OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the first-stage decisions impact the second-stage constraints. Our modified problem extends the second-stage problem to a more general setting where logical expressions of the first-stage solutions enforce constraints in the second stage. We also propose a complementary problem and solution method which can be used for many of the same applications. In the complementary problem we have second-stage costs impacted by expressions of the first-stage decisions. In both settings, we convexify the second-stage problems using BDDs and parametrize either the arc costs or capacities of these BDDs with first-stage solutions depending on the problem. We further extend this work by incorporating conditional value-at-risk and we propose, to our knowledge, the first decomposition method for two-stage stochastic programs with binary recourse and a risk measure. We apply these methods to a novel stochastic dominating set problem and present numerical results to demonstrate the effectiveness of the proposed methods

Single‐commodity stochastic network design under demand and topological uncertainties with insufficient data

Stochastic network design is fundamental to transportation and logistic problems in practice, yet faces new modeling and computational challenges resulted from heterogeneous sources of uncertainties and their unknown distributions given limited data. In this article, we design arcs in a network to optimize the cost of single‐commodity flows under random demand and arc disruptions. We minimize the network design cost plus cost associated with network performance under uncertainty evaluated by two schemes. The first scheme restricts demand and arc capacities in budgeted uncertainty sets and minimizes the worst‐case cost of supply generation and network flows for any possible realizations. The second scheme generates a finite set of samples from statistical information (e.g., moments) of data and minimizes the expected cost of supplies and flows, for which we bound the worst‐case cost using budgeted uncertainty sets. We develop cutting‐plane algorithms for solving the mixed‐integer nonlinear programming reformulations of the problem under the two schemes. We compare the computational efficacy of different approaches and analyze the results by testing diverse instances of random and real‐world networks. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 154–173, 2017Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/1/nav21739_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137236/2/nav21739.pd

Robust and stochastic approaches to network capacity design under demand uncertainty

This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique

Effects of fuel cost uncertainty on optimal energy flows in U.S.

The research is motivated by the need for economic efficiency and risk management in the national electric system. Stochastic costs of natural gas are introduced in a generalized network flow model of the integrated power energy system to explore the effects of uncertain fuel costs on the optimal energy flows in U.S. The fuel costs are modeled as discretely distributed random variables and a rolling two-stage approach is applied to solve the stochastic recourse problem. All the data are derived from publicly available information for the year 2002. The natural gas price forecasts by the Energy Information Administration are adapted to generate scenarios that are considered in the stochastic problem. Compared to the expected value solution from the deterministic model, the recourse problem solution obtained from the stochastic model has higher total cost, lower natural gas consumption and less subregional power trade but a flow mix which is closer to the 2002 real data. Surprisingly, increasing the uncertainty level of the scenarios leads to a recourse problem solution with slightly lower total cost but this effect may be distributed to the inaccuracy of the forecasts. The comparison demonstrates the stochastic model\u27s capability of forecasting energy flows. The stochastic model assists decision makers to better understand how the uncertain fuel costs would affect future flows within the national electric energy system

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

A maritime inventory routing problem with stochastic sailing and port times

This paper describes a stochastic short sea shipping problem where a company is responsible for both the distribution of oil products between islands and the inventory management of those products at consumption storage tanks located at ports. In general, ship routing and scheduling is associated with uncertainty in weather conditions and unpredictable waiting times at ports. In this work, both sailing times and port times are considered to be stochastic parameters. A two-stage stochastic programming model with recourse is presented where the first stage consists of routing, loading and unloading decisions, and the second stage consists of scheduling and inventory decisions. The model is solved using a decomposition approach similar to an L-shaped algorithm where optimality cuts are added dynamically, and this solution process is embedded within the sample average approximation method. A computational study based on real-world instances is presented