## 1 Introduction  
Maritime traffic is the main type of transport for goods, accounting for over 11 billion tons in 2018 [1], and it is directly related to a country's economic activity: higher volumes of traffic yield greater activity and vice versa. In this context, port congestion implies a loss of time and money for all the actors in the logistic chain and therefore undermines the competitive position of ports and the ecosystem of companies in port communities [2]. Port infrastructure is costly and time consuming, and currently, bearing sustainability in mind, construction of new port terminals is probably not the best solution. It is important to keep in mind that in liquid bulk terminals, especially when managing IMDG products (international maritime dangerous goods), berth allocation is highly constrained, typically not because of the berthing infrastructure but because the loading arm, which is highly specific with respect to the good to load/unload (e.g., phenol, methanol, gasoline, jet fuel, LNG) have particular chemical characteristics or temperature requirements. This limited flexibility in allocation results in the appearance of congestion limitations when they reach around 30-40% occupancy. From the perspective of port management, optimizing quay operations to reduce congestion and delays in the loading and unloading of vessels is addressed by the so-called berth allocation problem (BAP). The objective of berth allocation is to serve a set of vessels on a set of piers for a given period in order to optimize parameters like total vessel operation time, fuel consumption, and emissions. The improvement of berth usage reduces not only the port costs of loading and unloading vessels but their downtime costs. Thus, economic growth for ports and their activity, client loyalty, and attracting new clients are expected, all of which indirectly influence society. The study of the berth allocation problem has been extensively developed for container terminals. However, liquid bulk terminals have received little attention in recent years, mainly due to the uncertainties and more demanding restrictions in the operation of these types of goods. In liquid bulk terminals, the berth where a vessel must stay is often determined by the goods to be loaded or unloaded since specific pipes and facilities are required. For this reason, there are few or no possibilities of changing operations from congested quays to other, less congested terminals or quays, which is a common approach to reducing congestion in container-based operations. From a commercial point of view, there are a few software tools to manage liquid bulk berths. The existing ones are all costly and have been developed for container terminals, sometimes even for specific terminals, such as Posidonia Operation [3], Dropboard [4], and Marine Enterprise Suite [5]. In addition, all these tools share opacity in terms of the optimization or heuristic models used for berth assignment, and they allow for little improvement from the user interface. Furthermore, maritime logistic chains involve many agents and companies with different interests. In multi-client port terminals, the quay infrastructure is shared among terminal operators with conflicting interests, although all clients have the common goal of reducing the anchoring time caused by vessel congestion and increasing operational capacity. In liquid bulk terminals, vessel arrival times can frequently be macroscopically determined by terminal owners or petrochemical companies far in advance due to the terms of trading contracts. Thus, fostering temporal coordination among terminal operators to produce schedules that avoid simultaneous vessel arrivals at the same terminal can be a solution to congestion anchoring. Currently, company/terminal operators work individually using their own equipment, and there is no communication among them, even though they share the same resources offered by the port authority.