John M. Mulvey

A New Scenario Decomposition Method for Large-Scale Stochastic Optimization

A novel parallel decomposition algorithm is developed for large, multistage stochastic optimization problems. The method decomposes the problem into subproblems that correspond to scenarios. The subproblems are modified by separable quadratic terms to coordinate the scenario solutions. Convergence of the coordination procedure is proven for linear programs. Subproblems are solved using a nonlinear interior point algorithm. The approach adjusts the degree of decomposition to fit the available hardware environment. Initial testing on a distributed network of workstations shows that an optimal number of computers depends upon the work per subproblem and its relation to the communication capacities. The algorithm has promise for solving stochastic programs that lie outside current capabilities.

Solving capacitated clustering problems

Abstract This paper presents two effective algorithms for clustering n entities into p mutually exclusive and exhaustive groups where the ‘size’ of each group is restricted. As its objective, the clustering model minimizes the sum of distance between each entity and a designated group median. Empirical results using both a primal heuristic and a hybrid heuristic-subgradient method for problems having n ⩽ 100 (i.e. 10 100 binary variables) show that the algorithms locate close to optimal solutions without resorting to tree enumeration. The capacitated clustering model is applied to the problem of sales force territorial design.

Stochastic network optimization models for investment planning

We describe and compare stochastic network optimization models for investment planning under uncertainty. Emphasis is placed on multiperiod a sset allocation and active portfolio management problems. Myopic as well as multiple period models are considered. In the case of multiperiod models, the uncertainty in asset returns filters into the constraint coefficient matrix, yielding a multi-scenario program formulation. Different scenario generation procedures are examined. The use of utility functions to reflect risk bearing attitudes results in nonlinear stochastic network models. We adopt a newly proposed decomposition procedure for solving these multiperiod stochastic programs. The performance of the models in simulations based on historical data is discussed.

Applying the progressive hedging algorithm to stochastic generalized networks

The introduction of uncertainty to mathematical programs greatly increases the size of the resulting optimization problems. Specialized methods that exploit program structures and advances in computer technology promise to overcome the computational complexity of certain classes of stochastic programs. In this paper we examine the progressive hedging algorithm for solving multi-scenario generalized networks. We present computational results demonstrating the effect of various internal tactics on the algorithms performance. Comparisons with alternative solution methods are provided.

Strategic financial risk management and operations research

Abstract Risk management has become a vital topic for financial institutions in the 1990s. Strategically, asset/liability management systems are important tools for controlling a firms financial risks. They manage these risks by dynamically balancing the firms asset and liabilities to achieve the firms objectives. We discuss such leading international firms as Towers Perrin, Frank Russell, and Falcon Asset Management, which apply asset/liability management for efficiently managing risk over extended time periods. Three components of asset/liability management are described: 1) a multi-stage stochastic program for coordinating the asset/liability decisions; 2) a scenario generation procedure for modeling the stochastic parameters; and 3) solution algorithms for solving the resulting large-scale optimization problem.

A diagonal quadratic approximation method for large scale linear programs

An augmented Lagrangian method is proposed for handling the common rows in large scale linear programming problems with block-diagonal structure and linking constraints. Using a diagonal quadratic approximation of the augmented Lagrangian one obtains subproblems that can be readily solved in parallel by a nonlinear primal-dual barrier method for convex separable programs. The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.

On Reporting Computational Experiments with Mathematical Software

Many papers appearing in journals reporting computational experiments use computer generated evidence to compare or rank competing mathematical software techmques. Unfortunately, to date there have been no standards or gmdehnes indicating how computer experiments should be conducted or how the results should be presented. An initial attempt is made to rectify this situation, and a summary of unportant points which should be considered when writing or evaluating a paper m which computational results are reported is provided.

A classroom/time assignment model

Abstract Typically, university classroom space is grossly underutilized as measured by factor such as the number of vacant classroom slots and the percentage of empty seats. This inefficiency is caused, in part, by the propensity of faculty and students to select classes in the prime periods (9 A.M. – 12 and 1 P.M. – 3 P.M.) to the exclusion of alternative time slots. However, another difficulty is the combinatorial size of realistic scheduling problems; most optimization models cannot cope with even example problems. The trend has been to develop pure heuristic techniques. The author has devised a network-based optimizing approach to the classroom/time model which rapidly approximates the solutions. This model combines the insight of the scheduler with combinatorial and searching ability of a computer via a transshipment optimization network model.

An Asset and Liability Management System for Towers Perrin-Tillinghast

Towers Perrin-Tillinghast employs a stochastic asset-and-liability management system for helping its pension plan and insurance clients understand the risks and opportunities related to capital market investments and other major decisions. The system has three major components: (1) a stochastic scenario generator (CAP:Link); (2) a nonlinear optimization simulation model (OPT:Link); and (3) a flexible liability- and financial-reporting module (FIN:Link). Each part improves over existing technology as compared with traditional actuarial approaches. The integrated investment system links asset risks to liabilities so that company goals are best achieved. For example, US WEST saved

Financial planning via multi-stage stochastic optimization

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