Brenda L. Dietrich

Resource planning for business services

Over the past several decades mathematical models of supply chains have been developed and used for resource planning. Significant gains in supply chain efficiency have been attributed to the use of such models, together with the supporting IT infrastructure. Manufacturing resource planning (MRP), which automated the calculations of material requirements within manufacturing, evolved into enterprise resource planning (ERP), which monitors manufacturing enterprise processes and provides an information base for mathematically based advanced planning.

Efficient reformulation for 0-1 programs: methods and computational results

Abstract We introduce two general methods for 0–1 program reformulation. Our first method generalizes coefficient reduction, our second method generalizes lifting. Together they provide a unifying interpretation of many previously described automatic reformulation methods. The particular model structures that we consider are individual knapsack constraints, pairs of knapsack constraints, clique and cover induced inequalities, variable upper bounding constraints and capacity expansion constraints. We describe several easy applications of our reformulation procedures. Some computational experience is reported, including the currently best known results on a well-known 147 × 2655 benchmark problem.

A circuit set characterization of antimatroids

Abstract Antimatroids generalize the notion of convexity in much the same way as matroids generalize the notion of linear dependence. Definitions and examples of antimatroids are presented. Rooted circuits of anitmatroids are defined, and a new characterization of antimatroids is given. This characterization involves a rooted circuit elimination property that is reminiscent of the matroid circuit elimination property.

Matroids and antimatroids—a survey

Similarities and differences between matroids (abstract dependence systems) and antimatroids (abstract convexity systems) are discussed and several analogous characterizations of these structures are compared. While both structures are subclasses of greedoids and arise (in different ways) from common structures (e.g. graphs, finite collections of points in R n ), no relation analogous to matroid duality exists for antimatroids.

On greedy algorithms, partially ordered sets, and submodular functions

Recent developments in the use of greedy algorithms in linear programming are reviewed and extended. We find a common generalization of some theorems of Queyranne–Spieksma– Tardella, Faigle–Kern, and Fujishige about greedy algorithms for linear programs in diverse contexts. Additionally, we extend a well-known theorem of Topkis about submodular functions on the product of chains to submodular functions on the product of lattices.

Monge sequences, antimatroids, and the transportation problem with forbidden arcs

Abstract This paper considers the transportation problem, both in the standard form and in the case where flow is prohibited on some arcs. We review the celebrated Monge sequence result for the standard problem, give an antimatroid interpretation of an algorithm for constructing Monge sequences or determining that none exist, and extend this algorithm and the antimatroid interpretation to include the case of forbidden arcs.

Order selection on a single machine with high set-up costs

We study the problem of allocating a limited quantity of a single manufacturing resource to produce a subset of possible part-types. Customer orders require one or more part-types. We assume that revenue is received for an order only if it is completely filled, and that set-up costs and order revenues dominate the variable costs of production. We present a heuristic for the solution of our problem, as well as families of cutting-planes for an integer programming formulation. Computational results on a set of random test problems indicate that the heuristic is quite effective in producing near optimal solutions. The cutting-planes appear to be quite useful in reducing the number of linear programming solutions required by branch-and-bound.

An abstract duality

Abstract We present a notion of abstract duality that provides a common characterization of several combinatorial dualities, as well as the orthogonality relation on vector spaces coordinatized over fields having no nontrivial involutory automorphism.

Business leadership through analytics

Weak economic growth, increasing business complexity, and intensifying competition are among the motivations for the growing use of analytics across organizations of all types. In this business environment, enterprise leadership requires new tools and new insights to make better decisions. While analytic techniques, no matter how primitive, have been used to improve the effectiveness and efficiency of organizations for decades, if not centuries, capability and sophistication are now growing rapidly. Advanced analytics is proving to be a transformational technology for businesses, providing a source of competitive advantage and delivering significant, measurable outcomes. Risk management, sales-force productivity, workforce optimization, enterprise planning, and market intelligence are a few examples of core business processes that have significantly benefited from emerging analytical methodologies. As analytic tools used to transform business processes are integrated into enterprise IT (information technology) systems for use by senior business leaders, they are driving new innovations to address the size, speed, and complexity issues faced by large, global enterprises. This position paper explores emerging trends in the leadership application of analytics in global business organizations.

The Promise of Information Technology in the Travel Industry

Two words best characterize the future for the travel industry: growth and change. Many global forces have driven companies in this industry to adapt quickly to survive and remain competitive. Information technology plays a vital role in the way the travel industry responds as the world is “getting connected” at almost every level. The purpose of this paper is three-fold. First, the effect of network computing, the combination of electronic ticketing and smart cards, corporate travel management systems, and other trends that are transforming the travel industry will be examined. Second, the public policy issues involved such as the liberalization of government regulations, affordability and ease-of-use, and data security and privacy will be examined. Finally, the future direction of underlying technologies such as displays, storage, and microprocessors and advancements in the global networking infrastructure, mobility, and speech recognition will be presented.