MANAGERIAL ECONOMICS & DECISION SCIENCES; OPERATIONS
Interim Dean, Kellogg School of Management
IBM Professor of Operations Management and Information Systems
Sunil Chopra is Interim Dean of the Kellogg School of Management at Northwestern University. He is also the IBM Distinguished Professor of Operations Management. From 2006 – 2009, he served as Senior Associate Dean: Curriculum and Teaching. He became a faculty member of the school in 1989. Previously he was an Assistant Professor at the Stern School of Business Administration at New York University. He has a PhD in Operations Research from SUNY Stony Brook.
Professor Chopra’s research and teaching interests are in Operations Management, Logistics and Distribution Management, design of communication networks and design of distribution networks. He has co-authored the books Managing Business Process Flows and Supply Chain Management: Strategy, Planning, and Operation. Both books are published by Prentice Hall and are used at several of the top business schools to teach Operations Management and Supply Chain Management respectively. The Supply Chain Management book was awarded the best book of the year for 2002 by the Institute of Industrial Engineers (IIE). Professor Chopra has won several teaching awards at Kellogg.
He has been Departmental Editor for the journals Management Science and an Associate Editor for the Decision Sciences Journal, Manufacturing & Service Operations Management and Operations Research. His recent research has focused on risk management in supply chains. He has also studied distribution systems in a variety of companies trying to identify market, manufacturing, and product characteristics that drive the structure of a supply chain.
He has consulted for a variety of firms including Boise Cascade Office Products, GE Capital, W.W. Grainger, Motorola, Intel, and Sara Lee.
Manufacturing
Optimization
Reengineering
Response Time Management
Supply Chain Management and Logistics
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This paper focuses on the importance of decoupling recurrent supply risk and disruption risk when planning appropriate mitigation strategies. We show that bundling the two uncertainties leads a manager to underutilize a reliable source while over utilizing a cheaper but less reliable supplier. As in Dada et al. (working paper, University of Illinois, Champaign, IL, 2003), we show that increasing quantity from a cheaper but less reliable source is an effective risk mitigation strategy if most of the supply risk growth comes from an increase in recurrent uncertainty. In contrast, we show that a firm should order more from a reliable source and less from a cheaper but less reliable source if most of the supply risk growth comes from an increase in disruption probability.
Traditional analysis of managing services has emphasized that services cannot be held in inventory. Consequently, the focus has been operating services in a make-to-order fashion ignoring lessons learned from operating make-to-stock supply chains. We argue that this conventional view is built on a very limited notion of inventory as finished goods. In reality, inventory can be held in partially completed forms that serve to store work. This notion of inventory as a way to store work is valid for both goods and services and provides a novel way to think of designing service processes. In this article, we define service inventory as all process steps that are completed prior to the customer’s arrival. Much like inventories of physical products, service inventories affect how quickly – and at what cost – a firm can fill demand. By leveraging service inventories, companies have the potential to offer greater quality, speed, and variety to its customers at reasonable prices. We discuss how service inventories allow firms to improve service operations, how service inventories interact with other drivers of process performance, and how lessons from conventional supply chain management apply to the management of service inventory.
Operations and Supply Chains is the current title for a department that has evolved through several different titles in recent years, reflecting its eveolving mission from a focus on classical operations research at the time of ORSA's 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 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 Marin (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.
This paper describes a framework for designing the distribution network in a supply chain. Various factors influencing the choice of distribution networks are described.
Focuses on supply chain management processes that affect the enterprise software market. Emergence of extended supply chain management; Different macro processes in supply chain management; Brief description of supplier relationship management.
Network design models with more than one facility type have many applications in communication and distribution problems. Due to their complexity, previous studies have focused on finding good heuristic solutions. In this study, we develop algorithms that solve the multi-level network design problem to optimality. In our approach, the problem is converted to a Steiner tree problem and is solved by a branch-and-cut approach. Our computational study shows that the approach outperforms a dual ascent approach in the literature (Mirchandani, INFORMS J. Comput. 8 (3) (1996) 202) not only on solution times but also on the quality of the solutions.
We analyze a cost allocation problem which could naturally arise from a situation wherein a tree network T = (NU{0}, E), serving heterogeneous customers, has to be constructed. The customers, located at N, require some service from a central supplier, located at vertex 0. The customers have heterogeneous preferences for the level or quality of service received from the central supplier. We formulate the above cost allocation problem as a cooperative game, referred to as an extended tree game. The extended tree game is a proper extension of Megiddo's (1978) tree game, wherein all the customers have identical preferences regarding the level of service received. We prove that an extended tree game is convex, and we show that its Shapley value can be computed in tex-math$\scr{O}(p|N|)$/tex-math time, where p is the number of distinct preference levels. We further provide a complete facial description of the core polytope of an extended tree game, and demonstrate that even when there are only two classes of customers, the number of nonredundant core constraints could be exponential in |N|. Nevertheless, we are able to construct an tex-math$\scr{O}(p|N|)$/tex-math algorithm to check the core membership of an arbitrary cost allocation, which can be used to construct an tex-math$\scr{O}(p|N|^{3})$/tex-math combinatorial algorithm to compute the nucleolus of an extended tree game. Finally, we show that the complements of the facet-defining coalitions for the core are all connected in an auxiliary tree graph with node set N.
The Internet is revolutionizing the way companies conduct business. Or is it? We argue that the value of the internet for a firm is strongly dependent on the firm's industry and on the strategy it pursues. A survey of firms with an online presence displays wide disparities in performance. while Dell has succesfully used the internet to boost revenues and earnings, Amazon lost $585 million on revenues of $1.6 billion in 1999. Firms that fully exploit the revenue enhancements and cost reduction opportunities offered by the interent and optimally integrate e-business with existing channels are likely to be the big winners in the internet age.
Let H = (V, E) be an undirected hypergraph and Asubset of or equal toC. We consider the problem of finding a minimum cost partition of V that separates every pair of nodes in A. We consider three formulations of the problem and show that the theoretical lower bounds to the integer optimal objective value provided by the LP-relaxations in all three cases are identical. We describe our empiical findings with each formulation.
Consider a directed graph G = (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.
We consider the problem of sending flow from a source to a destination where there are flow costs on each arc and fixed costs toward the purchase of capacity. Capacity can be purchased in batches of C units on each arc. We show the problem to be NP-hard in general. If d is the quantity to be shipped from the source to the destination, we give an algorithm that solves the problem in time polynomial in the size of the graph but exponential in [d/C]. Thus, for bounded values of [d/C]the problem can be solved in polynomial time. This is useful since a simple heuristic gives a very good approximation of the optimal solution for large values of [d/C]. We also show a similar result to hold for the case when there are no flow costs but capacity can be purchased either in batches of 1 unit or C units. The results characterizing optimal solutions with a minimum number of free arcs are used to obtain extended formulations in each of the two cases. The LP-relaxations of the extended formulations are shown to be stronger than the natural formulations considered by earlier authors, even with a family of strong valid inequalities added.
Let G=(V, E) be an undirected graph andA⊆V. We consider the problem of finding a minimum cost set of edges whose deletion separates every pair of nodes inA. We consider two extended formulations using both node and edge variables. An edge variable formulation has previously been considered for this problem (Chopra and Rao (1991), Cunningham (1991)). We show that the LP-relaxations of the extended formulations are stronger than the LP-relaxation of the edge variable formulation (even with an extra class of valid inequalities added). This is interesting because, while the LP-relaxations of the extended formulations can be solved in polynomial time, the LP-relaxation of the edge variable formulation cannot. We also give a class of valid inequalities for one of the extended formulations. Computational results using the extended formulations are performed.
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.
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.
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.
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.
We consider ternary matrices, i.e., integer matrices having all entries 0, 1 or 2. Three associated problems—the group problem, covering, and packing—are studied. General classes of vertices and facets are discussed in each case. Certain lifting procedures are also described. For all three problems techniques used are natural extensions of those used in the binary case.
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.
Corresponding to every group problem is a row module. Duality for group problems is developed using the duality or orthogonality of the corresponding row modules. The row module corresponding to a group problem is shown to include Gomory's fractional cuts for the group polyhedron and all the vertices of the polyhedron of the blocking group problem. The polyhedra corresponding to a pair of blocking group problems are shown to have a blocking nature i.e. the vertices of one include some of the facets of the other and mutatis mutandis. The entire development is constructive. The notions of contraction, deletion, expansion and extension are defined constructively and related to homomorphic liftings and suproblems in a dual setting. Roughly speaking a homomorphic lifting is dual to forming a subproblem. A proof of the Gastou-Johnson generalization of Gomory's homomorphic lifting theorem is given, and dual constructions are discussed. A generalization of Gomory's subadditive characterization to subproblems is given. In the binary case, it is closely related to the work of Seymour on cones arising from binary matroids.
In this paper, we extend the concept of chaining introduced by Jordan and Graves (1995) for designing a robust supply chain network in which the link and nodes are susceptible to disruptions. We introduce the concept of fragility to quantify the change in system performance resulting from a disruption. Although one may anticipate that networks with longer chains will be more robust (smaller fragility) than shorter ones, our study reveals that this is not always true. We show that the fragility with respect to a single link failure decreases as the size of the chain decreases; however, the fragility with respect to a single node failure increases as the size of the chain increases. We also show that multiple failures in a network can be decomposed into a set of multiple subnetworks with a single failure; hence we can analyze the impact of large-scale disruptions by studying each single failure networks. Simulation experiments are used to extend insights from single link or node failures to multiple failure cases.
This is the second edition of our 1999 text on operations management.
This is a text book for supply chain management.
The case focuses on the diamond retailing industry toward the end of 2008, with the United States in an economic downturn. All diamond retailers are hit by the downturn and are facing a critical look at their strategies. Given the basic performance information on Blue Nile, Zales, and Tiffany, students are asked to consider the strengths and weaknesses of each business model with the goal of understanding business models that are better suited to handling a downturn.
This case examines a company that rents and leases computers. The primary objective of the case is to provide a scenario where students can see the link between operational flow measures such as inventory, throughput, and flow time and financial flows. The case presents a scenario where a firm sees financial performance worsen even though sales increase. A link between the operational measures and financial flows allows students to understand the causes.
This case can be used to introduce statistical process control (SPC). It looks at the introduction of SPC into a distribution center servicing a department store chain. The case focuses on the receiving process in the distribution center and describes how SPC methodology is introduced. The ideas discussed include run charts, pareto diagrams, and control limits.
This note describes the concept of postponement of product variety and how it may be used to better match supply and demand while lowering inventories. The note discusses situations where postponement is more or less valuable. Several industry examples of postponement are discussed.
Quality Wireless has been receiving customer complaints about long hold times at its call center. To address these complaints it has put into place certain process changes at its call center. After one month, the company wants to make a decision regarding whether improvement has taken place or not. Part (A) uses this context for students to understand the “check” phase of the plan-do-check-act cycle of Deming using basic statistical principles. In Part (B) the manager is gone for ten days and returns to find that performance is not as good as when he left. Yelling at the supervisors results in performance improving over the next ten days. Part (B) allows the instructor to introduce the Statistical Process Control (SPC) framework for students to decide whether the manager’s response was appropriate or not.
Quality Wireless has been receiving customer complaints about long hold times at its call center. To address these complaints it has put into place certain process changes at its call center. After one month, the company wants to make a decision regarding whether improvement has taken place or not. Part (A) uses this context for students to understand the “check” phase of the plan-do-check-act cycle of Deming using basic statistical principles. In Part (B) the manager is gone for ten days and returns to find that performance is not as good as when he left. Yelling at the supervisors results in performance improving over the next ten days. Part (B) allows the instructor to introduce the Statistical Process Control (SPC) framework for students to decide whether the manager’s response was appropriate or not.
The case discusses the structure of the Seven Eleven Japan supply chain in terms of its facilities network, inventory management, distribution, and information. The case can be used to discuss how Seven Eleven has made consistent supply chain choices to support its business strategy of providing convenience to customers. In particular, the case points to how Seven Eleven has used information and aggregation in transportation to improve supply chain responsiveness at relatively low cost.
The case assumes an understanding of statistical process control (SPC) and focuses on highlighting why Six Sigma quality is useful. In particular, it takes the issue of a bearing being worn out at a tire manufacturer leading to a mean shift (while producing defectives). In contrast, it is shown how a Six Sigma process would quickly detect the mean shift while producing hardly any defectives. The case may be used to introduce the methodology of statistical process control but is best used to illustrate the value of Six Sigma after students have understood SPC.
The purpose of this note is to update a person already familiar with third-party logistics companies (3PLs) on issues facing the industry, and also to provide a listing of available resources on the World Wide Web related to 3PLs. We first cover basic concepts about 3PLs, and the benefits and risks of outsourcing logistics functions to these companies. Then we discuss current issues facing 3PLs. Finally, we present a summary of some of the most important 3PL-related sites organized by content.
This note addresses the concept of vendor managed inventories (VMI). It discusses best practices and issues that occur when introducing VMI. It also highlights some of the potential problems that may arise when implementing VMI.
This case addresses how flow times and capacity calculations can be made for a service process such as the Bariatric surgery center at a clinic. This case highlights how these calculations can be made for a service process just as in any manufacturing setting. In the course of the case, students should understand the notion of critical paths and bottlenecks and what factors affect both time and capacity. This understanding is then used to discuss the relative profitability of two types of Bariatric surgery. The goal here is to link product profitability to the process.
In 2003, ITC responded to the high level of obsolete inventory by shifting risk from finished products to manufacturing and raw materials. This required that their supply chain be much more flexible and responsive than it was in the past. By 2006, changes in the supply chain that included moving manufacturing in-house improved flexibility and responsiveness. Obsolete inventory was significantly reduced and the company was much better at matching supply and demand. Cost, however, continued to be higher than that at third parties. The company had to decide on the appropriate tradeoff between cost and responsiveness when structuring its supply chain.
This course counts toward the following majors: Analytical Consulting, Operations, Technology Industry Management.
What are the key capabilities a supply chain must develop to support the business strategy of a firm? What is the relationship between the desired capabilities and the structure of a supply chain? This course provides a framework to answer these questions. We define supply chain structure in terms of the following drivers of performance: facilities, information, inventory and transportation. The relationship between structure and performance is analyzed using various case studies that require students to develop analytical spreadsheet models to support their decision making. Students are taught the strategic role of the supply chain. The course also discusses methodologies for designing and planning a supply chain.
Prerequisites: OPNS-430, MECN-430.
Operations Management examines the basic principles of managing the production and distribution of goods and services. The course approaches operations as a managerial integration function and provides frameworks and tools to target and implement improvements in business processes.
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