Maritime scheduling is a complex problem. Without advanced analytical tools, optimizing a maritime plan for a small fleet would require manual evaluation, which could amount to billions of potential alternative schedules/routes. Shippers have successfully adapted optimization modeling techniques to address such an overwhelming task. And yet, a crucial and recurrent element in maritime transportation needs to be addressed by planning models: uncertainty. 

Uncertainty is a Constant Presence in Maritime Transportation 

Weather, unplanned maintenance, geopolitical tensions, and even sabotage are a few sources of uncertainty in maritime transportation planning.  In recent weeks, tension mounting in the Red Sea has caused significant disruption to global freight transportation. Shippers are now faced with a tough choice: continue to ship via the Red Sea with higher risk and premium or take a longer route around Africa via the Cape of Good Hope (extending travel by more than a week and incurring higher fuel costs and emissions). 

Disruptions in vital waterways that wreak havoc in global transportation are not uncommon – in 2021, the Ever Given, a 400m-long container ship, was stuck and blocked traffic in the Suez Canal and caused a week-long blockage of the canal, resulting in a hefty logistics and financial disaster.  This event, compounded by the COVID-19 pandemic impact, revealed how little resiliency companies have been building into their supply chain network and the dominance of the “just-in-time” scheme.  Since then, companies have sought to bring more resilience back into their operation by leaning back into a “just-in-case” strategy (aka. stock-up) amid shifts in global trade flow. 

To protect their operations, companies must develop resilient plans that effectively handle disruptions. But what, exactly, does a resilient plan mean? 

Resilience and optimality: a simple example 

“There is no free lunch” is a common term used in economics and analytics, and resiliency is no exception. It’s a crucial focus for maritime transportation planning. Specifically, building robustness in a maritime schedule has a perceived cost only if we evaluate the plan against perfect conditions and no disruptions.  However, the price we need to pay to increase the resiliency of our operation is often misunderstood.  If we evaluate these robust plans under probabilistic scenarios, considering possible disruptions, properly derived robust plans result in lower expected costs than their corresponding deterministic “optimal” (which could be unachievable in practice). 

To illustrate this point, we present a simple example with three ships (Vessels 1, 2, and 3) that need to deliver goods from a loading port (Port S) to thirteen different ports (Ports P1 to P13) each month.  The trip from P2 to P3 requires a canal and there is no other access to P3.  On the canal segment, there is a 0.1% likelihood that there is a disruption, and if the disruption does occur, it can last anywhere between 1 to 30 days with different likelihoods (Figure 1a).  Figure 1b and 1c represent two potential routing solutions.  In each solution, the vessel travels to the load port, S1, followed by several consecutive discharges.  The assignment discharge port to vessel is different between the two schedules.  

Figure 1. Likelihood of disruption duration (a) and two alternative schedules (b) and (c). 

There are three important differences between routing schedules 1 and 2.  

  • Schedule 2 incurs longer trips (highlighted in yellow in Figure 1c). Because of this, the total travel costs of schedule 2 are higher (Table 1).  
  • Vessel 1 (V1), which travels the canal segment, has considerably more idle time in schedule 2 than in schedule 1. This provides a direct buffer in case of disruptions in the canal operation.  
  • The Canal segment takes place early in the route, and in combination with the buffer, provides schedule 2 with additional flexibility: if a disruption happens towards the start of the trip, the vessel can turn around to visit the other two ports before traversing the canal. This additional optionality reduces the likelihood of canal disruptions delaying the next pickup.  

When put together, the total expected cost of schedule 2 is lower than the total expected cost of schedule 1 by almost 4% (even if the travel cost is higher by 2.3%).  

Table 1: Normalized expected cost 

  Schedule 1  Schedule 2 
Travel cost  100.0%  102.3% 
E[Disruption cost]  8.8%  2.4% 
E[total cost]  108.8%  104.7% 


This simple example illustrates two key components in maritime scheduling: optimization and resiliency.  In practice, the routing and scheduling decisions are significantly more complex, and with the ever-present uncertainty, how can a company develop these types of optimal and robust schedules more systematically for supply chain optimization? 

Unlock the secrets to developing optimal and robust schedules with our one-pager. We’ll take you through the steps you need to schedule efficiently. Whether you’re managing projects, teams, or resources, our guide systematically supercharges your scheduling process. 

Download Strategic Routing: Your Guide to Supply Chain Optimization 


  How to develop optimal and robust schedules   Get step-by-step directions on how to route efficiently for maximum impact.   



Aimpoint Digital is a leading partner for businesses seeking to enhance their logistics operations and supply chain optimization through mathematical optimization. Leveraging cutting-edge algorithms and advanced analytics, Aimpoint Digital provides a comprehensive suite of solutions designed to streamline and optimize various facets of the logistics process.  

By harnessing mathematical optimization, companies can efficiently address complex challenges such as route planning, inventory management, and resource allocation. Businesses benefit from improved efficiency, cost savings, and enhanced decision-making capabilities as Aimpoint Digital employs mathematical models to analyze vast datasets and recommend optimal solutions.  

Whether optimizing delivery routes to minimize transit times or strategically managing inventory levels to reduce holding costs, Aimpoint Digital’s mathematical optimization capabilities offer a strategic advantage in the competitive landscape of modern logistics.