Why the problem is genuinely hard
The current liner industry sits at the intersection of extreme competition, trade wars, economic instability, supply-demand imbalance, soaring fuel prices and a demand for continuous innovation. None of these are solved by another spreadsheet.
An Elsevier study of liner-company profit functions sets the empirical baseline: freight rates exert a statistically significant positive effect on profits; bunker prices, the most significant element of operating costs at around 40%, exert a statistically negative effect; and the impact of economies of scale and chartered:owned vessel ratios are at best obscured. Bunker optimisation strategies — slow steaming, hull and propeller cleaning, route network planning — are where most of the recoverable cost actually sits.
“Bunkers form 40% of vessel cost. Slow steaming, hull and propeller cleaning, and route network planning are the practical levers.”
Supply and demand do not match
Looking at the Shanghai Container Freight Index, the China–USWC and China–South America trades show a negative correlation — the index fluctuates between 1,000 and 2,000 across the same period. The two trades do not move together. Supply and demand do not match.
Liner companies respond by constantly changing proforma schedules to chase cargo flow. The commercial impact is a sustained drop in scheduled TEUs and container vessel calls — visible in China port traffic between Dec 2017 and Mar 2020 — adjusted by blank sailings and idled ships. Schedule reliability falls, customer confidence falls with it, and operations gets caught between two losing positions: shut out export cargo or reroute import cargo with external feeders.
5.4 million variables — a real case
Consider a liner with 1,500 port pairs, 60 ships ranging from 500 to 4,000 TEU, 10 commodity types, 6 equipment types, daily fluctuating demand, multiple port discharge, and varying draft restrictions across ports. The dimensionality of the resulting decision space — which ship on which service, loading which port pair, of which commodity, in what quantity in TEUs / tons, with what equipment types — comes out to roughly 5.4 million variables.
That is the actual problem the planner is asked to solve every period. It is not solvable manually. It is, however, solvable with the right optimisation model.
The five-step approach
The methodology Solverminds applies is a five-step cloud-based loop. None of the steps are exotic — what matters is that the whole loop runs end-to-end rather than stopping at the analysis step like most consulting engagements do.
- Plan — service, vessel, port call and demand to optimise across
- Connect — data to cloud via RESTful API (vessel master, port master, costs, constraints, services, demand, equipment surplus / deficit, contribution)
- Optimize — run the optimiser and generate the result
- Analyze — the output schedule plan and the profitability it produces
- Apply — push the generated solution to client production
The optimisation model — constraint groups
The model carries hundreds of constraints, sorted into four groups. Each one would compromise the schedule if dropped.
“The objective function is explicit: maximise the contribution profit, subject to every constraint above.”
- Port-based — load and discharge restriction, allowed draft, LOA / beam, crane availability, allowed air draft, terminal crane productivity, nighttime arrival restriction, high-tide arrival, port cost, terminal handling charges by equipment, weather conditions, port congestion / holidays / strikes
- Vessel-based — DWT / lightship, TEU and weight capacity, summer draft (TPC vs draft), max and economical speed, fuel type and cost, fuel tank capacity, fuel consumption at both speeds, vessel's own cranes, reefer plugs, high-cube limitation, VSA partner volumes, vessel-related cost
- Empty equipment — imbalance by port, stock status, minimum threshold stock, empty repositioning cost, one-way empty moves
- Port pair / commercial — port pair routing, service contribution per TEU, service TEU range, service weight range, minimum TEU commitment per customer
What the optimiser outputs
The output is not a single number — it is four interlocking plans the operations team can act on directly.
- Financial profitability — total profit for the month, profit by service and by vessel, total laden contribution, total operating cost, total repositioning cost
- Commercial plan — which port pairs to serve, which customers to target, vessel utilisation by TEU and weight, TEU and tonnage loaded per port pair, all port pairs within lower- and upper-bound range, negative-contribution services or port pairs identified and minimised
- Operational plan — vessel schedule with port rotation and dates, vessels planned per service, total vessel cost broken into bunker, charter hire, port and canal cost, larger-capacity vessels routed to higher-demand port pairs, excess vessels off-hired
- Empty equipment plan — repositioning between surplus and deficit ports, empty lifting per vessel and voyage within stock limit, before-and-after surplus / deficit status
The algorithm stack and the team
Underneath the model is a deliberate engineering stack. Optimisation programming covers Linear Programming, Mixed Integer Programming, Mixed Integer Linear and Non-Linear Programming, and heuristic algorithms. The AI / ML layer adds Gradient Boosting, SVM, KNN, Random Forest, a data-wrangling platform, and integration with Google Cloud Platform and SageMaker. Deep-learning components include Convolutional Neural Networks, Recurrent Neural Networks / LSTM, and NLP / text analytics.
The cloud deployment runs as SaaS, on subscription, with REST API data integration, an ETL platform for export and transformation, and HTTPS security. The work is delivered by a team of 20+ professionals with experience in large-scale optimisation models, more than 17 years of combined experience in optimisation, application development and ML for shipping, and 25+ years of experience across Liner, Bulk, Tanker and Logistics.