Stowage context model

1. Overview

Manages cargo stowage assignment decisions — which items go to which positions — including load weight computation, payload calculation, total weight, and max load weight.

1. Dependent Contexts

Aircraft

2. Concepts / Entities

1. Item

A cargo item with destination, weight, ULD, location tags, cargo type, priority, and status.

$i d_{i}$ : Item unique identifier.

$d e s t_{i}$ : Destination (IATA code).

$w e i g h t_{i}$ : Item weight, unit kg.

$u l d_{i}$ : Associated ULD (optional).

$l o c a t i o n_{i}$ : Location tags (Main/Low/Bulk/Head/Tail).

$c a r g o_{i}$ : Cargo type and priority.

$s t a t u s_{i}$ : Status (Loaded/Preassigned/Optional/Reserved/AdjustmentNeeded).

$o r d e r_{i}$ : Order information (hardstand time, reweigh time, car-board info).

2. Position

Stowage position with max load amount (MLA), predicate load weight (PLW), recommended load weight, and status.

$s p a c e N a m e_{j}$ : Space name.

$m l a_{j}$ : Max Load Amount.

$p l w_{j}$ : Predicate Load Weight, its definition is further specified in Stowage.

$m l w_{j}$ : Max Load Weight, its definition is further specified in Airworthiness Security.

$c o o r d i n a t e_{j}$ : Coordinate (longitudinal arm, lateral arm).

$l o c a t i o n_{j}$ : Set of location tags.

3. Flight

Flight information.

$f l i g h t N o$ : Flight number.

$d e p a r t u r e$ : Departure airport (IATA code).

$a r r i v a l$ : Arrival airport (IATA code).

4. Appointment

Pre-assigned item-to-position appointments.

$a p p o i n t m e n t$ : Item-to-position pre-assignment mapping.

5. Ballast

Ballast weight for balance correction.

$m i n B a l l a s t W e i g h t$ : Minimum ballast weight.

3. Variables

1. Decision Variables

$x_{i j}$ : Whether item $i$ is assigned to position $j$ , binary variable, domain is ${0, 1}$ , for feasible pairs $(i, j) \in I J^{f e a s}$ ; status-fixed pairs are fixed to zero or one.

$y_{j}$ : Predicate load weight at position $j$ , continuous variable (kg), domain is $[0, M L W_{j}]$ , $\forall j \in P o s i t i o n s$ .

$z_{j}$ : Recommended load weight at position $j$ , integer variable (kg), domain is $[0, ⌊ M L W_{j} ⌋]$ , $\forall j \in P o s i t i o n s$ .

2. Auxiliary Variables

$u_{i j}$ : Adjustment variable for item $i$ at position $j$ , balance-ternary variable, domain is ${- 1, 0, 1}$ , for adjustment pairs $(i, j) \in I J^{a d j}$ ; non-adjustment pairs are fixed to zero.

4. Predicates

1. Item Status Predicates

stowageNeeded(item) : Item requires position assignment (status is Preassigned or Optional).

adjustmentNeeded(item) : Item requires position adjustment (status is AdjustmentNeeded).

loaded(item) : Item is loaded (status is Loaded or AdjustmentNeeded).

2. Position Status Predicates

stowageNeeded(position) : Position requires item assignment.

available(position) : Position is available for loading.

predicateWeightNeeded(position) : Position requires predicate weight variable.

recommendedWeightNeeded(position) : Position requires recommended weight variable.

5. Sets

1. Items

$I$ : Set of all cargo items.

$I^{p r e}$ : Subset of items satisfying predicate stowageNeeded, items requiring position assignment.

$I^{a d j}$ : Subset of items satisfying predicate adjustmentNeeded, items requiring position adjustment.

$I^{o p t}$ : Subset of items with Optional status, optionally loaded items.

2. Positions

$J$ : Set of all stowage positions.

$J^{a v l}$ : Subset of positions satisfying predicate available, positions available for loading.

$J^{p w}$ : Subset of positions satisfying predicate predicateWeightNeeded, positions requiring predicate weight.

$J^{r w}$ : Subset of positions satisfying predicate recommendedWeightNeeded, positions requiring recommended weight.

3. Item-Position Pairs

$I J^{f e a s}$ : Set of feasible item-position assignment pairs, i.e., $(i, j)$ pairs satisfying stowageNeeded(item, position).

6. Intermediate Values

1. Load Amount

Description: Number of items loaded at each position.

l o a d A m o u n t_{j} = \sum_{i \in I} s t o w a g e_{i j}, \forall j \in J

2. Actual Load Weight

Description: Actual load weight at each position.

a c t u a l L o a d W e i g h t_{j} = \sum_{i \in I} w e i g h t_{i} \cdot s t o w a g e_{i j}, \forall j \in J

3. Estimate Load Weight

Description: Estimated load weight including predicate and recommended weights.

e s t i m a t e L o a d W e i g h t_{j} = \sum_{i \in I} w e i g h t_{i} \cdot s t o w a g e_{i j} + y_{j} + z_{j}, \forall j \in J

The stowage expression is the status-aware bridge $s_{i j} = x_{i j} + u_{i j} + l o a d e d_{i j}$ for pairs that need stowage and is zero for inapplicable pairs. The model fixes y and z according to the predicateWeightNeeded and recommendedWeightNeeded position predicates.

7. Assertions

The data model requires unique item/position identifiers and a valid aircraft weight unit. Loaded items and unavailable positions have fixed contributions; they are not free solver decisions. Appointment pairs are a subset of feasible pairs, and every item in $I^{p r e}$ has at least one feasible position.

8. Constraints

1. Item Assignment Limit

[CN]: 货物分配限制

Description: Each item requiring stowage must be assigned to exactly one position.

s . t . \sum_{j \in J} x_{i j} = 1, \forall i \in I^{p r e}

2. Load Amount Limit

[CN]: 装载数量限制

Description: Load amount per position must not exceed the maximum load amount (MLA).

s . t . \sum_{i \in I} s t o w a g e_{i j} \leq m l a_{j}, \forall j \in J

3. Load Weight Limit

[CN]: 装载重量限制

Description: Load weight per position must not exceed the maximum load weight (MLW).

s . t . a c t u a l L o a d W e i g h t_{j} \leq m l w_{j}, \forall j \in J

4. Appointment Limit

[CN]: 预约限制

Description: Pre-assigned item-to-position appointments must be respected.

s . t . x_{i j} = 1, \forall (i, j) \in A p p o i n t m e n t

9. Objective Function (if applicable)

This context does not define an independent objective function; it only provides constraints.

10. Algorithm References

Algorithm	Source boundary	Used for
Benders decomposition	mode-specific application master/subproblem registration	separating stowage and airworthiness pipelines

11. Ubiquitous Language

Term	Symbol	Definition
Item	`Item`	Cargo unit to be loaded
Position	`Position`	Cargo loading position on aircraft
Stowage	`Stowage`	Item-to-position assignment decision
Load	`Load`	Load weight and amount at position
Payload	`Payload`	Total cargo weight on aircraft
Total Weight	`TotalWeight`	Aircraft total weight per flight phase
Max Load Weight	`MaxLoadWeight`	Maximum allowable load weight at position
Ballast	`Ballast`	Ballast weight for balance
Predicate Load Weight	`PLW`	Predicted load weight
Max Load Amount	`MLA`	Maximum load amount at position

12. Design Decisions

Decision	Alternatives	Rationale
Stowage Mode Selection	FullLoad / Predistribution / WeightRecommendation	Different modes for different business scenarios
Benders Decomposition	Master/Sub problem separation	Airworthiness constraints in sub problem, others in master

13. Change Log

Version	Change	Reason
1.1	Clarified status predicates, balance-ternary adjustment, and local model boundary	Match the `Stowage` aggregate and pipeline registration

Stowage context model ​

1. Overview ​

1. Dependent Contexts ​

2. Concepts / Entities ​

1. Item ​

2. Position ​

3. Flight ​

4. Appointment ​

5. Ballast ​

3. Variables ​

1. Decision Variables ​

2. Auxiliary Variables ​

4. Predicates ​

1. Item Status Predicates ​

2. Position Status Predicates ​

5. Sets ​

1. Items ​

2. Positions ​

3. Item-Position Pairs ​

6. Intermediate Values ​

1. Load Amount ​

2. Actual Load Weight ​

3. Estimate Load Weight ​

7. Assertions ​

8. Constraints ​

1. Item Assignment Limit ​

2. Load Amount Limit ​

3. Load Weight Limit ​

4. Appointment Limit ​

9. Objective Function (if applicable) ​

10. Algorithm References ​

11. Ubiquitous Language ​

12. Design Decisions ​

13. Change Log ​