## 1 Introduction  
Inland waterway transportation (IWT) is a potential alternative that plays an important role in the transport of goods to every region of the world [1]. There are around 623,000 km of navigable waterways around the world [2], and as most of these are part of a river system, the network of rivers and river basins connects hundreds of cities and industrial areas. IWT is the most economical mode of inland transportation and an environmentally friendly alternative compared with other modes of transport [3, 4]. In addition, it helps to reduce road congestion in densely populated regions. Bulk cargo is one of the most important cargo groups involved in inland waterway transportation, and it includes the carriage of bulk goods, such as coal, soil, rocks, cement, rice, sugar, and tapioca, among others. Today, attention is focused on the continuously increasing environmental impact of air emissions, especially those from cargo ships [5]. The International Maritime Organization (IMO) [6] is expected to increase its emissions by 150-250% from 2012 to 2050 based on a business-as-usual scenario due to a tripling of world trade. This trend of emissions growth has resulted in proactive GHG management, which will be essential to enable the transportation industry to achieve its goal of limiting the effects of climate change [5, 7, 8]. A waterway transportation plan aimed at minimizing CO\({}_{2}\) emissions will reduce both air and water pollution, and also help to promote a positive image for environment conservation organizations. In Thailand, bulk transportation is widely used on the Chao Phraya River. Over the years, many waterway transportation carriers and company-owned cargo terminals have attempted to collaborate to produce centralized decisions by employing a control tower to plan and control waterway transportation, reduce costs, and improve CO\({}_{2}\) emission efficiency. This control tower is responsible for integrating information and resources from all collaborative parties to solve the green ship routing and scheduling problem (GSRSP) as it applies to IWT. Another important consideration is that several often-contrasting objectives can be considered for the GSRSP. In the real world, most of them involve multiple objectives. Moreover, a control tower must focus on the berthing timeslots of each port when planning barge routes and schedules. We call this problem the green ship routing and scheduling problem (GSRSP) with berth time-window constraints (GSRSP-BT). Currently, decisions on ship routing and scheduling for IWT are made using a heuristic method, leading to non-optimal solutions and the provision of just one solution. Therefore, the control tower needs a high-performance technique that can solve the problem from a centralized decision-making position to obtain a Pareto frontier to make a decision tradeoff between the two objectives from that plot. In this paper, we present a bi-objective set covering model based on route representation to solve the green ship routing and scheduling problem with berth time-window constraints (GSRSP-BT) for multiple bulk ports to minimize CO\({}_{2}\) equivalent (CO\({}_{2}\)e) emissions and the total travel time, subject to the limited number of berths in each port, berthing time windows, and time window required for each job. We also plot a Pareto frontier using the \(\varepsilon\)-constraint method. In addition, we developed three constraints to specifically use with the proposed bi-objective set covering model based on route representation include (1) time window required for each job constraint, (2) time windows for each berth constraint, and (3) constraint to ensure that the berth does not serve more than one barge simultaneously. The proposed method is applied to inland waterway shipping for dry bulk cargo on the Chao Phrava River, Thailand. The remainder of this paper is organized as follows.