Anito Joseph

Using formal MS/OR modeling to support disaster recovery planning

Abstract All organizations are susceptible to a non-zero risk of experiencing out-of-course events, whether natural or man-made, that can lead to internal “disasters” with respect to business operations. Different types of events (e.g. flood, earthquake, fire, theft, computer failure) have implications for the operations of modern organizations. Hence, there is a critical need for planning and recovery strategies for the effects of disasters. Disaster recovery plans (DRPs) aim at ensuring that organizations can function effectively during and following the occurrence of a disaster. As such, they possess cost, performance, reliability, and complexity characteristics that make their development and selection non-trivial. To date, there has been little modeling of disaster recovery issues in the MS/OR literature. We believe that many of the issues involved can benefit from the application of quantitative decision-making techniques. Consequently, in this paper our contribution is prescriptive rather than descriptive in nature and we propose the use of mathematical modeling as a decision support tool for successful development of a DRP. In arriving at a final DRP, decision-makers must consider a number of options or subplans and select a subset of these subplans for inclusion in the final plan. We present a mathematical programming model which helps the decision maker to select among competing subplans, a subset of subplans which maximizes the “value” of the recovery capability of a recovery strategy. We use hypothetical situations to illustrate how this technique can be used to support the planning process.

Generating consensus priority point vectors: a logarithmic goal programming approach

Abstract The analytic hierarchy process (Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, NewYork: McGraw-Hill 1980) is a popular technique for addressing multiple-criteria decision-making problems (MCDMs). Various techniques have been proposed for using the AHP in group situations. Fundamental to the AHP is the generation of priority point vectors from matrices of pairwise comparison data. In this paper, we present a logarithmic goal programming model for generating the ‘consensus’ priority point vector from the set of individual priority point vectors. Scope and purpose Within modern organizations, multiple-criteria decision-making problems (MCDMs) often occur within a group context, and individual priorities for decision alternatives must be synthesized into a single set of priorities which represents the consensus opinion for the group. This requires a process for aggregating individual priorities into a set of group priorities. In this paper, we examine the use of the analytic hierarchy process (AHP) MCDM technique for the group situation, and present an approach for aggregating individual priorities into a set of group ‘consensus’ priorities.

Generating consensus priority interval vectors for group decision‐making in the AHP

Many practical and important decision-making problems are complicated by at least two factors: (1) the qualitative/subjective nature of some criteria often results in uncertainty in the individual ratings; and (2) group decision-making is involved and some means of aggregating individual ratings is required. Traditionally, both individual and group priorities have been represented as point estimates, but this approach presents severe limitations for accommodating imprecision in the decision-making process. This paper examines the group decision-making problem in the context where priorities are represented as numeric intervals. A set of techniques that could be used at some of the phases of an analytic hierarchy process (AHP)-based group decision-making process, which has the objective of generating a ‘consensus’ priority that represents the groups opinion with regards to the relative importance of a set of N objects (e.g. criteria, alternatives), is presented. Copyright

Generating consensus fuzzy cognitive maps

The Fuzzy Cognitive Maps (FCM) of B. Kosko (1986) are useful tools for exploring the impacts of inputs to fuzzy dynamical systems. The development of an FCM often occurs within a group context because it is felt that the variety of perspectives on the given dynamical system improves the effort to identify the relevant concepts and the causal relationships between the concepts. The assumption is that combining incomplete, conflicting opinions of different experts may cancel out the effects of oversight, ignorance and prejudice. There is also then need to accommodate the inherent fuzziness of the problem. We present an integrated process for rating of the intensity of causal relationships, generating mean FCMs, assessing group consensus, and supporting the building of group consensus.

A concurrent processing framework for the set partitioning problem

A scheme for domain decomposition of the set partitioning problem is presented. Similar to the exploitation of special structure to improve algorithm performance, special structure can be exploited to divide the set partitioning problem into smaller subproblems. Real-world set partitioning problems from the airline industry are used to study the potential advantages of solving multiple subproblems to identify optimal solutions. The results of the study show that the decomposition is especially successful when applied to large problems that are difficult when solved using a single processor. For these cases, decomposition was able to produce smaller problems that, in the majority of cases, were far easier to solve than the original problem. Also, optimal solutions were identified in significantly less time than the time taken to solve the original problem. The results suggest that concurrent processing of subproblems should be investigated as an alternative method for solving large set partitioning problems typically encountered in real-world applications.

Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies

This book represents the results of cross-fertilization between OR/MS and CS/AI. It is this interface of OR/CS that makes possible advances that could not have been achieved in isolation. Taken collectively, these articles are indicative of the state-of-the-art in the interface between OR/MS and CS/AI and of the high caliber of research being conducted by members of the INFORMS Computing Society.

Parametric linear programming and cluster analysis

Abstract In the cluster analysis problem one seeks to partition a finite set of objects into disjoint groups (or clusters) such that each group contains relatively similar objects and, relatively dissimilar objects are placed in different groups. For certain classes of the problem or, under certain assumptions, the partitioning exercise can be formulated as a sequence of linear programs (LPs), each with a parametric objective function. Such LPs can be solved using the parametric linear programming procedure developed by Gass and Saaty [(Gass, S., Saaty, T. (1955), Naval Research Logistics Quarterly 2, 39–45)]. In this paper, a parametric linear programming model for solving cluster analysis problems is presented. We show how this model can be used to find optimal solutions for certain variations of the clustering problem or, in other cases, for an approximation of the general clustering problem.

An objective hyperplane search procedure for solving the general all-integer linear programming (ILP) problem

We describe an objective hyperplane search method for solving a class of integer linear programming (ILP) problems. We formulate the search as a bounded knapsack problem and develop requisite theory for formulating knapsack problems with composite constraints and composite objective functions that facilitate convergence to an ILP solution. A heuristic solution algorithm was developed and used to solve a variety of test problems found in the literature. The method obtains optimal or near-optimal solutions in acceptable ranges of computational effort.

W-efficient partitions and the solution of the sequential clustering problem

Clustering involves partitioning a set of related objects into a set of mutually exclusive and completely exhaustive clusters. The objective is to form clusters which reflect minimum difference among objects as measured by the relevant clustering criterion. Most statements of clustering problems assume that the number of clusters, g, in the partition is known. In reality, a value for g may not be immediately obvious. It is known that as g increases, there is an improvement in the value of the clustering criterion function. However, for some values of g, this rate of improvement may be less than expected. Because there may be a cost factor involved, there is also interest in identifying those values of g that offer attractive rates of improvement. Partitions that are optimal for a given g, and for which the given g offer an attractive rate of improvement, are referred to as being w-efficient; other partitions, even if optimal for a given g, are referred to as being w-inefficient. We present a linear programming approach for generating the w-efficient partitions of the sequential clustering problem, and demonstrate the importance of w-efficient partitions to the efficient solution of the sequential clustering problem.

Parametric formulation of the general integer linear programming problem

A parametric approach to the general integer programming problem is explored. If a solution to the general integer linear programming problem exists, it can be expressed as a convex combination of the extreme points of the convex polytope of the associated linear programming relaxation. The combination may or may not be unique for the convex polytope and will depend on the extreme points used in the determination. Therefore, a heuristic approach to solving the general integer programming problem can be taken by generating extreme points of the convex polytope and reformulating a mixed integer linear programming problem over these extreme points. This approach guarantees a feasible solution in a reasonable time frame. Further, such a technique can be used to provide quick lower bound information for an optimal search procedure.