Sunil Chopra

Designing the distribution network in a supply chain

Abstract This paper describes a framework for designing the distribution network in a supply chain. Various factors influencing the choice of distribution network are described. We then discuss different choices of distribution networks and their relative strengths and weaknesses. The paper concludes by identifying distribution networks that are best suited for a variety of customer and product characteristics.

Minimum cost capacity installation for multicommodity network flows

Consider a directed graphG = (V,A), and a set of traffic demands to be shipped between pairs of nodes inV. Capacity has to be installed on the edges of this graph (in integer multiples of a base unit) so that traffic can be routed. In this paper we consider the problem of minimum cost installation of capacity on the arcs to ensure that the required demands can be shipped simultaneously between node pairs. We study two different approaches for solving problems of this type. The first one is based on the idea of metric inequalities (see Onaga and Kakusho, On feasibility conditions of multicommodity flows in networks, IEEE Transactions on Circuit Theory, CT-18 (4) (1971) 425–429.), and uses a formulation with only |A| variables. The second uses an aggregated multicommodity flow formulation and has |V||A| variables. We first describe two classes of strong valid inequalities and use them to obtain a complete polyhedral description of the associated polyhedron for the complete graph on three nodes. Next we explain our solution methods for both of the approaches in detail and present computational results. Our computational experience shows that the two formulations are comparable and yield effective algorithms for solving real-life problems.

The partition problem

In this paper we describe several forms of thek-partition problem and give integer programming formulations of each case. The dimension of the associated polytopes and some basic facets are identified. We also give several valid and facet defining inequalities for each of the polytopes.

The Steiner tree problem I: formulations, compositions and extension of facets

In this paper we give some integer programming formulations for the Steiner tree problem on undirected and directed graphs and study the associated polyhedra. We give some families of facets for the undirected case along with some compositions and extensions. We also give a projection that relates the Steiner tree polyhedron on an undirected graph to the polyhedron for the corresponding directed graph. This is used to show that the LP-relaxation of the directed formulation is superior to the LP-relaxation of the undirected one.

The Effect of Lead Time Uncertainty on Safety Stocks

The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service-level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.

Solving the Steiner Tree Problem on a Graph Using Branch and Cut

In this paper we report computational experience with a branch and cut solver for the Steimer tree problem on a graph. The problem instances include complete graphs, randomly generated sparse graphs and grid graphs. The edge weights are either randomly generated or are the Euclidean distance between the endnodes that are placed at random on the plane. The effect of changing various problem parameters on solution time is studied. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

On the multiway cut polyhedron

Given a graph G = (V,E) and a set N ⊆ V, we consider the problem of finding a minimum-weight multiway cut that separates each pair of nodes in N. In this paper we give an integer programming formulation of this problem and study the associated polyhedron. We give some computational results to support the strength of our facets. We also give some efficiently solvable instances.

On the spanning tree polyhedron

Fulkerson [4] characterized the blocking matrix to the incidence matrix of all spanning trees of the graph. This paper gives a simple constructive proof of this characterization using a minimum spanning tree algorithm. We also identify all inequalities that are facets.

Five Decades of Operations Management and the Prospects Ahead

Operations and Supply Chains is the current title for a department that has evolved through several different titles in recent years, reflecting its evolving mission from a focus on classical operations research at the time of ORSAs founding 50 years ago toward an embrace of a broader body of theory. Throughout this evolution, the focus on applied problems and the goal of improving practice through the development of suitable theory has remained constant The Operations and Supply Chains Department promotes the theory underlying the practice of operations management, which encompasses the design and management of the transformation processes in manufacturing and service organizations that create value for society. Operations is the function that is uniquely associated with the design and management of these processes. The problem domains of concern to the department have been, and remain, the marshalling of inputs, the transformation itself, and the distribution of outputs in pursuit of this value-creating end. Over the past 50 years the department has had a variety of titles, reflecting an evolving understanding of the boundaries of the operations function. In this article we celebrate past accomplishments, identify current challenges, and anticipate a future that is as exciting and opportunity-rich as any our field has seen.

The Steiner tree problem II: properties and classes of facets

This is the second part of two papers addressing the study of the facial structure of the Steiner tree polyhedron. In this paper we identify several classes of facet defining inequalities and relate them to special classes of graphs on which the Steiner tree problem is known to be NP-hard.