David L. Jensen

Plant location with minimum inventory

We present an integer programming model for plant location with inventory costs. The linear programming relaxation has been solved by Dantzig-Wolfe decomposition. In this case the subproblems reduce to the minimum cut problem. We have used subgradient optimization to accelerate the convergence of the D-W algorithm. We present our experience with problems arising in the design of a distribution network for computer spare parts. In most cases, from a fractional solution we were able to derive integer solutions within 4% of optimality.

On the computational behavior of a polynomial-time network flow algorithm

A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined. This algorithm, which scales costs rather than right-hand sides, also runs in polynomial time. Large-scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed. Within several distributions of square, dense, capacitated transportation problems, a cost scaling code, SCALE, exhibits linear growth in average execution time with the number of edges, while two network simplex codes, RNET and GNET, exhibit greater than linear growth.Our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated. Moreover, for fixed problem size, individual execution times appear to behave as though they are approximately lognormally distributed with constant variance. The experiments also reveal sensitivity of the parameters in the models, and in the models themselves, to variations in the distribution of problems. This argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed.

Frontier: a graphical interface for portfolio optimization in a piecewise linear-quadratic risk framework

“Frontier” is a pilot graphical user interface for portfolio optimization built for the new IBM workstation, the RISC System/6000™, out of basic X-windows and OSL utilities. The program asks the user to select a piecewise linear-quadratic risk measure, draws a risk/reward efficient frontier, and permits the user to examine the efficient frontier using zoom and histogram display facilities. This paper describes the interfaces and discusses possible extensions.

Optimizing debt collections using constrained reinforcement learning

The problem of optimally managing the collections process by taxation authorities is one of prime importance, not only for the revenue it brings but also as a means to administer a fair taxing system. The analogous problem of debt collections management in the private sector, such as banks and credit card companies, is also increasingly gaining attention. With the recent successes in the applications of data analytics and optimization to various business areas, the question arises to what extent such collections processes can be improved by use of leading edge data modeling and optimization techniques. In this paper, we propose and develop a novel approach to this problem based on the framework of constrained Markov Decision Process (MDP), and report on our experience in an actual deployment of a tax collections optimization system at New York State Department of Taxation and Finance (NYS DTF).

The convergence of a modified barrier method for convex programming

We show, using elementary considerations, that a modified barrier function method for the solution of convex programming problems converges for any fixed positive setting of the barrier parameter. With mild conditions on the primal and dual feasible regions, we show how to use the modified barrier function method to obtain primal and dual optimal solutions, even in the presence of degeneracy. We illustrate the argument for convergence in the case of linear programming, and then generalize it to the convex programming case.

A decomposition method for quadratic programming

We discuss the algorithms used in the Optimization Subroutine Library for the solution of convex quadratic programming problems. The basic simplex algorithm for convex quadratic programming is described. We then show how the simplex method for linear programming can be used in a decomposition crash procedure to obtain a good initial basic solution for the quadratic programming algorithm. We show how this solution may be used as a starting solution for the simplex-based algorithm. Besides its ability to obtain good starting solutions, this procedure has several additional properties. It can be used directly to find an optimal solution to a quadratic program instead of simply finding a good initial solution; it provides both upper and lower bounds on the objective function value as the algorithm proceeds; it reduces the complexity of intermediate calculations; it avoids certain numerical difficulties that arise in quadratic, but not linear programming

Building business intelligence applications having prescriptive and predictive capabilities

Traditional Business Intelligence applications have focused on providing a one shop stop to integrate the enterprise information. The resulting applications are only capable of providing descriptive information viz: standard and ad-hoc reporting and drill-down capability. As part of an effort to provide prescriptive and predictive capability, we demonstrate a new architecture, methodology and implementation. Based on Cognos Business Intelligence platform and ILOG optimization engine, we showcase a truly predictive application that enables an optimal decision making in real-time analytical scenario.

Polyhedra of regular p -nary group problems

The duality for group problems developed in [3] is restricted top-nary group problems. Results for ternary group problems are obtained similar to those obtained by Fulkerson and Lehman for the binary case. A complete facet description of the group polyhedron is available for a group problem having the Fulkerson property. A group problem has the Fulkerson property if its vertices are the facets of the blocking group problem and if its facets are the vertices of the blocking group problem. The Fulkerson property is a generalization of the max-flow min-cut theorem of Ford and Fulkerson which is interpreted as a statement about the pair of row modules arising from a group problem. We show that a group problem has the Fulkerson property if the corresponding row module is regular.