# A Forecast Model of the Number of Containers for Containers by Voyage
## 1 Introduction  
Container transportation is a highly complicated process and involves numerous parties, necessitating close cooperation between ports, ships, shipping companies, and other relevant departments. Therefore, container transportation management is characterized by extremely detailed planning [1; 2]. For example, container terminals must formulate strategies such as berthing plans [3], container truck dispatch plans, yard planning systems, and yard stowage plans [4; 5; 6]. In addition, ships or shipping companies must formulate voyage stowage plans for container ships at the port of departure. The number of containers in the subsequent port must be predicted, and such prediction information forms a crucial basis for the subsequent plan. These processes must be completed before the development of a stowage system for full-route container ships [7]. Changes in the number of containers allocated to container ships are influenced by several factors, which are characterized by uncertain information; this thus engenders a complex nonlinear relationship between the number of allocated containers and influencing factors [8]. The number of allocated containers is influenced by the port of call, local GDP, port industrial structures, and collection and distribution systems; by shipping company-related factors such as the capacity of a company, inland turnaround time of containers, seasonal changes in cargo volume, and quantity of containers managed by the company; and by ship-related factors such as the transportation capacity of a single ship and the full-container-loading rate of the ship. Each of these factors exerts distinct effects on the number of containers allocated to a container ship for one voyage; therefore, describing these factors by usingan accurate mathematical model is difficult [9]. Traditional methods such as time series forecasting (including exponential smoothing [10], gray prediction [11], moving average [12], and seasonal periodic variation [13] approaches) and regression forecasting [14] typically rely on certain mathematical theories and assumptions and necessitate the establishment of mathematical models through deductive reasoning without considering influencing factors. By contrast, neural networks--constituting a nonlinear and nonparametric model--can describe the nonlinear relationship between a premeasured quantity and influencing factors, and they have self-learning and self-adaptation abilities to effectively avoid prediction errors caused by assumptions; accordingly, neural networks have been extensively applied in various project prediction processes. However, neural networks [15] have drawbacks such as an indeterminable network structure, overfitting, local minimum, and \"curse of dimensionality\". Support vector machines (SVMs) [16] solve the aforementioned drawbacks of neural networks by minimizing structural risk, and SVMs are highly suitable for predicting the number of containers allocated to a container ship for one voyage, a problem that involves characteristics such as nonlinearity, high dimensionality, and a small-scale sample [17; 18; 19; 20]. An SVM entails the selection of a kernel function, thus demonstrating the nonlinear processing ability of the learning machine; because a kernel function is selected [21], a feature space is defined [22; 23]. Nevertheless, a single kernel function cannot afford learning ability and generalization ability simultaneously in an SVM [24]. This paper proposes mixed kernels, which can effectively improve the predictive performance of an SVM model with weighted arrays of polynomial and radial basis kernel functions. As mentioned, each of the aforementioned factors exerts distinct effects on the various factors influencing the number of allocated containers in one voyage. If such differences are neglected, the prediction results would be distorted [25]. Therefore, this paper proposes a model based on gray relational analysis (GRA) theory [26] and mixed kernel SVM for predicting container allocation to a container ship.