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This paper presents a computationally efficient neuro-dynamic programming approximation method for the capacitated re-entrant line scheduling problem by reducing the number of feature functions. The method is based on a statistical assessment of the significance of the various feature functions. This assessment can be made by combining the weighted principal components with a thresholding algorithm. The efficacy of the new feature functions selected is tested by numerical experiments. The results indicate that the feature selection method presented here can extract a small number of significant features with the potential capability of providing a compact representation of the target value function in a neuro-dynamic programming framework. Moreover, the linear parametric architecture considered holds considerable promise as a way to provide effective and computationally efficient approximations for an optimal scheduling policy that consistently outperforms the heuristics typically employed. [ABSTRACT FROM AUTHOR]

This paper considers disassembly sequencing problems subjected to sequence dependent disassembly costs. In practice, the methods for dealing with such problems rely mainly on metaheuristic and heuristic methods, which intrinsically generate suboptimum solutions. Exact methods are NP-hard and therefore unsuitable to most of the practical problems. Nevertheless, it is useful to have exact methods available that can be applied in order to check, at least medium sized problems, to what extent the heuristically obtained solutions deviate from the optimum solution. The existing exact approaches, which are based on integer linear programming (ILP), become unmanageable, even for the cases of modest product complexity. To alleviate this problem to some extent, the iterative method that has been proposed by Lambert (2006) is applied here. This method is based on repeatedly solving a binary integer linear programming (BILP) problem instead of an ILP problem. The method appears to converge sufficiently quickly to be valuable for dealing with medium sized problems. We then use the iterative method for the validation of a new heuristic method that is also proposed in this paper. Finally, both the heuristic and the iterative BILP methods are implemented on a cellphone from practice consisting of 25 components that are represented, according to a set of precedence relationships, via a disassembly precedence graph. [ABSTRACT FROM AUTHOR]

Academicians and practitioners were surveyed as to what should be taught in the introductory Production Operations Management (POM) course. Study results indicate practitioners feel that the course should be more "concept" than "technique" oriented, while academicians feel that the mix should be more evenly split. Findings are discussed in terms of their implications for curriculum design. [ABSTRACT FROM AUTHOR]

The liaison between science and management, which has made terms such as linear programming and statistical decision theory part of the business vocabulary, is now being extended in this country and abroad to open new horizons for business and the scientist. Here is a quick roundup of developments to date and a look into the future. [ABSTRACT FROM AUTHOR]

Presenting an integrated lotsizing, loading, and scheduling model for the capacitated flexible flow shops with sequence-dependent setups is the main contribution of this paper. An exact formulation of the problem is provided as a mixed integer program. To solve this problem, mixed integer programming-based heuristics based on iterative procedures are provided. To test the accuracy of heuristics, two lower bounds are developed and compared against the optimal solution. The trade-offs between solution quality and computational time of heuristics are also provided. [ABSTRACT FROM AUTHOR]

This paper gives a modified PRP method which possesses the global convergence of nonconvex function and the R-linear convergence rate of uniformly convex function. Furthermore, the presented method has sufficiently descent property and characteristic of automatically being in a trust region without carrying out any line search technique. Numerical results indicate that the new method is interesting for the given test problems. [ABSTRACT FROM AUTHOR]

Abstract: In this work we present an outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery. The model relies on a continuous time representation making use of transfer events. The proposed algorithm focuses on effectively solving a mixed-integer linear programming (MILP) relaxation of the nonconvex MINLP to obtain a rigorous lower bound (LB) on the global optimum. Cutting planes derived by spatially decomposing the network are added to the MILP relaxation of the original nonconvex MINLP in order to reduce the solution time for the MILP relaxation. The solution of this relaxation is used as a heuristic to obtain a feasible solution to the MINLP which serves as an upper bound (UB). The lower and upper bounds are made to converge to within a specified tolerance in the proposed outer-approximation algorithm. On applying the proposed technique to test examples, significant savings are realized in the computational effort required to obtain provably global optimal solutions. [Copyright &y& Elsevier]

Composite indicators (CIs) are often used for benchmarking countries' performance, but they frequently stir controversies about the unavoidable subjectivity in their construction. Data Envelopment Analysis helps to overcome some key limitations, as it does not need any prior information on either the normalization of sub-indicators or on an agreed unique set of weights. Still, subjective decisions remain, and such modelling uncertainty propagates onto countries' CI scores and rankings. Uncertainty and sensitivity analysis are therefore needed to assess the robustness of the final outcome and to analyse how much each source of uncertainty contributes to the output variance. The current paper reports on these issues, using the Technology Achievement Index as an illustration. [ABSTRACT FROM AUTHOR]

First-year students entering the College of Arts & Sciences at Bucknell University (USA) are required to enroll in a first-year experience course called a foundation seminar during their first semester. A few months before arriving at Bucknell, students submit a prioritized list of foundation seminars of interest to them, given course descriptions of all available foundation seminar sections. Then, based on capacity and scheduling constraints, each student is assigned to a particular seminar. Currently, this assignment of students to specific seminars is carried out using both manual and heuristic methods. We propose to apply an optimization methodology to this interesting real-world problem in an attempt to determine assignments that better satisfy the highest preferences of entering first-year students. [ABSTRACT FROM AUTHOR]

Traditional sensitivity analysis in linear programming usually focuses on variations of one coefficient or term at a time. The tolerance approach was proposed to provide a decision maker with an effective and easy-to-use method to summarize the effects of simultaneous and independent changes in selected parameters. In particular, for variations of the objective function coefficients, the approach gives a maximum-tolerance percentage within which selected coefficients may vary from their estimated values (within a priori limits) while still retaining the same optimal basic feasible solution. Although an optimal solution may cease being optimal for variations beyond the maximum-tolerance percentage, it may still be close to optimal. Herein we characterize the potential loss of optimality for variations beyond the maximum-tolerance percentage as a maximum-regret function. We consider theoretical properties of this function and propose a method to compute a relevant portion of it. [ABSTRACT FROM AUTHOR]

Motivated by applications in freight handling and open-pit mining, Rhys, Balinski, and Picard studied the problems of selection and closure in papers published in Management Science in 1970 and 1976. They identified efficient algorithms based on linear programming and maximum-flow/minimum-cut procedures to solve these problems. This research has had major impact well beyond the initial applications, reaching across three decades and inspiring work on numerous applications and extensions. The extensions are nontrivial optimization problems that are of theoretical interest. The applications ranged from evolving technologies, image segmentation, revealed preferences, pricing, adjusting utilities for consistencies, just-in-time production, solving certain integer programs in polynomial time, and providing efficient 2-approximation algorithms for a wide variety of hard problems. A recent generalization to a convex objective function has even produced novel solutions to prediction and Bayesian estimation problems. This paper surveys the streams of research stimulated by these papers as an example of the impact of Management Science on the optimization field and an illustration of the far-reaching implications of good original research. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design of dynamic server assignment policies that maximize the capacity of queueing networks with flexible servers. Flexibility here means that each server may be capable of performing service at several different classes. We assume that the interarrival times and the service times are independent and identically distributed, and that routing is probabilistic. We also allow for server switching times, which we assume to be independent and identically distributed. We deduce the value of a tight upper bound on the achievable capacity by equating the capacity of the queueing network model with that of a limiting deterministic fluid model. The maximal capacity of the deterministic model is given by the solution to a linear programming problem that also provides optimal allocations of servers to classes. We construct particular server assignment policies, called generalized round-robin policies, that guarantee that the capacity of the queueing network will be arbitrarily close to the computed upper bound. The performance of such policies is studied using numerical examples. [ABSTRACT FROM AUTHOR]

The Traveling Salesman Problem (TSP), well known to operations research enthusiasts, is one of the most challenging combinatorial optimization problems. In this article, the authors present one approach to solving a classic TSP through a special purpose linear programming model, zero-one programming, and Microsoft Excel©Solver. [ABSTRACT FROM AUTHOR]

Linear programming (LP) is one of the great successes to emerge from operations research and management science. It is well developed and widely used. LP problems in practice are often based on numerical data that represent rough approximations of quantities that are inherently difficult to estimate. Because of this, most LP-based studies include a post-optimality investigation of how a change in the data changes the solution. Researchers routinely undertake this type of sensitivity analysis (SA), and most commercial packages for solving linear programs include the results of such an analysis as part of the standard output report. SA has shortcomings that run contrary to conventional wisdom. Alternate models address these shortcomings. [ABSTRACT FROM AUTHOR]

This paper describes a research strategy and its results, which guided a 40+ year collaboration between Abraham Charnes and William W. Cooper, which was initiated in a research center established at the (then) new Graduate School of Industrial Administration at Carnegie Institute of Technology (now Carnegie Mellon University). Initiated in collaboration with Bob Mellon of Gulf Oil Company, this strategy involved on-site collaborations with company personnel in more than 100 different companies and government agencies. An appendix to this paper describes the efforts of another team working from the same research center. This team, consisting of Charles Holt, Franco Modigliani, John Muth, and Herbert A. Simon, used a different research strategy with an accompanying application that also had important impacts on operations research/management science and other disciplines. [ABSTRACT FROM AUTHOR]

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This paper proposes a class of surrogate constraint heuristics for obtaining approximate, near optimal solutions to integer programming problems. These heuristics are based on a simple framework that illuminates the character of several earlier heuristic proposals and provides a variety of new alternatives. The paper also proposes additional heuristics that can be used either to supplement the surrogate constraint procedures or to provide independent solution strategies. Preliminary computational results are reported for applying one of these alternatives to a class of nonlinear generalized set covering problems involving approximately 100 constraints and 300-500 integer variables. The solutions obtained by the tested procedure had objective function values twice as good as values obtained by standard approaches (e.g., reducing the best objective function values of other methods from 85 to 40 on the average. Total solution time for the tested procedure ranged from ten to twenty seconds on the CDC 6600. [ABSTRACT FROM AUTHOR]

The Covering Tour Problem (CTP) is defined on a graph G = (V ∪ W, E), where W is a set of vertices that must be covered. The CTP consists of determining a minimum length Hamiltonian cycle on a subset of V such that every vertex of W is within a prespecified distance from the cycle. The problem is first formulated as an integer linear program, polyhedral properties of several classes of constraints are investigated, and an exact branch-and-cut algorithm is developed. A heuristic is also described. Extensive computational results are presented. [ABSTRACT FROM AUTHOR]

We study a class of models, known as overlay optimization problems, composed of "base" and "overlay" subproblems, linked by the requirement that the overlay solution be contained in the base solution. In some telecommunication settings, a feasible base solution is a spanning tree, and the overlay solution is an embedded Steiner tree or path. For the general overlay optimization problem, we describe a composite heuristic solution procedure that selects the better of two feasible solutions obtained by independently solving the base and the overlay subproblems, and establish worst-case performance guarantees (as a function of the worst-case bounds for the subproblems) for the composite heuristic as well as an LP relaxation of the model. For certain special cases, both the heuristic and the LP relaxation have a worst-case bound of 4/3. We extend this analysis to multiple overlays on the same base solution, producing the first known worst-case bounds (approximately proportional to the square root of the number of commodities) for the uncapacitated multicommodity network design problem. In a companion paper, we develop heuristic performance guarantees for various new multi-tier, survivable network design models that incorporate both multiple facility types and differential node connectivity levels. [ABSTRACT FROM AUTHOR]

Assessing the efficiency of organizational units has long been recognized as an important management problem but an extremely difficult one to solve, especially when one considers the multiplicity of resources and services or products associated with these units operating in a variety of industries. Data Envelopment Analysis (DEA), a promising approach for addressing this problem, is extended in this paper. The proposed extension, called Constrained Facet Analysis (CFA), provides a lower bound efficiency measure for organizational units that have a mix of resources and/or outputs that is different from any frontier point. In addition, CFA yields marginal rates of productivity and substitution associated with the lower bound efficiency measure. This lower bound analysis, combined with the upper bound efficiency analysis provided by the DEA, broadens the applicability of the DEA theory and methodology. [ABSTRACT FROM AUTHOR]

An existing analysis of the bounds on the Weber problem solution under uncertainty is incorrect. For the generalized problem with arbitrary measures of distance, we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found with little computational effort. Numerical examples illustrate the analysis. [ABSTRACT FROM AUTHOR]

The National Coal Model is a highly disaggregate model of domestic coal supply and demand markets. The model has been extensively and successfully applied, but its linear programming component is computationally burdensome. In this paper we report computational results from experiments to reduce solution time through decomposition. The model is decomposed into two capacitated pure networks: a supply side, whose units of flow are Btus of coal; and a demand side, whose units of flow are megawatts of electrical generation capacity. The method used tor integrating these components is a market equilibration ("cobweb") algorithm. The mechanism is not generally convergent, but it produces an excellent starting basis for completion by standard linear programming methods. Order of magnitude solution time reductions have been achieved by the combined procedure. A new decomposition algorithm tor linear programs is presented. The method is motivated by the present application, but has not been implemented. [ABSTRACT FROM AUTHOR]

In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have, in general, not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on potynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research. [ABSTRACT FROM AUTHOR]

A new approach to the one-dimensional cutting stock problem is described and compared to the classical model for which Gilmore and Gomory have developed a special column-generation technique. The new model is characterized by a dynamic use of simply structured cutting patterns. Nevertheless, it enables the representation of complex combinations of cuts. It can be advantageous in practical applications where many different stock lengths or a relatively large number of order lengths have to be dealt with. The new approach is applied to a real problem where the "trim loss" is not valueless, since it can be used for further demands arising in later planning periods. [ABSTRACT FROM AUTHOR]

One commonly employed branch-and-bound approach to 0-1 mixed-integer programming problems is to use bounds obtained from the Benders' partitioning of the problem as a device to restrict the enumeration. We investigate the strength of such bounds through the development of a Geoffrion-type strongest surrogate constraint for the Benders' problems. We show that such a surrogate constraint can be developed for the complete Benders' integer problem without explicit enumeration of any of the extreme-point constraints. The bound obtained from this surrogate constraint is then shown to be as strong as that obtained from any of the more common Benders-based approaches, but yet exactly equal to the bound obtained from the linear relaxation of the original mixed-integer program. [ABSTRACT FROM AUTHOR]

Because of the difficulties often experienced in formulating and understanding large-scale models, much current research is directed towards developing systems to support the construction and understanding of management science models. This paper discusses eight different methods for representing linear programming models during the formulation phase. The approaches discussed are matrix generators, block-schematic and algebraic languages, three different kinds of graphical schemes, a database-oriented approach and Structured Modeling. While these eight approaches do not cover the entire spectrum of possible representation schemes, they are representative of past and current approaches to developing interfaces for large-scale linear programming systems. The different model representation schemes are compared using a common example and the transformations that allow one to change from one representation to another are discussed. [ABSTRACT FROM AUTHOR]

We present an algorithm for a mixed set covering/partitioning model that includes as special cases the well-known set covering problem and set partitioning problem. The novel feature of our algorithm is the use of continuous heuristics applied to the dual of the linear programming relaxation to provide lower bounds for a branch and bound algorithm. The heuristics are continuous adaptations of the well-known greedy and 3-opt methods that have been applied to a variety of combinatorial optimization problems. Our algorithm has outperformed the current best set covering algorithm of Balas and Ho (1980) by about a factor of 3, and appears to improve on the best existing set partitioning algorithm by more than an order of magnitude. [ABSTRACT FROM AUTHOR]

This paper discusses the selection and design of heuristic procedures for solving one-dimensional roll trim problems. These are well-defined combinatorial problems which are too large to optimize. Five different roll trim problems from the paper and film industries are described along with the heuristic procedures that have been used successfully to improve the quality of the solutions generated. The paper concludes with some general guidelines for developing "industrial-grade" heuristic problem solving procedures. [ABSTRACT FROM AUTHOR]

An embedded network within a linear program is, roughly speaking, a subset of constraints that represent conservation of flow. We examine three broad classes of heuristic techniques-row-scanning deletion, column-scanning deletion, and row-scanning addition--for the extraction of large embedded networks. We present a variety of implementations, and compare their performance on realistic test problems. The success of our tests depends, in part, on several preprocessing steps that scale the constraint matrix and that ser aside certain rows and columns. Efficiency of the subsequent network extraction is dependent on the implementation, in predictable ways. Effectiveness is harder to exphin; the more sophisticated and expensive implementations seem to be most reliable, but much simpler implementations sometimes find larger networks. The largest networks are obtained by applying a final augmentation phase, which is studied in the second part of this paper. [ABSTRACT FROM AUTHOR]

In the scheduling situation considered here, we are given a set of routes, each associated with a particular school. A single bus is assigned to each route, picking up the students and arriving at their school within a specified time window. The scheduling problem is to find the fewest buses needed to cover all the routes while meeting the time window specifications. We present two integer programming formulations of the scheduling problem and apply them to actual data from New Haven, Connecticut for two different years, as well as to 30 randomly generated problems. Linear programming relaxations of these integer programs were found to produce integer solutions more than 75 percent of the time. In the remaining cases, we found that the few fractional values can be adjusted to integer values without increasing the number of buses needed. Our method reduces the number of buses needed by about 25 percent compared to the manual solutions developed by the New Haven school bus scheduler. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to apply a generalized version of the Farrell measure of technical efficiency to a sample of Illinois strip mines. We disaggregate the original Farrell measure (which was designed to measure lost output or wasted inputs due to underutilization of inputs) into three mutually exclusive and exhaustive components: (1) a measure of purely technical efficiency, (2) a measure of input congestion (overutilization of some input(s)), and (3) a measure of scale efficiency. This approach has the advantage that it provides additional information on the sources of inefficiency of production, which should be useful to managers, in general, not only in strip mining. Simple linear programming techniques are derived and used in calculating these efficiency measures for our sample. We final that Illinois strip mines are fairly efficient (relative to each other). The major source of inefficiency was due to deviations from the optimal scale of production. We also find suggestive evidence that inefficient mines tend to have relatively high stripping ratios, high labor-output ratios, single rather than multiple coal seams, and lower earth-moving capacity. [ABSTRACT FROM AUTHOR]

We give a worst-case analysis for two greedy heuristics for the integer programming problem minimize cx, Ax ≥ b, 0 ≤ x ≤ U, x integer, where the entries in A, b, and c are all nonnegative. The first heuristic is for the case where the entries in A and b are integral, the second only assumes the rows are scaled so that the smallest nonzero entry is at least 1. In both cases we compare the ratio of the value of the greedy solution to that of the integer optimal. The error bound grows logarithmically in the maximum column sum of A for both heuristics. [ABSTRACT FROM AUTHOR]

This article presents the author's comments on contributions made by the journal "Interfaces" in the field of management science and operations research (MS/OR). Every discipline follows, more or less, the same life cycle. First, initial discoveries focus attention on the subject. Initially, the first discoveries in linear programming and stochastic processes defined MS/OR. New ideas diffused into such activities as operations analysis and planning, corporate planning, marketing, and finance; into various sectors including business, health care, the military, and civilian government; and such subjects as computer science, engineering, sociology, and economics. The diffusion is so complete that many practitioners of MS/OR do not identify with the field at all. Under the strong leadership of Gary Lilien, Interfaces has prospered, gaining respect and broadening our understanding that successful practice goes beyond cost savings. He has encouraged more articles outside the area of operations management, covering such areas as the Turkish housing problem, risk management in transporting hazardous materials, and the use of models in the federal government. Gary has emphasized the point that successful implementation can be measured by more than just cost savings.

The article discusses the popularization of management science in China as of March 1986. Since the early sixties, China has been applying mathematical methods to production and planning problems in an environment where qualified personnel are scarce and where computers are not readily available. Popularization of mathematical methods has provided a way to extend the application and impact of management science in China. The optimization offers some of the most appropriate techniques for application at the level of the production facility. The problems that were faced in applying optimization methods in China were the relatively low level of education of the average worker and the lack of computational facilities for methods that require large amounts of calculation, such as linear and dynamic programming. Such problems often involve the optimization of an unknown continuous function, with a single maximum or minimum. These problems are therefore well suited for solution by trial optimization methods, many of which do not require complex calculations and which are also easy to popularize.

This article compares the performance of microcomputers in solving nonlinear programming test problems with that of a mainframe computer. Interest in the use of microcomputers in MS/OR has increased significantly over the past few years. So much in fact that microcomputers will likely be one of the major technological impacts upon the profession over the next five to 10 years. Microcomputers, along with corresponding advances in computer networking, provide alternatives to traditional centralized computing facilities. With proper equipment selection and implementation, processing can be placed closer to the user. Perhaps more important than the new options available to existing users is the opportunity to expand the realm of MS/OR practice to a new group of users. Traditionally the use of MS/OR has required substantial computer resources. This has created an entry barrier for small to medium organizations. The problems of obtaining and managing the data and computer resources still remain, but the approach is now technically feasible.

This article focuses on the operations research models, which are designed to support business applications, and can be measured in terms of insights that management gains from using models. Management, to cut costs, wanted to reduce the number of janitors in a particular building. Researchers discovered that the janitors' contract included job specifications that were "linear," for example, mopping 1,000 square feet would require 2 hours, mopping 2,000 square feet would require 4 hours, and so forth. They asked the building occupants for their perceptions on the utility of all the tasks the janitors performed. This led to two linear programming formulations. The first maximized the occupants' utility subject to constraints on the number of janitors and, in effect, yielded a task list for the janitors. The second formulation minimized the number of janitors subject to a constraint on the level of utility. Management virtually ignored both formulations. What they did not ignore were the insights gained from doing the analysis. This was the first time the building occupants had said what janitorial functions were important to them.

The article deals with the application of linear programming in management science and operations research. Many of the young engineers really believed then that companies in the process industries existed primarily to apply and display creations, refineries, chemical plants, pipelines, and so forth. Certainly these creations were visible to the general public and commanded a certain amount of bemused respect. Despite the flowering of general purpose, widely available software, LP in the mid-60's was mainly used by large, technically-oriented organizations. Wider use was delayed by high computer costs, limited availability of suitable computers, lack of management awareness of LP, and a shortage of capable LP practitioners. LP flourished in the steel, food and beverage, and forest product companies. But it was used most extensively in the petroleum industry. The large integrated oil companies used LP heavily, first for gasoline blending, then for refinery operations planning, crude oil allocation, and distribution planning. LP's marketplace has grown to include a host of new industries, as well as its traditional ones. Industries such as banking, financial services, health care, electric Dower generation, container manufacture, pipelining, and consumer products, all use LP.

Most Management Science students have been taught to formulate a linear programming model by writing a set of (row) equations. While this technique in suitable for the vast majority of problems usually encountered in industry. it falls short when an entire company must be modeled. In this article, a methodology for formulating linear programming models is presented which, though not new. has been largely ignored by authors of textbooks and the academic community. The author maintains that this approach could substantially improve interest in and comprehension of mathematical programming and provide a useful supplement to the Management Science curriculum. [ABSTRACT FROM AUTHOR]

Optimization of a given system is certainly different from design of an optimal system. It is remarkable that in the age of limited resources and lagging productivity it is the philosophy of linear programming, i.e., maximization of a function with respect to given constraints, which dominates Operations Research thinking, education, and practice. This philosophy is wasteful of resources, ignorant of productivity, and, more surprisingly, unconcerned about profits. It teaches how to "optimize" a given system without paying enough attention to how such a system comes into existence. It is the purpose of this paper to show that the main shortcoming of LP is neither its linearity assumption, nor its algorithmic and scale inefficiency, nor its single-objective simplification -- it is its inability to design an optimal system while concentrating on fine-tuning its "optimization" of a given system. How does the "given" come into being, that is the question. [ABSTRACT FROM AUTHOR]

The article deals with the gap between decision scientists and decision-makers or managers of businesses. In the early fifties, people developing the management sciences worked closely with the management making the decisions. People applying the techniques developed new statistical techniques. The development of management science and its use in making decisions went on simultaneously. There was less than a three-year gap between mathematician Dantzig's invention of the simplex algorithm of linear programming and its use in blending gasoline. The Monte Carlo technique proposed in the fifties was used in the fifties to solve real problems. New ways of designing experiments were developed for experiments being run at that time. It can be concluded then that management science has not had as big an impact in business as it should, and it is up to the management scientist to close the gap.

This is Part 1 of a two-part series. It shows how advances in network solution techniques have brought about improved computer-based planning. We give examples of practical problems and their network models that have resulted in dramatic cost savings for OR/MS practitioners. Not only are the models more convenient (easier to visualize and communicate) than customary LP models, but the new advances enable them to be solved more than 100 times faster than LP models. Part 2 (coming in the November issue) will show how related models have led to further cost savings in practical applications. [ABSTRACT FROM AUTHOR]