Resource management for flood response in Mexico

Emergency logistics is acquiring a crucial role aiming to provide adequate care and support for people affected by catastrophic situations; dealing with a large number of stakeholders, scarcity of resources and high stakes. Considering the importance of balancing resources from different participants to improve operations, this research introduces a bi-criteria response optimisation model aiming to maximise the service provided to disaster victims while making efficient use of resources. The model provides support for relief distribution, inventory management and resource allocation. But beyond the optimisation of logistical decisions, the model is able to determine which organisations to use at the appropriate timeframe, so as to prevent shortages and convergence. The model is applied to a case study on a flood in Mexico in order to compare its results with real activities performed by authorities and draw conclusions.


Introduction
Natural disasters are a constant threat for many countries, affecting an average of over 200 million people per year between 2000 and 2014 [1]. Emergency logistics arises as the "process of planning, managing and controlling the efficient flows of relief, information, and services from the points of origin to the points of destination to meet the urgent needs of the affected people under emergency conditions" [2].
Under disaster circumstances government agencies play a major role in aiding vulnerable population. But these are just one of the actors, being supported also by NGOs, civil organisations and aid shipped from other countries [3].
Despite the common belief that sending every resource available is the best policy to provide support, recent experiences globally have shown that it is important to manage closely resources available, to deploy the right organisations at the right time.
The purpose of this research is to provide a model capable of providing support for relief distribution and resource allocation considering the participation of different organisations.

Literature review
Relief distribution refers to the dispatch of different commodities to affected areas swiftly and efficiently [4]. This is a very challenging activity faced by responders [5] and also a crucial factor for high performance operations [6].
Using multi-objective approaches, Huang, Jiang [7] accounted for human suffering with three objectives; maximise lifesaving utility (i.e. preference of relief resources), minimise delay cost (similar to deprivation cost), and minimise the sum of squares of the distances between the demand fill rates and the ideal demand rate. Adõvar and Mert [8] looked at the coordination of international relief items using fuzzy logic to provide a collectiondistribution plan. The model minimises cost and maximises the minimum credibility of international organisations to deliver relief items on time. Incorporating uncertainty of relief demand by using forecasting, clustering and dynamic relief supply for logistic operations related to distribution, Sheu [5] designed a model to maximise fill rate and minimise distribution cost.
Chang, Tseng [9] designed two optimisation models with different organisation levels for floods. The models cluster demand and determine local rescue bases to minimise total cost. More recently, Altay [10] developed a static model to allocate response personnel, facilities, supplies and equipment to disaster-affected jurisdictions. The alternative objective functions are to minimise total deployment time or minimise maximum response time. Including uncertainty in the state of road network, Edrissi, Poorzahedy [11] presented a formulation to coordinate agencies considering strengthening structures around vulnerable areas, retrofitting transportation links and locating and equipping emergency response centres. They introduced a dynamic version of the preparedness optimisation model to ship relief aid in the response stage.
There is only a handful of papers considering the importance of sharing resources, whether between teams [e.g. 10,12], regions [e.g. 13], organisations [e.g. 8] or other agents [e.g. 11]. In the literature, however, there is no dynamic formulation for relief distribution optimising the number of actors involved determining the deployment and withdrawal of different agencies. Having the right expertise on the field at the right time are factors that can affect operational success in disaster response.
The purpose of this research is to provide a model incorporating several actors to identify the optimal combination of organisations and resources required per period.

Model design
The model developed in this research can provide support for decision-making for that interval of time. The dynamic formulation includes two objective functions, one related to cost and another focused on fill rate, thereby balancing efficiency and effectiveness. The model can determine what actors to involve and the appropriate moment for them to participate on the field.

Notation and definitions
The notation considered for the design of the model is presented as follows:  Amount of product n from organisation o supplied to DC i at period t

Model formulation
The response optimisation model is looking to balance resources available during the whole disaster. The model chooses which agencies to activate depending on the circumstances and the stage of the emergency, designing a policy tailored to the situation. The formulation of the model is presented as follows: (1) Expression (1) minimises cost in terms of the number of organisations involved, procurement cost and transportation cost. Function (2) seeks the minimisation of the total unfulfillment of shelter care, healthcare and relief distribution across all demand areas and all periods. Constraint (3) determines the unfulfillment level depending on the priority of the product from the number of unsatisfied demand established on equation (4). Expression (5) is enforcing that the combination of the consumption at every demand area of every product every three periods is at least a certain percentage of the total demand at all shelters over the same periods. Equations (6) and (7) determine the levels of inventory of DCs and demand areas, respectively. Expression (8) makes sure that items procured and delivered are aligned with the supply capacity from the organisations activated. Constraints (9) and (10) restrict the storage capacity of DCs and demand areas, respectively. Expression (11) ensures a minimum number of personnel allocated to DCs even for partial opening, whereas equations (12) and (13)  The information gathered was in terms of relief items, prepositioned stock, shelters used, number of people sheltered per period, distribution centres activated costs, required number of employees per activity and personnel available per agency.

Solution of the model
Using the information the model was solved using the weighted-sum method and the εconstraint method with loops of 150 iterations and a time limit of 600 seconds per iteration. A total of 142 non-dominated solutions were obtained.
More data was collected from the participating organisations. The purpose was to recreate the situation obtained according to the real activities. The only information unavailable was related to allocation of resources and services, which was optimised to obtain the best possible outcome that could have been achieved by authorities. The comparison can be seen in Figure 1. The figure shows how independent decision-making was not a suitable policy for the disaster as there is no organisation capable of coping with the conditions of the disaster. It can also be seen that assuming a coordinated approach the real decisions made by authorities represented an acceptable fill rate but at a very high cost compared to the potential solution delivered by the model.

Conclusions
This research introduced a novel dynamic optimisation model for disaster management considering the involvement of several organisations. Resource management is a significant component of response activities such as relief distribution and inventory management. The results of the model showed the potential to handle several organisations and deploy them according to the circumstances. The model was capable of providing a 100% of satisfaction rate with the resources available without the need to involve all of the organisations that participated in reality in the disaster.
The comparison with independent decision-making showed the incapability of any of the organisations involved to handle the situation on their own, whereas the comparison to real activities exhibited the room of improvement for future operations in terms of cost and fill rate.
The result of the study highlights the importance of considering the management of resources for logistical decisions in disaster management and the need to integrate the different actors to avoid duplications of effort and achieve more successful operations.