The article, “A dynamic logistics coordination model for evacuation and support in disaster response activities”, by authors Wei Yi and Linet Ozdamar, and published in the European Journal of Operational Research, presents a robust two-phase optimization model to advance the accurate delivery of both material and human resources to and from both permanent and temporary facilities within the affected zone of natural disaster. In the model, a simulated earthquake affecting urban area of Istanbul, Turkey (which is expected to happen within 30 years of this publication) is used for example. The scenario presented outlines the several time periods throughout the initial phases of the disaster response, including the initial phases of setting up and making operational temporary facilities through which to treat light-medium to heavy healthcare needs for disaster victims, as well as the reconfiguration of optimal routing to reach optimal facility locations within the most drastically affected zones. Later in the model, time periods focus on replenishing of supplies and relocation of further human resources to appropriate facilities based on the queuing that occurs at each location.
The model developed and implemented in this paper is a mixed integer, multi-commodity network flow model that treats vehicles as integer commodity flows as opposed to binary variables. This allows the model to construct an optimal vehicle route and load instruction sheet, based on demand of various supplies along a given route. The goal is to minimize the delay in making priority commodity and human resources deliveries to affected areas. The optimization of both integer material and human resources and vehicles, and then re-calculates the optimal distribution of these resources after delivery in each time period is made. The model both makes suggestions on the location of temporary response facilities within the affected disaster area, and minimizes the transportation delay for patients with different medical treatment level requirements and at different locations. The model can adjust to regular information updates including the interruption of roadways and supply lines, the breakdown of vehicles (taking them out of the pool of availability and re-ordering priority) and re-allocation of service capacities. The model is based on the assumption that information flow after a disaster is within a planning horizon that is extremely short and initial feedback from sites is scarce, until later periods where information more accurately resembles the demands at local emergency sites.
The model is a Location Routing problem, which takes into its development aspects of both Vehicle Routing and Facility Location type problems. The model involves split-delivery, deterministic demand that is dynamic as opposed to static over a number of time periods, involves multiple capacitated facilities with size optimization requirements, and a heterogeneous fleet of vehicles (in this case, helicopters, trucks and ambulance) each with different capacities.
The Vehicle routing sub-problem deals with several special considerations. Supply availability is limited due to the disaster’s impact is difficult to immediately determine, and there exists a transportation delay from major warehouses. In addition, the ability to have in-stock levels of commodities required at the onset of disaster may not be possible, and supplies may need to be redirected from other locations to that facility first. In addition, vehicles may be redirected from one delivery endpoint to another node of delivery and pickup, and not simply back to a point of origin, making the need for the VRP to be run at each time period considering the location and needs as re-prioritized in each time period.
However, the benefits are great. The flexibility of the model, and the holistic allocation of resources and commodities to the location they are most needed in order of priority, reduces unnecessary injury complications and possible casualties as well as using scare resources where they will have the greatest overall impact.
The model is ideal for the type of unique scenarios that disasters create; however, because demand information may not be immediate and the model uses a deterministic approach to re-evaluating demand over time periods, it does not make decisions as to the pre-positioning of supplies at locations before the disaster event in preparation of the possibility of occurrence. Therefore, more efficiency may be gained by expanding the model to include the probabilistic considerations of likelihood of various scenarios, the range of labor and material demands and the location of warehouses before the onset of disaster. This would benefit the model by positioning the resources for response more within the likely best-required location at the start of the deterministic model. Because it is impossible to anticipate when or where the disaster event will occur, it makes sense to minimize the cost of the best possible pre-positioning of goods for various probabilistic scenarios. However, a tradeoff occurs in which, based on probability of a disaster event occurring, products of a high dollar value may also have a high priority value in time of actual disaster. Therefore the value of products must be weighted against storage requirements (inventory) costs as well as product purchase costs. Mete and Zabinsky provide a mathematical formulation for determining the value of goods in inventory at warehouse locations prior to a natural disaster: (Part 1) Minimize the Sum of (Cost of Operations for a Warehouse X Number of Warehouses Operating in a Pre-positioning Capacity) +A Probabilistic Value (Part 2) Based on the Demand Probability of Various Scenarios, subject to supply storage space constraints of each available warehouse, and maximum availability levels of the range of medical supplies.
The probabilistic value of demand is based on the occurrence of numerous iterations of simulated scenarios whereby the LRP uses various levels of supply and warehouse location, as well as the level of unsatisfied demand under those scenarios. What this creates is a feedback loop of optimization of warehouse location and inventory levels based on probabilistic demand, and then deterministically responds to the crises, effectively optimizing both the emergency response preparedness and the disaster response.
Other possible directions with which the original model can be developed include scaling the problem for minimum and maximum affected areas so that local, regional and larger scale disasters can be considered simultaneously with a weighted probability for each scenario to occur. Another possible consideration is the determination of vehicle capacity on various roadways affected by disaster, so as to determine the better option for a delivery route over two open roadways with different capacity flow levels (1 versus 2 lane; popularity among local residents for use during peak, off-peak and emergency hours); and work schedule assignment constraints such as maximum hours allowable for healthcare and response individuals to work before rest is required (considering the effect on service levels and service times, the queuing scenario and next best options for staffing).
The two-part LRP is a great development in the study of emergency response because it considers the time constraints and the immediate necessity of the initial phases of disaster recovery. When coupling this phase with the upstream and down stream linkages in the supply chain, as well as considering the pre-planning stage and the concurrent modifications and limitations of the local, regional or larger scale infrastructure, as well as both deterministic and probabilistic modeling within simulation and optimization approaches, the best case scenario can alleviate suffering, save lives and best allocate scarce and costly material and human capital.
References:
Mete and Zabinsky. Preparing for Disasters: Medical Supply Location and Distribution, Interfaces (2009)
Yazici, M.A. Ozbay, K. Impact of Probabilistic Road Capacity Constraints on the Spatial Distribution of Hurricane Evacuation Shelter Capacities. Transportation Research Record 2022 (2007) 55-62
Yi, W. and Ozdamar, L. European Journal of Operational Research 179 (2007) 1177–1193

