Ningxiong Xu

Modeling supplier selection and the use of option contracts for global supply chain design

As supply chains become more and more dependent on the efficient movement of materials among facilities that are geographically dispersed there is more opportunity for disruption. One of the common disruptions is the loss of production capability at supplier sites. We formulate a two-stage stochastic program and a solution procedure to optimize supplier selection to hedge against these disruptions. This model allows for the effective quantitative exploration of the trade-off between cost and risks to support improved decision-making in global supply chain design. A realistic case study is explored.

Optimizing Regional Earthquake Mitigation Investment Strategies

Regional mitigation analysis is a systematic procedure to determine how much to spend on mitigation versus post-event reconstruction and to prioritize alternative mitigation strategies. It requires at least the following information: magnitude and character of the regional risk, costs and benefits associated with all possible mitigation alternatives, available budget, and specific regional objectives for risk management. Currently available loss estimation models provide increasingly comprehensive estimates of regional risk, but offer little guidance about how to use that information to make mitigation resource allocation decisions. This paper describes a linear program developed to support systematic regional earthquake mitigation analysis, and illustrates its application through a case study in Los Angeles County. Results suggest which buildings—by structural type, occupancy type, and census tract location—should be upgraded so as to minimize total mitigation and expected post-earthquake reconstruction costs.

Investment Planning for Electric Power Systems Under Terrorist Threat

Access to electric power is critical to societal welfare. In this paper, we analyze the interaction between a defender and a terrorist who threatens the operation of an electric power system. The defender wants to find a strategic defense to minimize the consequences of an attack. Both parties have limited budgets and behave in their own self-interest. The problem is formulated as a multi-level mixed-integer programming problem. A Tabu Search with an embedded greedy algorithm for the attack problem is implemented to find the optimum defense strategy. We apply the algorithm to a 24-bus network for a combination of four different defense budgets, three attack budgets, and three assumptions as to how the terrorists craft their attacks.

Augmenting priority rule heuristics with justification and rollout to solve the resource-constrained project scheduling problem

The key question addressed by the resource-constrained project scheduling problem (RCPSP) is to determine the start times for each activity such that precedence and resource constraints are satisfied while achieving some objective. Priority rule-based heuristics are widely used for large problems. Rollout and justification can be integrated with priority rule heuristics to solve the RCPSP. We develop several such procedures and examine the resulting solution quality and computational cost. We present empirical evidence that these procedures are competitive with the best solution procedures described in the literature.

Bilevel Optimization for Integrated Shelter Location Analysis and Transportation Planning for Hurricane Events

Responding to hurricanes is an exceedingly complex task, the effectiveness of which can significantly influence the final effects of a hurricane. Despite a lot of progress, recent events and unchecked population growth in hurricane-prone regions make it clear that many challenges remain. Hurricane Katrina has shown that having appropriate shelter options and an appropriate shelter evacuation plan are very important for hurricane evacuations. This paper proposes a scenario-based shelter location model for optimizing a set of shelter locations among potential alternatives that are robust across a range of hurricane events. This model considers the influence of changing the selection of shelter locations on driver route-choice behavior and the resulting traffic congestion. The state of North Carolina is used as a case study to show the applicability of the model.

Application of regional earthquake mitigation optimization

A linear program was developed to help seismically active communities decide: (1) how much to spend on pre-earthquake mitigation that aims to reduce future losses versus waiting until after an event and paying for reconstruction, and (2) which of the many possible mitigation activities to fund so as to minimize overall risk. The mitigation alternatives considered are structural upgrading policies for groups of buildings. Benefits of mitigation are losses avoided in future earthquakes, including structural, non-structural, contents, and time-related losses, and casualties. The model is intended to be used as a tool to support the public regional mitigation planning process. In realistic applications, the model includes millions of variables, thus requiring a special solution method. This paper focuses on two efficient solution algorithms to solve the model-a Dantzig-Wolfe decomposition algorithm and a greedy heuristic algorithm. A comprehensive numerical study compares the two algorithms in terms of solution quality and solution time. The study shows that, compared to the Dantzig-Wolfe algorithm, the heuristic algorithm is much faster as expected, and provides comparable solution quality.

Multi-period dynamic supply contracts with cancellation

This paper considers a class of multi-period dynamic supply contracts in which a buyer orders a product from a supplier in each period and the supplier allows the buyer to cancel a portion of an outstanding order with penalty during a planning horizon. We assume that both the buyer and the supplier have common knowledge. We first characterize the buyers ordering and canceling policy that minimizes his expected cost during the planning horizon. We also characterize the suppliers optimal production policy under a very mild assumption on the costs of production and storage. Based on this structure, we then use simulation to show how the supplier chooses cancellation costs that minimize her expected cost during the planning horizon. Our simulation shows that both the buyer and the supplier would benefit from the contract.

The risk-return tradeoff in optimizing regional earthquake mitigation investment

Earthquakes are low probability-high consequence events, regional earthquake mitigation is therefore a risky investment. Despite its importance, the risk-return tradeoff is often not examined explicitly in regional earthquake risk management resource allocation decisions. This paper introduces a stochastic optimization model developed to help decision-makers understand the risk-return tradeoff in regional earthquake risk mitigation, and to help state and local governments comply with the Disaster Mitigation Act of 2000 requirement that they develop a mitigation plan. Taking advantage of the special structure of the optimization, Dantzig-Wolfe decomposition is used as the solution method. A case study for Central and Eastern Los Angeles illustrates an application of the model. Results include a graph of the tradeoff between risk and return, quantification of the relative contributions of each possible earthquake scenario, and discussion of the effect of risk aversion on the selection of mitigation alternatives.

Managing Portfolios of Projects under Uncertainty

Managers of projects and multi-project programs often face considerable uncertainty in the duration and outcomes of specific tasks, as well as in the overall level of resources required by tasks. They must decide, in these uncertain conditions, how to allocate and manage scarce resources across many projects that have competing needs. This paper develops a nonlinear mixed-integer programming model for optimizing the resource allocations to individual tasks to minimize the completion times of a collection of projects. The model contains a very flexible representation of the effects of changing resource allocations on the probability distribution of task duration, so it can accommodate a wide variety of practical situations. A heuristic solution procedure is proposed that works quite effectively. An illustration involving a collection of bridge construction projects is provided.

Transmission and Generation Expansion to Mitigate Seismic Risk

This paper develops a two-stage stochastic program and solution procedure to optimize the selection of capacity enhancement strategies to increase the resilience of electric power systems to earthquakes. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage to be experienced. This is important because electric power systems are spatially distributed; hence their performance is driven by the distribution of damage to the components. We test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnect where the seismic hazard primarily stems from the New Madrid Seismic Zone. We show the feasibility of optimized capacity expansion to improve the resilience of large-scale power systems with respect to large earthquakes.