Jonathan H. Owen

General Motors Increases Its Production Throughput

In the late 1980s, General Motors Corporation (GM) initiated a long-term project to predict and improve the throughput performance of its production lines to increase productivity throughout its manufacturing operations and provide GM with a strategic competitive advantage. GM quantified throughput performance and focused improvement efforts in the design and operations of its manufacturing systems through coordinated activities in three areas: (1) it developed algorithms for estimating throughput performance, identifying bottlenecks, and optimizing buffer allocation, (2) it installed real-time plant-floor data-collection systems to support the algorithms, and (3) it established common processes for identifying opportunities and implementing performance improvements. Through these activities, GM has increased revenue and saved over 2.1 billion in over 30 vehicle plants and 10 countries.

On the Value of Binary Expansions for General Mixed-Integer Linear Programs

We study the use of binary variables in reformulating general mixed-integer linear programs. We show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching. We also give computational results on the performance of such reformulations in solving the mixed-integer programs, which support our theoretical results.

A disjunctive cutting plane procedure for general mixed-integer linear programs

Abstract.In this paper we develop a cutting plane algorithm for solving mixed-integer linear programs with general-integer variables. A novel feature of the algorithm is that it generates inequalities at all γ-optimal vertices of the LP-relaxation at each iteration. The cutting planes generated in the procedure are found by considering a natural generalization of the 0-1 disjunction used by Balas, Ceria, and Cornuéjols in the context of solving binary mixed-integer linear programs [3, 4].

Experimental Results on Using General Disjunctions in Branch-and-Bound for General-Integer Linear Programs

Typical implementations of branch-and-bound for integer linear programs choose to branch on single variables. In this paper we explore the use of general disjunctions for branching when solving linear programs with general-integer variables. We give computational results that show that the size of the enumeration tree can be greatly reduced by branching on such disjunctions rather than on single variables.

Effects of operating speed on production quality and throughput

A key determinant of a manufacturing systems performance is its operating speed. While it is generally assumed that overall production throughput increases with operating speed, this is not necessarily the case where quality deteriorates as a result of the higher speed. In this paper we derive a representative quality–speed relationship and examine the productivity implications. We develop models to capture the effects of rework, repair, and scrap on system throughput and illustrate the resulting trade-off between higher productivity and the need for additional processing. Empirical evidence is also presented to motivate the work.

Extended formulations for the A-cut problem

LetG=(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.

Local improvements that degrade system performance: case studies and discussion for throughput analysis

Much of our intuition about production system performance dynamics is grounded in an understanding of simple serial lines. For this reason, practitioners tend to rely on concepts and principles that have successfully guided the design and improvement of these lines, even in the analysis of significantly more complex systems. Based on this intuition, there is a natural tendency to believe that improving any specific feature of a system will result in comparable or improved overall performance. Unfortunately, this is not always the case. In this paper, we present three case study examples which demonstrate that local improvements to station speed or buffer capacity can result in an overall degradation of system performance for non-serial production systems.

A note on formulations for the A -partition problem on hypergraphs

Let H = (V, E) be an undirected hypergraph and A⊆C. 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.

Practical Modeling in Automotive Production

We all want to make a difference. We all want our work to enrich the world. As production planners, we have a great opportunity. Since the industrial revolution, production planning has enabled industry to extract the most from the era’s manufacturing technology. Henry Ford’s assembly line, with its associated production planning, dramatically improved production efficiency. While production planning continues to advance productivity thereby enhancing society’s prosperity and quality of life, the benefits from production systems modeling are often not realized in practice. As noted by the editors, there is a widening gap between research and the needs of industry. The cause is not that the models are not sophisticated enough to capture the complexities of the real world. Neither is it that there is a lack of technology transfer. From our experience in industry, the gap arises from underdeveloped modeling. Underdeveloped modeling is diverting us from making a bigger difference. To impact production, we need models that can be put into practice. Not necessarily simple, but actionable. If a firm cannot act on a model, the model (and its associated solution methodologies) will not enhance the firm’s performance. The authors admit to straying from this advice themselves. But we have learned that models implemented gratify the most. Therefore, we propose that the most fruitful future research direction is practical modeling.

Optimizing New-Vehicle Inventory at General Motors

This paper describes how General Motors (GM) uses operations research to optimize its new-vehicle inventory. The solution answers two complementary questions: (1) what is the optimal number of vehicles to build? and (2) what are the optimal vehicle configurations? To answer the first question, for each vehicle model, we find the inventory that maximizes profit less inventory carrying costs, which differs from the standard approach of finding the inventory needed to satisfy a given fill rate. To answer the second question, we provide a decision support tool to help dealers order the best variations for each vehicle model using a set-covering philosophy, which differs from the standard approach of recommending the highest-selling variants. This paper describes the business processes surrounding these decisions, how the need for implementation and ongoing use guided our solution development, and the impact on the business.