Dynamic decision making for graphical models applied to oil exploration

We present a framework for sequential decision making in problems described by graphical models. The setting is given by dependent discrete random variables with associated costs or revenues. In our examples, the dependent variables are the potential outcomes (oil, gas or dry) when drilling a petroleum well. The goal is to develop an optimal selection strategy of wells that incorporates a chosen utility function within an approximated dynamic programming scheme. We propose and compare different approximations, from naive and myopic heuristics to more complex look-ahead schemes, and we discuss their computational properties. We apply these strategies to oil exploration over multiple prospects modeled by a directed acyclic graph, and to a reservoir drilling decision problem modeled by a Markov random field. The results show that the suggested strategies clearly improve the naive or myopic constructions used in petroleum industry today. This is useful for decision makers planning petroleum exploration policies.     

A procedure for optimizing tactical response in oil spill clean up operations

The Tactical Decision Problem (TDP) associated with oil spill clean up operations allocates available components to compose response systems so that the clean up requirement for each time period over the entire planning horizon is met. The objective is to minimize total response time to allow for the most effective clean up possible. The TDP is formulated as a general integer program, a problem that is difficult to solve due to its combinatorial nature. In this paper, we develop an optimization procedure that is based on an aggregation scheme and strong cutting plane methods. The solution of the resulting Aggregated Tactical Model is used in reformulating the TDP, in generating a family of facets for the TDP, and in several preprocessing methods. Computational experience in also reported in application to a realistic scenario representing the Galveston Bay Area.     

A synthesis algorithm for an oil spill problem of complementary locations on networks

This paper develops a synthesis algorithm on networks for the problem of (a) locating appropriate levels and types of cleanup capability to respond to oil spills that may occur in a given area, and (b) allocating such capability among points of high oil spill potential in that area. The heuristic algorithm takes into account frequency of spill occurrence, variability of spill volumes, differing cleanup technologies, equipment efficiency and operability, fixed costs of opening facilities, equipment acquisition, transportation and operating costs, and costs of damage as functions of spill volume and level of response. The algorithm can also accept stipulations on response times. The results of the heuristic algorithm have been compared with results obtained by a Linear Programming (LP) formulation, and the highest deviation observed was around 1%. The advantage of the developed algorithm is apparent in real-life oil spill problems which are large-scale in nature and which cannot be solved by the LP procedure.     

Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

Optimal location and capacity of emergency cleanup equipment for oil spill response

Myopic planning and tactical decision-making with regards to oil spill events result in severely inefficient cleanup efforts with high fixed, operating and cleanup/damage costs. We propose an integrated framework that addresses some important strategic issues such as determining the optimal location and capacity of cleanup equipment, taking into account their post event implications. We develop a linear integer programming model, exhibit its complexity and propose a solution method by solving a relaxation of the original problem. Realistic examples applied to the Florida peninsula are presented.     

A graphical characterization of the largest chain graphs

The paper presents a graphical characterization of the largest chain graphs which serve as unique representatives of classes of Markov equivalent chain graphs. The characterization is a basis for an algorithm constructing, for a given chain graph, the largest chain graph equivalent to it. The algorithm was used to generate a catalog of the largest chain graphs with at most five vertices. Every item of the catalog contains the largest chain graph of a class of Markov equivalent chain graphs and an economical record of the induced independency model.     

On a risk management analysis of oil spill risk using maritime transportation system simulation

Is it safer for New Orleans river gambling boats to be underway than to be dockside? Is oil transportation risk reduced by lowering wind restrictions from 45 to 35 knots at Hinchinbrook Entrance for laden oil tankers departing Valdez, Alaska? Should the International Safety Management (ISM) code be implemented fleet-wide for the Washington State Ferries in Seattle, or does it make more sense to invest in additional life craft? Can ferry service in San Francisco Bay be expanded in a safe manner to relieve high way congestion? These risk management questions were raised in a series of projects spanning a time frame of more than 10 years. They were addressed using a risk management analysis methodology developed over these years by a consortium of universities. In this paper we shall briefly review this methodology which integrates simulation of Maritime Transportation Systems (MTS) with incident/accident data collection, expert judgment elicitation and a consequence model. We shall describe recent advances with respect to this methodology in more detail. These improvements were made in the context of a two-year oil transportation risk study conducted from 2006?C2008 in the Puget Sound and surrounding waters. An application of this methodology shall be presented comparing the risk reduction effectiveness analysis of a one-way zone, an escorting and a double hull requirement in the same context.     

A graphical bicriteria approach to the resource allocation problem

This paper propses a simple graphical method of solving the resource allocation problem with the objective function being the sum of returns; it is formulated as a bicriteria nonlinear programming problem. The Comparative Trade-Off Method developed by Sadagopan and Ravindran is used as the basis of described method.     

A graphical method for assessing multivariate normality

Summary  In this paper we suggest a simple graphical device for assessing multivariate normality. The method is based on the characteristic that linear combinations of the sample mean and sample covariance matrix are independent if and only if the random variable is normally distributed. We demonstrate the usage of the suggested method and compare it to the classical Q-Q plot by using some multivariate data sets.     

A conjecture on bipartite graphical regular representations

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.     

A graphical method for valuing switching options

This paper introduces a graphical method for valuing options on real asset investments that allow the investor to switch between different operating modes at a single point-in-time. The technique uses mixtures of truncated exponential functions to approximate both the probability density function for project value and the expressions for option value of each alternative. The distribution for project value is transformed into an expected cash flow function for the option under each mode of operation. After determining an optimal exercise strategy, these functions are used to determine the option value. The graphical method allows the option exercise strategy to be communicated effectively through a graphical representation of the expected cash flow functions. A comparison of this approach to the existing binomial lattice method is presented. The efficiency of the graphical method is comparable to the binomial lattice and in some cases accurate solutions can be obtained with less CPU time.     

A new algorithm for decomposition of graphical models

In this paper, we combine Leimer’s algorithm with MCS-M algorithm to decompose graphical models into marginal models on prime blocks. It is shown by experiments that our method has an easier and faster implementation than Leimer’s algorithm.     

A generalization of Rado's Theorem for almost graphical boundaries

In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is ``almost graphical' in some sense, that the surface must be graphical once we move sufficiently far from the boundary.