​

1. Route graph ​

2. Flight-task bunch ​

3. Shadow-price map ​

3. Variables ​

4. Predicates ​

5. Sets ​

6. Intermediate Values ​

7. Assertions ​

8. Constraints ​

9. Objective Function (if applicable) ​

10. Algorithm References ​

11. Ubiquitous Language ​

12. Design Decisions ​

13. Change Log ​