A matter of definition

Berth capacity is a key concept in terminal analysis and design. However, it’s often overlooked in at least two aspects: how it’s defined, and how it’s calculated. It’s common to hear capacity being defined as the “absolute maximum” throughput of containers that a terminal can achieve (although clients would turn away from a terminal much before this state is reached), and calculated based on deterministic expressions that disregard important stochastic effects found in the real world.

This article uses a simple case study to illustrate that the concept and calculation of a berthing capacity value can present interesting challenges.

In this sample case study, we consider a terminal with five quay cranes, two berths, 2,000 lifts per vessel call, and two possible arrival patterns: a kind one, with higher likelihood of on-time arrivals, and harsh one, with lower likelihood of on-time arrivals.

For each of these two patterns, we considered three levels of demand: six calls per week (which corresponds to 900,000 teu per year); seven calls per week (or 1.1m teu per year); and eight calls per week (or 1.2m teu per year).

AECOM’s proprietary BERTHA model simulation tool was used in this study to allow the user to perform quality assurance of the model logic and its assumptions as the model runs, and to get valuable insights of what parameters matter the most and how to improve system performance.

Apart from visual feedback, the model provides a detailed output report at the end of each run, showing individual crane performances (total lifts, total vessels, down time, gross and net productivity), quay performance as a whole (global productivity), and the level of service provided (statistics on number of vessels waiting to berth and waiting times).

No hard rule

A fundamental concept that simulations help to understand is that, in stochastic systems (where randomness play a relevant role), there isn’t one hard number that can be called “the terminal capacity”. As demand increases, the terminal throughput also increases, but at the expense of the level of the service provided. Defining a “capacity” for a terminal, thus, implies defining a minimum level of service considered acceptable by the clients.

One variable commonly used to express level of service of container terminals is the probability of a vessel having to wait for a vacant berth. Figure 1 shows how this variable behaved in each simulated scenario. The figure confirms that the kinder arrival pattern results in shorter waiting times. The actual value of this type of exercise, however, is to quantify the difference. If we are, for example, to assume that the terminal should operate with vessel queues at no more than 5% of the time, we can then state that the simulated terminal has a capacity between 1.1m and 1.2m teu per year, depending on the arrival pattern. The difference of 9% is due to only an apparently small change in arrival patterns.

In conclusion, this case study shows that:

• “Capacity” is not a black and white quantity dependent only on the size, shape and equipment installed. Instead, it depends also on how demand behaves (arrival patterns) and what levels of service are acceptable
• Relatively small changes in the demand behavior (and other stochastic events) can have a significant impact on the system’s performance.
• Simulation models are excellent tools to represent complex variables such as probabilistic vessels arrivals, resources down time due to maintenance or bad weather, and others.

This example only scratches the surface of what is possible with simulation. Besides helping to estimate performance, simulation models can help analysts learn about systems and their complexities.

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