System Module Active

Post-Service Optimization

Minimize the gap between work completion and actual vessel departure. Release delays compound by blocking the next admission wave.

Layer Scope

Departure Release Coordination

The third MECE optimization layer controls the interval T_dep minus T_workdone -- the post-work release delay.

Departure Release Coordination

Synchronize the formal departure clearance with actual work completion to eliminate administrative lag.

Tug/Pilot Departure Sequencing

Schedule unberthing marine resources so they arrive just-in-time after work completion, not after idle waiting.

Berth Clearance Timing

Minimize the gap between work-done and berth-free so the next vessel can commence berthing sooner.

Release-Side Conflict Management

Resolve departure-channel contention when multiple vessels complete work simultaneously.

Why This Seemingly Small Layer Matters

The Post-Service layer is typically smaller in magnitude than the Service layer. But it is critically important because release delays spill back into the next vessel admission wave. A berth that remains occupied by a completed vessel directly blocks the Pre-Berth layer from admitting the next arrival -- creating a compounding cascade through the entire system.

Decision Variables

--Departure release time: scheduled moment of formal unberthing clearance per vessel
--Tug/pilot departure assignment: which marine resources and at what time
--Berth clearance window: planned interval from work-done to berth-free

Hard Constraints

--Berth clearance safety: minimum safe unberthing separation enforced
--Marine resource availability: tug/pilot must be physically available at departure time
--Channel access timing: departure slot must align with tidal and channel windows

Objective

--Primary: minimize weighted post-work release delay across all vessels
--Penalty: release-blocking cost when a completed vessel holds a berth needed downstream
--Sub-objectives decompose into clearance, unberthing coordination, and idle occupancy

Ontology I/O

--Inputs from graph: SHIP, VOYAGE, BERTH, QUAY entities and relations
--Receives projected work completion times from Service layer
--Outputs ReleaseEvaluation to Global Coordinator for next admission cycle

Ontology Graph Entities

SHIPVOYAGEBERTHQUAY

Why This Matters

Upstream Propagation

A delayed berth release does not just affect one vessel -- it propagates backwards through the entire admission pipeline.

Work Completes

Cargo operations finish at T_workdone

Release Delay

Tug/pilot unavailable, clearance paperwork, channel conflict

Berth Blocked

Completed vessel occupies berth meant for next arrival

Admission Delayed

Next vessel's Pre-Berth admission cycle cannot start

Compound Effect

Delay propagates upstream through entire vessel queue

Cascade Formula

T_{\text{release}}(b) = T_{\text{done}}(v) + \delta_{\text{release}}(v) \quad \Rightarrow \quad T_{\text{admit}}(v') \geq T_{\text{release}}(b) + \tau_{\text{safe}} \quad \Rightarrow \quad \Delta(v') = \max\!\big(0,\; T_{\text{release}}(b) + \tau_{\text{safe}} - T_{\text{eta}}(v')\big)

Late release at berth b delays admission of next vessel v':
  --> propagates to all queued vessels behind v'

Even a small delta_release compounds across vessel queues because each delayed release shifts the admission window for all subsequent arrivals.

IMPORTANT

Even small post-service delays compound across vessel queues because they directly block the next Pre-Berth admission cycle. A 30-minute release delay on one berth can cascade into hours of accumulated waiting across the arriving vessel queue.

Objective Function

Post-Work Release Minimization

Minimize weighted departure delay plus release-blocking penalties.

Primary Objective

\min \sum_{v \in V} w_v \big( T^{\text{dep}}_v - T^{\text{done}}_v \big) \;+\; \nu_1 \, C^{\text{release}}_{\text{blocking}}

where:
  w_v             = vessel priority weight
  T^dep_v         = actual departure time
  T^done_v        = work completion time
  C^release_blocking = penalty for blocking
                       downstream admissions

The gap (T_dep - T_done) is the post-service delay this layer seeks to eliminate. The release-blocking penalty captures downstream spillover costs.

Sub-Objectives (L2 MECE Decomposition)

\begin{aligned} S_1: \quad & \min \sum_{v} \big( T^{\text{clearance}}_v - T^{\text{done}}_v \big) \\[6pt] S_2: \quad & \min \sum_{v} \big( T^{\text{tug\_arrive}}_v - T^{\text{done}}_v \big) \\[6pt] S_3: \quad & \min \sum_{b \in B} \big( T^{\text{berth\_free}}_b - T^{\text{done}}_v \big) \end{aligned}

These three sub-objectives are MECE under
the post-work release delay interval.

Each sub-objective targets a distinct component of the release delay. Together they exhaustively cover the full T_dep - T_done interval.

Post-Service Quick Reference

Cadence

Event-driven, triggered by work completion signals from Service layer

Key Variables

T^dep_v -- actual departure time
T^workdone_v -- work completion time
C^release_blocking -- release blocking cost
delta_release(v) -- release delay per vessel

Graph Nodes

SHIPVOYAGEBERTHQUAY

Output Schema

ReleaseEvaluation {
  vessel_id
  projected_departure_ready_time
  projected_berth_release_time
  departure_resource_conflict
  release_delay_penalty
}

Constraints

Hard & Soft Boundaries

Hard constraints define safe departure feasibility. Soft constraints refine release quality and sequencing.

Hard Constraints

Berth Clearance Safety

Minimum safe separation time between unberthing of one vessel and berthing of the next. Accounts for mooring line handling and physical clearance.

Marine Resource Availability

Departure tugs and pilots must be physically available and not committed to another operation at the assigned departure time.

Channel Access Timing

Vessel departure must align with available channel windows, tidal conditions, and VTS (Vessel Traffic Service) clearance.

Soft Constraints

Minimize Occupied-But-Idle Berth Time

Reduce the interval where a vessel has completed all cargo work but still occupies the berth, blocking the next arrival.

Tug/Pilot Scheduling Preference

Prefer departure resource assignments that minimize repositioning time and avoid contention with inbound operations.

Smooth Release Sequencing

When multiple vessels complete work in a narrow window, sequence departures to avoid channel congestion and resource thrashing.

Execution Policy

Event-Driven Recovery

Post-Service recovery uses a reforecast-then-reschedule loop triggered by deviations from projected completion times.

Trigger

Work completion earlier or later than projected

Action

Re-forecast departure readiness, re-sequence tug/pilot assignments around the shifted completion time

Trigger

Marine resource shift (tug breakdown, pilot reassignment)

Action

Recompute feasible departure windows for affected vessels, redistribute departure resources

Trigger

Berth damage or sudden safety constraint

Action

Immediate constrained replan with elevated priority on clearing the affected berth

Recovery Strategy

Post-Service recovery uses an event-driven repair heuristic. Rather than re-solving the full departure schedule, it locally re-optimizes around the disturbed region.

Approach: Reforecast + reschedule loop. First update the projected completion/departure times, then re-sequence affected departures.

Scope: Local reoptimization only. Only vessels whose departure windows overlap with the disrupted region are re-planned.

Stability: Preserve committed departure sequences for unaffected vessels. Minimize plan churn.

Global Feedback

Feedback to Global Coordinator

What the Post-Service layer sends back to close the optimization loop.

Estimated Berth Release Times

Projected moment each berth becomes physically available for the next vessel, accounting for unberthing and clearance.

Departure-Side Conflicts

Identified contention in departure channels, tug availability, or pilot scheduling that may delay release.

Residual Occupancy Effects

Quantified impact of any remaining occupied-but-idle berth time on downstream admission windows.

Closing The Loop

The Post-Service layer's ReleaseEvaluation output feeds directly into the next Pre-Berth admission cycle. Projected berth release times determine when the Pre-Berth layer can begin scheduling inbound vessels for those berths. This creates a closed feedback loop across all three temporal layers: Pre-Berth admission windows depend on Post-Service release forecasts, which depend on Service layer work completion projections.

KEY INSIGHT

The three temporal layers form a closed loop: Post-Service release forecasts determine Pre-Berth admission windows, which determine Service layer work schedules, which determine the next round of Post-Service release times. The Global Coordinator arbitrates this cycle.