# A Network-Based Model for Optimization of Container Location Assignment at Inland Terminals
## 1 Introduction  
As international trade develops, an increasing number of large container ships arrive at container seaports, creating storage problems. The limited yard space at container seaports and pressure from shippers to deliver goods to end users as quickly as possible have led many seaports to connect with inland terminals [1]. Seaports are attractive not only because of their reliability and nautical qualities, but also because of their hinterland connectivity and capacity [2].  
Container storage is one of the most important operations at any terminal, including container seaports and inland terminals. Optimal storage means proper management, rapid retrieval time, and a minimum number of unproductive manipulations, defined as manipulations (e.g., to access a specific container among many others) that do not bring the container closer to its final destination. Such manipulations generate significant additional costs and take time. The challenge of optimal storage is known as the \"location assignment (stacking) problem\" because it involves the allocation of containers to stacks [3].  
Reducing the number of unproductive manipulations becomes more complex when different types of containers are involved (e.g., different dimensions, weights, cargo type), as well as when the departure time of the containers is unknown [4]. Reducing these manipulations and optimizing container location assignment and storage space allocation have been studied thoroughly at seaports. In Section 2 a literature review on container allocation at seaports and inland terminals has been presented. Most studies have aimed tominimize transportation costs and maximize space utilization. In contrast, studies of the container location assignment problem at inland terminals are lacking.  
Optimizing methods to allocate and collect containers depends on the storage surface available, the degree of mechanization, and the management policies [5]. Whatever storage allocation methods at inland terminals are applied, they should be harmonized with technological processes at seaports in order to ensure optimal container processing.  
The present study developed a new network-based mathematical model for determining the order of inbound container storage and their allocation, according to the retention time estimated from container parameters, which were identified after the analysis of European inland terminals (Section 4). The purpose of the model is to reduce unproductive inbound manipulations and their associated costs at inland terminals. The model assigns container locations in a way that minimizes container handling costs related to unproductive manipulations, while taking into account the spatial and operational constraints of inbound operations. The assumptions in the network are based on the analysis of technological processes involving inbound containers at representative European inland terminals. For the model proposed, first we analyzed the parameters (criteria) for container location assignment at the representative inland terminals (Section 3). The resulting parameters were used to evaluate the hierarchy of container location assignment criteria by calculating the parameter potentials defined for container storage determination. The proposed model determines the inbound container assignment location according to criterion potentials and ranks based on the consistent approximation preference stream for the case when container departure time is unknown. To determine the hierarchy of parameter potentials for optimizing container storage, we implemented a novel potential method. We validated the model on one of the analyzed inland terminals using the FlexSim simulation environment (Sections 5 and 6). Our results suggest that the model can determine exact container locations at inland terminals in a way that minimizes unproductive manipulations and reduces operating costs.