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\section{Introduction}  As stated by the United Nations Office for Disaster Risk Reduction (UNISDR), the term ``natural disaster'' does not exist\cite{UNISDR website}. Instead, disasters follow natural hazards, which are the direct result of various incidents such as floods, storms, droughts, earthquakes, and so on. The same reference indicates that about a thousand of natural incidents resulting in loss of life have happened solely in 2014. The overall loss cost is estimated to be beyond 1,500m USD. As a matter of fact, the global community has come into an agreement that a universal framework must be adopted by governments for the purpose of disaster risk reduction. \cite{UNISDR}   Aiming for mitigating the effects of disasters, the disaster risk reduction comprises several actions and efforts varying from wise managing the land and the environment to building and fortifying structures with the aim of protecting them against the impacts of disasters, the inevitable fact is that such incidents are part of human being life on the earth. Hence, the importance of preparedness for such events is of significant importance. To support various preparedness actions, we need to be equipped with a comprehensive set of tools that allow us optimal design and development of a comprehensive solution. This refers to all actions before the incident happens (such as establishing the warning systems, food and first-aid reservoirs, evacuation plans etc.) and after the incident happens (such as supply of relief-items from the local and/or global resources, relief-item distribution regimes, etc.)   The concept of supply chains (SC) exists more than a century and the related rich body of research works comprise supply chain management (SCM). As defined by Simchi-Levi et al. \cite{Simchi-Levi}, SCM is the set of approaches that guarantees the on-time production and distribution of merchandises by integrating suppliers, manufacturers, warehouses, and stores, which aim to minimize the system-wide costs and satisfy the required service levels. For years, the SCM researchers have studied commercial (business) SCs, i.e., the ones that involve the cooperation of various agents with the aim of producing profits. In contrast, the term ``humanitarian logistics'' and its related challenges, until relatively recently, have not attracted serious consideration by academic community at large \cite{ChristopherTatham}.   Despite a number of similarities, the humanitarian logistics is differentiated from business SCM through several key aspects. First, while the satisfaction of the customers must ultimately lead to more profit for the agents involved in the business SCM, the humanitarian logistics is about the customers' cost reduction (cost of life and property loss and injuries). Second, several decisions in business SCs are made for the long-run, whereas the decisions in the humanitarian logistics are temporary and subject to change according the type and the location of the disaster. Third, the time-sensitivity of making optimal decisions is significantly more pronounced in humanitarian logistics; often the time-window to take actions is very tight and the whole system (human being, structures, etc.) may incur a significant amount of costs if the decision-making process takes considerable amount of time. There are some other aspects that have been pointed out in the literature. For example, Christopher and Tatham \cite{ChristopherTatham} mention the absence of clarity in identifying the customers and their needs when studying humanitarian logistics.   The concept of uncertainty has very-well studied within the SCM framework. In particular, the inherent uncertainties in the demand and the lead time has been the focal points of several studies. While being similar, the uncertainty poses a more serious challenge in humanitarian logistics compared to business SCs.     \begin{itemize}  \item The opportunity to learn from the realization of uncertainties is far richer in business SCs. First, business SCs are more prevalently employed in the real-world. This allows gathering more data about the uncertainty, which allow better prediction about the outcomes. Besides, there is more opportunities to learn about uncertainty and its impacts through benchmarking from similar business SCs. As a result, more samples are available, which permits better understanding about the random outcomes of the uncertainties.     \item There are more uncertain parameters that are to be considered when studying humanitarian logistics compared to business logistics. For example, the location of warehouses, the availability of the distribution networks, and the physical locations of the demand points (e.g., affected people) are naturally uncertain. In contrast, for example, the location/allocation decision in commercial SCs remain unchanged often for longer period of time.     \item The outcomes of the uncertainty can have very catastrophic impacts on human lives. While the errors and wrong decisions due to the randomness in business SCs are measured in monetary values, the worst-case outcomes of natural disasters may be loss of lives. As a result, the models that immune the preparedness actions against the worst outcomes may seem more appropriate compared to the ones that are built upon the expected costs.     \end{itemize}   Hence, it is crucial to devote independent efforts to study the uncertainty and its impacts in humanitarian logistics.  ``Mathematical programming'', ``Probability and Statistics'', and ``Simulation'' are a few of the widely-used approaches to study humanitarian logistics problems. Among the aforementioned approaches, mathematical programming has attracted the most attention of OR community over the last decade \cite{RahaAkhavanORModelsSurvery}. In particular, several optimization problems under uncertainty have been studied that arise in response planning, preparedness planning, mitigation planning, etc. The reader is advised to refer to \cite{,,} for further details in this regard.   Several approaches to incorporate the uncertainty within optimization problems have been proposed since the realization of the need adopt more realistic mathematical programs. In particular, the majority of the efforts have been devoted to one of the two most prominent paradigms: 1) stochastic programs, and 2) robust optimization problems. While the latter emphasizes on the importance of immunization against the worst-case scenario, the former is more focused on the expected costs in the long-run. Also, while the robust optimization paradigm has attracted the researchers' attention over the last two decades, the stochastic programming is one of the first approaches to study uncertain mathematical programs and have been widely used in the literature.   By realizing the dominance of the uncertain mathematical programs in studying humanitarian logistics, we aim to report on notable research works that employ stochastic programs or robust optimization. We have carefully studied the literature and have found {\color{red}{HOW MANY}} journal publications that are particularly focused on either of the aforementioned approaches. For each work, we provide a paragraph explaining the motivation of the work, the modeling approach and its characteristics, the solution technique, and the computation study (if any) of the suggested model and solution technique. It is worth mentioning that our survey is limited to the solution techniques that are able to optimally solve the mathematical program.   The remainder of this paper is as follows. In Section \ref{sec2}, we briefly introduce stochastic programs and report on the notable works that have employed stochastic programs. Section \ref{sec3} report on few research works that employ robust optimization. Future research and conclusions are stated in Section \ref{sec4}.