## 1 Introduction  
In recent years, the low-carbon concept is widely popularized in society, which uses new technologies and modes to reduce carbon emissions. As a supporting industry, logistics-related enterprises contribute a lot of the total carbon emissions. Subsequently, road transport contributed 92% of total CO\({}_{2}\) emissions for freight transport in China among various modes, and roughly 6% of total domestic CO\({}_{2}\) emissions [1]. [PERSON] et al. [2] presented that increased awareness of environmental issues has resulted in a shift towards creating environmentally sustainable logistics planning and it is key to incorporate environmental concerns in planning and optimization of existing logistics systems. [PERSON] et al. [3] stated that operations research leads to a more efficient use of resources, which is not only cost-attractive, but also tends to create less emissions of greenhouse gases through the identification of trade-offs between environmental aspects and costs. Hence, low carbon practices should be integrated into logistics operations. Low carbon logistics has attracted increased attention in logistics operations from enterprises and professionals [4, 5].  
The vehicle routing problem (VRP) is a well-known combination optimization problem in logistics operations and exists in many real-life situations, such as school bus scheduling [6], snow removal and street sweeping [7], waste collection [8], and so on. It aims to identify a set of transport routes to provide efficient service to all customers with minimum cost. It was first proposed by [PERSON] in 1959 [9] and many kinds of variants of VRP have been developed since [10]. In this paper, we explore a new variant of VRP called the multi-trip heterogeneous vehicle routing problem with prioritized customers and incompatible cargoes (MTHVRP-PCIC) which is inspired by a real application in the hazardous chemicals road transportation industry. The problem differs from the general vehicle routing problem (GVRP) in the following five aspects: (1) the vehicles are heterogeneous; (2) some customers are given priority over others; (3) more than one kind of cargo is transported and some cargo types are incompatible with others, which means they cannot be loaded into the same vehicle; (4) the vehicles can continue to serve customers after returning to the depot within the trip duration; and (5) carbon emission cost is considered.  
The study aims to reach a trade-off between cost (including fixed cost and travel cost) and carbon emissions through integrating the low carbon economy into the logistics operations. A route optimization model in terms of the characteristics of road transportation of hazardous chemicals is developed. A two-phase hybrid metaheuristic algorithm is designed to solve the problem. The overall cost and carbon emissions are reduced with the developed model and solution method.  
The remainder of this paper is organized as follows. Related literature is presented in Section 2. Section 3 defines and describes the problem and develops the formulation mathematically for optimizing the route plan. This is followed by Section 4 which devises a two-phase hybrid metaheuristic algorithm. Section 5 outlines key data from road transportation practices for hazardous chemicals, which will be used as inputs to test the performance of the model and algorithm. Finally, the conclusion is presented in Section 6.