# Dynamic Relief Items Distribution Model with Sliding Time Window in the Post-Disaster Environment
## 1 Introduction  
Millions of citizens in several cities have been extremely affected by the growth of disasters [1]. To minimize the impact of disaster, effective distribution of relief items becomes a crucial aspect of smart cities in humanitarian supply chain management to support disaster survivors. However, after any disaster, constraints such as time, cost, priorities, limited resources and asymmetric relief demand make the Relief Items Distribution (RID) challenging [2]. In addition to these challenges, the available information immediately after a disaster is highly irregular, which potentially affects the distribution relief management strategies. For example, during the post-disaster relief management of the Tohoku disaster of 2011 in Japan, it was observed that there had been a sudden demand for food and water, particularly in areas that were not highly affected by the tsunami [3]. Information such as vehicle availability, disaster region priority, available transportation routes and their conditions are among the crucial factors for effective relief items distribution. In most of the disaster environments, supply points are equipped with limited resources and have a direct impact on the efficiency of the distribution task [4]. Additionally, for effective RID, the number of the affected population has always been the primary concern [5]. To incorporate these issues in the RID model, the distribution of relief items should consider the causality level and relief item demand across the disaster regions [6]. Consideration of the affected population rather than the total population in the distribution task makes the distribution more rational regarding all the disaster regions. In other words, the distribution plan must consider the number of disaster victims across all the disaster regions, which can be the estimation, based on senses data [7]. It has also been argued that the traditional distribution strategies mainly depend on static data rather than dynamic data, which may lead to an imbalance between supply and demand for relief items over a relief items distribution period [8]. Another concern in the disaster scenarios is setting distribution priorities, which appear as one of the major objectives for decision-makers to balance disaster impact levels in the distribution plan [9]. The other objective of any disaster relief distribution model is to address the uncertainty and changing disaster information for each time period [10,11]. In other words, the distribution schedule must be planned iteratively with multiple time-periods based on available information, relief items and other resources. Apart from these, under disaster environments, road conditions and traffic flow changes dynamically, which brings additional complexity to the distribution plan [12]. This complexity of the relief items transportation path has a significant impact on routing vehicles; therefore, the transportation routes should also be considered as an objective of the path selection model [13]. Considering the different challenges that appeared for the implementation of RID in disaster environments, there is a need for an effective RID model that can address the discussed issues and make the distribution task operative. The aim of this study is to develop an effective RID model that reflects the more realistic disaster scenarios and also covers as many different disaster-related aspects as possible to help the decision-makers in post-disaster relief items distribution management. In this paper, a dynamic relief distribution model with a sliding time window is presented that generates an optimised distribution schedule for each time slot based on the updated information. The initial optimum distribution schedule is generated with the available information on disaster regions, casualty levels, available resources and transportation routes. The schedule is re-optimised at each time slot with the updated information. The main contributions of this paper can be summarised as:  
1.