Optimal Design and Operation of WHO-EPI Vaccine Distribution Chains

Vaccination has been proven to be the most effective method to prevent infectious diseases and in 1974 the World Health Organization (WHO) established the Expanded Programme on Immunization (EPI) to provide universal access to all important vaccines for all children, with a special focus on underserved low- and middle-income countries. However, there are still roughly 20 million infants worldwide who lack access to routine immunization services and remain at risk, and millions of additional deaths could be avoided if global vaccination coverage could improve. The broad goal of this research is to optimize the design and operation of the WHO-EPI vaccine distribution chain in these underserved low- and middle-income countries. We first present a network design problem for a general WHO-EPI vaccine distribution network by developing a mathematical model that formulates the network design problem as a mixed integer program (MIP). We then present three algorithms for typical problems that are too large to be solved using commercial MIP software. We test the algorithms using data derived from four different countries in sub-Saharan Africa and show that with our final algorithm, high-quality solutions are obtained for even the largest problems within a few minutes. We then discuss the problem of outreach to remote population centers when resources are limited and direct clinic service is unavailable. A set of these remote population centers is chosen, and over an appropriate planning period, teams of clinicians and support personnel are sent from a depot to set up mobile clinics at these locations to vaccinate people there and in the immediate surrounding area. We formulate the problem of designing outreach efforts as an MIP that is a combination of a set covering problem and a vehicle routing problem. We then incorporate uncertainty to study the robustness of the worst-case solutions and the related issue of the value of information. Finally, we study a variation of the outreach problem that combines Set Covering and the Traveling Salesmen Problem and provides an MIP formulation to solve the problem. Motivated by applications where the optimal policy needs to be updated on a regular basis and where repetitively solving this via MIP can be computationally expensive, we propose a machine learning approach to effectively deal with this problem by providing an opportunity to learn from historical optimal solutions that are derived from the MIP formulation. We also present a case study on outreach operations and provide numerical results. Our results show that while the novel machine learning based mechanism generates high quality solution repeatedly for problems that resemble instances in the training set, it does not generalize as well on a different set of optimization problems. These mixed results indicate that there are promising research opportunities to use machine learning to achieve tractability and scalability

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

The SNS logistics network design : location and vehicle routing.

Large-scale emergencies caused by earthquake, tornado, pandemic flu, terrorism attacks and so on can wreak havoc to communities. In order to mitigate the impact of the events, emergency stockpiles of food, water, medicine and other materials have been set up around the US to be delivered to the affected areas during relief operations. One type of stockpile is called the Strategic National Stockpile (SNS). The SNS logistics network is designed to have multiple stages of facilities, each of which is managed by different levels of governmental authorities - federal, state and local authorities. The design of a logistics network for delivery of the SNS materials within a state are explored in this dissertation. There are three major areas of focus in this dissertation: (1) the SNS facility location model, which is used to determine sites for locating Receiving, Staging and Storage (RSS) and Regional Distribution Nodes (RDNs) to form a logistics network to deliver relief material to Points of Demand (PODs), where the materials are directly delivered to the affected population; (2) the SNS Vehicle Routing Problem (VRP), which is used to assist the SNS staff in determining the numbers of various types of trucks, and the routing schedules of each truck to develop an operational plan for delivering the required relief materials to the assigned PODs within the required duration; (3) the location-routing analysis of emergency scenarios, in which the facility location model and the VRP solution are integrated through the use of a computer program to run on several assumed emergency scenarios. Using real data from the department of public health in the Commonwealth of Kentucky, a transshipment and location model is formulated to determine the facility locations and the transshipment quantities of materials; a multiple-vehicle routing model allowing split deliveries and multiple routes per vehicle that must be completed within a required duration is formulated to determine the routing and scheduling of trucks. The facility location model is implemented using Microsoft Solver Foundation and C#. An algorithm combining the Clark and Wright saving algorithm and Simulated Annealing is designed and implemented in C# to solve the VRP. The algorithm can determine whether there is shortage of transportation capacity, and if so, how many of various types of trucks should be added for optimal performance. All the solution algorithms are integrated into a web-based SNS planning tool. In the location-routing analysis of emergency scenarios, a binary location model and an algorithm for solving VRP solution are integrated as a computer program to forecast the feasibility of distribution plans and the numbers of required trucks of various types. The model also compares the costs and benefits of direct and indirect shipment. A large-scale emergency scenario in which a specific type of vaccine is required to be delivered to the entire state of Kentucky is considered. The experiments are designed based on the real data provided by the Kentucky state government. Thus the experimental results provide valuable suggestions for future SNS preparedness planning

Hub maximal covering problems - novel mathematical models and solution methods

Hab lokacijski problemi, zbog brojnih primena u raznim oblastima realnog života, predstavlja važnu klasu problema optimizacije...Hub Location Problems (HLP) represent an important class of optimization problems due to their numerous applications in many areas of real life. They often arise from practical situations that require routing of the flow from origin node (supplier) to the destination node (customer) under given conditions, such that the value of considered objective function is optimal. Hubs are special objects (nodes in the network) that represent centres for consolidation and flow collection between two selected locations - suppliers and customers. As transportation costs (per unit of flow) along the links that connect hub nodes are lower compared to other links in the network, directing the flow to hubs may lead to significant reductions of transportation cost in the network..

New Model of Maximal Covering Location Problem with Fuzzy Conditions

The objective of Maximal Covering Location Problem is locating facilities such that they cover the maximal number of locations in a given radius or travel time. MCLP is applied in many different real-world problems with several modifications. In this paper a new model of MCLP with fuzzy conditions is presented. It uses two types of fuzzy numbers for describing two main parameters of MCLP - coverage radius and distances between locations. First, the model is defined, then Particle Swarm Optimization method for solving the problem is described and tested

Bilevel facility location problems: theory and applications.

In this doctoral thesis we focus on studying facility location problems considering customer preferences. In these problems, there is a set of customers or users who demand a service or product that must be supplied by one or more facilities. By facilities it is understood some object or structure that offers some service to customers. One of the most important assumptions is that customers have established their own preferences over the facilities and should be taken into account in the customer-facility assignment. In real life, customers choose facilities based on costs, preferences, a predetermined contract, or a loyalty coefficient, among others. That is, they are free to choose the facilities that will serve them. The situation described above is commonly modeled by bilevel programming, where the upper level corresponds to location decisions to optimize a predefined criteria, such as, minimize location and distribution costs or maximize the demand covered by the facilities; and the lower level is associated to -customer allocation- to optimize customer preferences. The hierarchy among both levels is justified because the decision taken in the upper level directly affects the decision’s space in the lower level

El problema de localización de hubs con flota limitada

Tesis (Ingeniero Industrial)En los modelos matemáticos de localización de hubs en donde se busca maximizar la cobertura no considera una flota limitada, tanto en capacidad como en cantidad, o bien, un presupuesto limitado. Pero, ¿Cómo solucionar los problemas de cobertura en organizaciones que no cuentan con una flota, o un presupuesto grande? Se podría considerar minimizar la distancia de cada viaje, esto involucra realizar transbordos de vehículos, pero realizar esta acción, la gran mayoría de las veces, incrementa los costos. Es por esto que, en la siguiente investigación, se propone un nuevo modelo que podrá ser muy útil para organizaciones de distribución en la toma decisiones, sobre cómo realizar la distribución de sus centros logísticos, cuantos vehículos necesitará y cuantos clientes logrará atender con el presupuesto disponible