Maritime Shipping
Overview
Maritime shipping optimization helps shipping companies and port operators plan vessel routes, schedule port calls, and allocate cargo across a fleet of ships to minimize voyage costs while meeting delivery schedules. Maritime logistics involves unique challenges: vessels carry thousands of containers, port berths have limited availability, and voyage times span days or weeks with weather and fuel considerations.
With maritime transport carrying over 80% of global trade by volume, even incremental improvements in vessel utilization or port scheduling create substantial cost savings.
When to Use This
Best for: Shipping line planners, port operations managers, and freight coordinators who need to optimize vessel assignments, port schedules, and cargo loading plans across complex maritime networks.
- Scenario: You operate a fleet of vessels serving multiple ports, and need to decide which vessels visit which ports, in what order, and how to allocate cargo to minimize total voyage cost while meeting delivery commitments
- Industry: Container shipping, bulk carriers, tanker operations, ferry services, port terminal operations, offshore logistics
- ROI: Typical fuel cost reduction of 5-15%, berth utilization improvement of 10-20%, and fewer empty repositioning voyages
Step-by-Step Walkthrough
1. Define the fleet
List each vessel with its capacity (TEU for containers, deadweight tonnes for bulk), fuel consumption rate, operating cost per day, and current position. Different vessel classes have different speed-fuel trade-offs.
2. Map the port network
Define ports with berth availability windows, handling rates (containers per hour), port fees, and draft restrictions. Specify distances and sailing times between port pairs.
3. Define cargo demand
List shipments with origin port, destination port, volume, weight, and delivery deadline. Group compatible cargo types and note any hazardous material handling requirements.
4. Add maritime constraints
- Berth availability windows at each port
- Vessel draft restrictions for shallow ports
- Crew rest requirements and maximum continuous sailing time
- Container weight distribution for vessel stability
- Bunker fuel availability and refueling ports
5. Set the objective
Typically minimize total voyage cost (fuel + port fees + time charter) or maximize cargo revenue minus operating costs.
6. Review the sailing schedule
The solver produces a schedule showing each vessel's port rotation, arrival and departure times, and cargo assignments. Verify berth availability at each port, check fuel adequacy for each leg, and confirm all cargo meets its delivery deadline.
Example Parameters
import httpx
API_URL = "https://api.jaot.io/api/v2"
headers = {"Authorization": "Bearer ok_live_your_key_here"}
# Schedule 3 vessels across 5 ports (simplified assignment)
response = httpx.post(f"{API_URL}/solve", headers=headers, json={
"variables": [
# vessel_port = 1 if vessel calls at port
{"name": "vessel1_singapore", "type": "binary"},
{"name": "vessel1_shanghai", "type": "binary"},
{"name": "vessel1_busan", "type": "binary"},
{"name": "vessel1_rotterdam", "type": "binary"},
{"name": "vessel1_hamburg", "type": "binary"},
{"name": "vessel2_singapore", "type": "binary"},
{"name": "vessel2_shanghai", "type": "binary"},
{"name": "vessel2_busan", "type": "binary"},
{"name": "vessel2_rotterdam", "type": "binary"},
{"name": "vessel2_hamburg", "type": "binary"},
{"name": "vessel3_singapore", "type": "binary"},
{"name": "vessel3_shanghai", "type": "binary"},
{"name": "vessel3_busan", "type": "binary"},
{"name": "vessel3_rotterdam", "type": "binary"},
{"name": "vessel3_hamburg", "type": "binary"},
],
"objective": {
"sense": "minimize",
"coefficients": {
"vessel1_singapore": 45000, "vessel1_shanghai": 38000,
"vessel1_busan": 32000, "vessel1_rotterdam": 65000,
"vessel1_hamburg": 68000,
"vessel2_singapore": 52000, "vessel2_shanghai": 42000,
"vessel2_busan": 36000, "vessel2_rotterdam": 58000,
"vessel2_hamburg": 61000,
"vessel3_singapore": 48000, "vessel3_shanghai": 40000,
"vessel3_busan": 34000, "vessel3_rotterdam": 72000,
"vessel3_hamburg": 75000,
},
},
"constraints": [
{
"name": "singapore_served",
"coefficients": {
"vessel1_singapore": 1, "vessel2_singapore": 1,
"vessel3_singapore": 1
},
"sense": ">=",
"rhs": 1,
},
{
"name": "shanghai_served",
"coefficients": {
"vessel1_shanghai": 1, "vessel2_shanghai": 1,
"vessel3_shanghai": 1
},
"sense": ">=",
"rhs": 1,
},
{
"name": "rotterdam_served",
"coefficients": {
"vessel1_rotterdam": 1, "vessel2_rotterdam": 1,
"vessel3_rotterdam": 1
},
"sense": ">=",
"rhs": 1,
},
{
"name": "vessel1_max_ports",
"coefficients": {
"vessel1_singapore": 1, "vessel1_shanghai": 1,
"vessel1_busan": 1, "vessel1_rotterdam": 1,
"vessel1_hamburg": 1
},
"sense": "<=",
"rhs": 3,
},
{
"name": "vessel2_max_ports",
"coefficients": {
"vessel2_singapore": 1, "vessel2_shanghai": 1,
"vessel2_busan": 1, "vessel2_rotterdam": 1,
"vessel2_hamburg": 1
},
"sense": "<=",
"rhs": 3,
},
{
"name": "vessel3_max_ports",
"coefficients": {
"vessel3_singapore": 1, "vessel3_shanghai": 1,
"vessel3_busan": 1, "vessel3_rotterdam": 1,
"vessel3_hamburg": 1
},
"sense": "<=",
"rhs": 3,
},
],
})
result = response.json()
print(f"Minimum total voyage cost: ${result['objective_value']:,.0f}")
for var in result["variables"]:
if var["value"] > 0.5:
print(f" {var['name']}: assigned")Templates
Next Steps
- Railway Operations -- Optimize rail scheduling and rolling stock allocation
advanced - Warehouse Layout & Operations -- Optimize port-side and inland warehouse operations
intermediate - Transportation Network Design -- Design multi-modal freight networks combining sea, rail, and road
advanced