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Several comments on the papers by L. V. Kantorovich reproduced in this volume. Bibliography: 16 titles. [ABSTRACT FROM AUTHOR]

The article presents comments on the management science paper "On Sequencing n Jobs on One Machine to Minimize the Number of Late Jobs," by William L. Maxwell. The paper focused on an integer programming formulation of a one-machine job shop problem. The author contends that Maxwell made in error in proving the validity of an optimal algorithm by applying cutting plane constraints to the problem. The author explains that the problem cannot be solved through traditional cutting plane procedures. The author provides a mathematical model in an attempt to correct the proof.

In this paper, we address an instance of the dynamic capacitated multi-item lot-sizing problem (CMILSP) typically encountered in steel rolling mills. Production planning is carried out at the master production schedule level, where the various end items lot sizes are determined such that the total cost is minimised. Through incorporating the various technological constraints associated with the manufacturing process, the integrated production-inventory problem is formulated as a mixed integer bilinear program (MIBLP). Typically, such class of mathematical models is solved via linearisation techniques which transform the model to an equivalent MILP (mixed integer linear program) at the expense of increased model dimensionality. This paper presents an alternative branch-and-bound based algorithm that exploits the special structure of the mathematical model to minimise the number of branches and obtain the bound at each node. The performance of our algorithm is benchmarked against that of a classical linearisation technique for several problem instances and the obtained results are reported. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show how certain ideas in the so called decomposition theory of mathematical programming can be exploited for the computation of equilibrium in a system of linear capital markets. The fact that economic decision-making is made in a decentralized, i.e., independent, fashion by economic agents has a long been recognized and led economists to build models which, in one way or another, incorporated this feature. Two main departments of economic theory undertook the study of decentralization: on the one hand, the theory of decentralization of decisions inside the firm and the related decomposition theory of mathematical programming and, on the other hand, the study of general equilibrium systems and the decentralizing properties of competitive prices. The purpose of this paper is to show how certain ideas in the so called decomposition theory of mathematical programming can be exploited for the computation of equilibrium in a system of linear capital markets. The fact that economic decision-making is made in a decentralized, i.e., independent, fashion by economic agents has a long been recognized and led economists to build models which, in one way or another, incorporated this feature. Two main departments of economic theory undertook the study of decentralization: on the one hand, the theory of decentralization of decisions inside the firm and the related decomposition theory of mathematical programming and, on the other hand, the study of general equilibrium systems and the decentralizing properties of competitive prices. [ABSTRACT FROM AUTHOR]

Project management is a process that schemes and controls the project life cycle via the easiest and the best way to achieve project goals. Project managers always aim to simultaneously handle conflicting goals in the organization. In this paper, a new mathematical model is proposed that simultaneously minimizes total cost and completion time and maximizes the quality in the project management decision problem. Contractual penalty cost and contractual reward cost with a new method are the other consideration in the proposed model. In the projects, the relation between time and direct cost is a nonlinear function. Hence, a linearization technique is presented with attention to variable change and piecewise linearization, in which nonlinear function is converted to the linear programming model. On the other hand, in real conditions according to uncertainty in environmental situations and incomplete information, there can be ambiguity in parameters and variables of the problem. The uncertainty of the parameters and variables is expressed with fuzzy sets theory and fuzzy mathematical programming. The other aim of this paper is to introduce a modified version of fully fuzzy multi-objective linear programming for the problem. For analyzing a fully fuzzy time–cost–quality project management model, a practical example of the literature is provided. By examining the results of the model with conflicting objectives, two scenarios are presented to explore the interactions of conflicting objectives on the project, and the results are reported. [ABSTRACT FROM AUTHOR]

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem into a set of scalar optimization subproblems and optimizes them in a collaborative manner. Subproblems and solutions are two sets of agents that naturally exist in MOEA/D. The selection of promising solutions for subproblems can be regarded as a matching between subproblems and solutions. Stable matching, proposed in economics, can effectively resolve conflicts of interests among selfish agents in the market. In this paper, we advocate the use of a simple and effective stable matching (STM) model to coordinate the selection process in MOEA/D. In this model, subproblem agents can express their preferences over the solution agents, and vice versa. The stable outcome produced by the STM model matches each subproblem with one single solution, and it tradeoffs convergence and diversity of the evolutionary search. Comprehensive experiments have shown the effectiveness and competitiveness of our MOEA/D algorithm with the STM model. We have also demonstrated that user-preference information can be readily used in our proposed algorithm to find a region that decision makers are interested in. [ABSTRACT FROM AUTHOR]

The first of this two-paper series proposes a methodology to characterize generation investment equilibria in a pool-based network-constrained electricity market, where the producers behave strategically. To this end, the investment problem of each strategic producer is represented using a bilevel model, whose upper-level problem determines the optimal investment and the supply offering curves to maximize its profit, and whose several lower-level problems represent different market clearing scenarios. This model is transformed into a mathematical program with equilibrium constraint (MPEC) through replacing the lower-level problems by their optimality conditions. The joint consideration of all producer MPECs, one per producer, constitutes an equilibrium problem with equilibrium constraints (EPEC). To identify the solutions of this EPEC, each MPEC problem is replaced by its Karush-Kuhn-Tucker (KKT) conditions, which are in turn linearized. The resulting mixed-integer linear system of equalities and inequalities allows determining the EPEC equilibria through an auxiliary MILP problem. [ABSTRACT FROM PUBLISHER]

The problem of optimal flow production planning at the operational scheduling stage is being studied, using the example of the out-of-furnace department of a converter-based steel-making production in the iron metallurgy industry. To solve this problem, a linear integer programming model is proposed, which fully describes the specifics of the investigated technological processes. A major advantage of this approach is its scalability for solving related optimization problems in the industry of plant logistics, as well as flexibility in adapting to changes and fine-tuning the system of constraints and objective function. The software implementation of the developed model forms the basis of the operational scheduling module of the optimal flow production planning system, which is used for a large-scale computational experiment on real-world data. [ABSTRACT FROM AUTHOR]

This paper studies the linear programming problem in which all coefficients (even those of the stipulations matrix) are rational functions of a single parameter t called ‘time,’ and provides an algorithm that can serve problems of the following two types: (1) Steady-state behavior [the algorithm can be used to determine the functional form x(t) of the optimal solution as a function of t, this form being valid for all ‘sufficiently large’ values of t], and (2) sensitivity analysis [if a value t0 of ‘time’ is given, the algorithm can be used to determine the two possible functional forms of the optimal solution for all values of t ‘sufficiently dose’ to t0 (the first functional form valid for t«t0, the second for t»t0)]. In addition, the paper gives certain qualitative information regarding steady-state behavior, including the following result: If for some one of the properties of consistency, boundedness, or bounded constraint set, there exists a sequence tn↗+∞ such that the linear program at tn has this property for all n, then the program has this property for all ‘sufficiently large’ values of t. [ABSTRACT FROM AUTHOR]

The availability of data regarding variables of interest in forecasting problems is sometimes limited, but experts may possess a great deal of relevant information. The approach taken in this paper involves the development of adaptive forecasting models based on such information. Since the models and their parameters are difficult to consider intuitively, information from the experts is elicited in terms of predictive distributions of the variable to be forecasted. Various models can then be considered, and attempting to "fit" a model to the predictive distributions is analogous to attempting to fit a model to a set of observations. This general approach to forecasting is developed in this paper, and a specific model, a linear model with normally distributed errors, is considered in some detail. An actual application involving the forecasting of fatigue life of asphalt pavements illustrates the development of forecasting models from experts' predictive distributions. [ABSTRACT FROM AUTHOR]

With the wide application of location theory in a variety of industries, the presence of barriers ‎merits the attention of managers and engineers.‎ In this paper, we assess the Weber location problem in the presence of a polyhedral barrier which probabilistically occurs on a given horizontal barrier route in the rectilinear space. A left triangular distribution function is used for the starting point of the barrier and therefore an expected rectilinear barrier distance function is formulated. In addition, a modification of the polyhedral barrier is presented which is equivalent to the original problem. Therefore, a mixed integer nonlinear programming model, which has a nonconvex solution space, is presented. Furthermore, by decomposing the feasible space into a finite number of convex solution spaces, an exact heuristic solution method is proposed. Then, a lower bound problem based on the forbidden region is applied. Some theorems and an example are reported. [ABSTRACT FROM PUBLISHER]

The fractional transportation problem (FTP) plays an important role in logistics and supply management for reducing cost and improving service. In the real world, however, the parameters in the models are seldom known exactly and have to be estimated. This paper investigates the FTP where the cost coefficients and right-hand sides are represented by fuzzy parameters. Intuitively, when the parameters in the FTP are fuzzy numbers, the derived objective value should be also a fuzzy number. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the fuzzy objective value of the FTP with fuzzy parameters. By applying the dual formulation of linear fractional programming and variable substitution techniques, the two-level mathematical programs are transformed into ordinary one-level linear programs to solve. At a specific $$\alpha $$ -cut, solving the pair of linear programs produces the bounds of the objective value of the fuzzy FTP. By collecting the bounds from different $$\alpha $$ levels, one can depict the shape of the membership function. An example illustrates how to apply the concept of this paper to solve the fuzzy FTP problem. [ABSTRACT FROM AUTHOR]

This paper studies the single-hoist cyclic scheduling problem in electroplating systems with two extended features. One extension is that the products must visit some processing tanks more than once (multi-function tanks). Another is that more than one identical tank is used at some stages. These extensions are common in practical electroplating lines and can increase the lines' processing capacity. However, they make the hoist scheduling problem more complicated and little research has been done to optimize the hoist moves in such extended practical systems. In this paper, we develop a comprehensive mixed integer linear programming model to find optimal solutions to the single-hoist cyclic scheduling problem for electroplating lines with these extensions. Examples are given to demonstrate the effectiveness of the model in different types of problems. [ABSTRACT FROM AUTHOR]

This paper presents an integer linear programming formulation for the problem of extracting a subset of stimuli from a confusion matrix. The objective is to select stimuli such that total confusion among the stimuli is minimized for a particular subset size. This formulation provides a drastic reduction in the number of variables and constraints relative to a previously proposed formulation for the same problem. An extension of the formulation is provided for a biobjective problem that considers both confusion and recognition in the objective function. Demonstrations using an empirical interletter confusion matrix from the psychological literature revealed that a commercial branch-and-bound integer programming code was always able to identify optimal solutions for both the single-objective and biobjective formulations within a matter of seconds. A further extension and demonstration of the model is provided for the extraction of multiple subsets of stimuli, wherein the objectives are to maximize similarity within subsets and minimize similarity between subsets. [ABSTRACT FROM AUTHOR]

This paper is a compendium of results--theoretical and computational--from a series of recent papers developing a new American option valuation technique based on linear programming (LP). Some further computational results are included for completeness. A proof of the basic analytical theorem is given, as is the analysis needed to solve the inverse problem of determining local (one-factor) volatility from market data. The ideas behind a fast accurate revised simplex method, whose performance is linear in time and space discretizations, are described and the practicalities of fitting the volatility smile are discussed. Numerical results are presented which show the LP valuation technique to be extremely fast--lattice speed with PDE accuracy. American options valued in the paper range from vanilla, through exotic with constant volatility, to exotic options fitting the volatility smile. [ABSTRACT FROM AUTHOR]

This paper compares two approaches to the solution of weighted multiobjective linear programming problems: the fuzzy linear programming method and the minmax distance metric. The two models produce an identical solution for equally weighted objectives, but the solutions differ when the objectives are unequally weighted. This is due to the under-lying meaning of the weights attached to each solution method. The paper illustrates the graphical meaning of the weights and the implications to the decision maker. [ABSTRACT FROM AUTHOR]

At the heart of van der Linden's approach to automated test assembly ( ATA) is a linear programming/integer programming ( LP/ IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from traditional computer programming, through LP/ IP-specific modeling languages, to plug-ins for common software such as Excel. The features of several of the major IP solvers are briefly reviewed, describing which of the features are more or less useful in the context of ATA. The appendices include a list of resources that I have found particularly useful. [ABSTRACT FROM AUTHOR]

The optimum coupon schedule for serial bonds issued by municipalities has been solved as a knapsack problem, and is widely implemented in bank and nonbank underwriting firms. A large subset of issues carries the additional requirement that limits the number of distinct coupons which the underwriters may assign to the issue. The paper formulates this problem as a dynamic programming model and discusses the computational aspects relating to this formulation by comparing it with a direct 0/1 integer programming model. Some computational experience is also provided. [ABSTRACT FROM AUTHOR]

The paper focuses on multi-stage production systems. If such a system is of the more general type than a production line and many products have to be manufactured according to different technological sequence restrictions then two problems arise: (1) scheduling and (2) sequencing. The formulation of that problem requires the simultaneous consideration of the scheduling and sequencing aspect. The paper integrates these two functions into one single model using zero-one programming. [ABSTRACT FROM AUTHOR]

This paper gives a detailed description of an algorithm for the solution of a specialized Linear Programming model, to be called the Machine Loading model. It is a generalization of the Transportation Problem, in that weighting factors are applied to the individual elements which form the row and column sums. For the Machine Loading model, the simplex method reduces to a specialized algorithm which generalizes the stepping stone method of the Transportation Problem [2], [3]. With the resulting generalized stepping stone method, it becomes practicable to solve many large-scale problems for which the direct application of the simplex method would be impracticable. The present paper is restricted to a discussion of the following topics: (I) the general characteristics of the model and its topological features; (ii) a detailed solution algorithm, including a consideration of degenerate cases and the use of a computer; (iii) a more restrictive capacitated model and the corresponding modifications to the solution algorithm; and (iv) the complete illustrative solution of a numerical example. The purpose is to aid interested readers in gaining familiarity with the algorithm and facility in the solution of numerical problems. No derivations or proofs will be included. [ABSTRACT FROM AUTHOR]

This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a grey linear programming problem with grey coefficients is discussed. In particular, the duality results as one of the important results on linear programming with grey parameters is established. First, some definitions and concepts of Grey System Theory are introduced and then a dual problem is defined for the primal grey linear programming problem. In particular, for establishing the duality theory, the fundamental theorems and results, such as weak and strong duality and optimality condition is proved. The study emphasizes that the established results can be usefulfor providing a new approach to solve the dual problem directly on the primal simplex tableau. [ABSTRACT FROM AUTHOR]

This paper proposes a relaxed mathematical model to solve the restoration problem of radial and balanced electrical distribution systems. The mathematical model is a mixed-integer linear programming formulation that can be efficiently solved by commercial solvers. After a restoration problem is solved using this model, the quality and feasibility of the corresponding solution can be verified by using a conventional radial power flow. The performance of the proposed relaxed model is evaluated through exhaustive tests and the solutions found are compared with the ones provided by an exact mathematical formulation. The results obtained demonstrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the overarching goal of enhancing service quality and optimizing berth utilization rates, this article proposes a mathematical programming model that minimizes the total waiting time of vessels and the overall completion time of vessel service. The formulated model is a mixed-integer linear programming problem that deterministic optimization techniques can globally solve. For large-scale problems, this study develops a genetic algorithm optimization approach to improve computational efficiency in reaching a near-optimal solution. Several numerical experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper transmission network planning will be presented in which the competition ability associated with minimum investment costs is considered. This type of transmission expansion can be addressed as an open access transmission expansion planning. Such open access transmission planning is modeled regarding extreme and feasible generating scenarios. A mathematical modeling of transmission expansion problem, considering generation scenarios is solved via a constructive heuristic algorithm using an iterative technique. In this paper a constructive heuristic algorithm solves several non-linear programming in order to identify the most important transmission line that should be constructed. The proposed methodology is implemented to the Garver as well as IEEE 24-bus test systems to show its significant performance. [ABSTRACT FROM AUTHOR]

This paper introduces two new one-dimensional cutting stock models: the generalized assortment problem (GAP) and the best cutting stock length (BSL) problem. These new models provide the potential to reduce waste to values lower than the optimum of current models, under the right management circumstances. In the GAP, management has a standard length and can select one or more of any additional custom stock lengths, and management wishes to minimize cutting stock waste. This model is different from existing models that assume that the selection is from a small fixed set of stock lengths. In the BSL problem, management chooses any number of custom stock lengths, but wishes to find the fewest custom stock lengths in order to have zero waste. Results show waste reductions of 80% with just one custom stock length compared with solutions from standard cutting stock formulations, when item lengths are long relative to the stock length. The models are most effective when the item lengths are nearly as long as the stock length. Solutions from the model have been implemented for a manufacturer. The model is easily generalized to allow multiple existing stock lengths and different costs. [ABSTRACT FROM AUTHOR]

This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities and decision makers' predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a portfolio selection problem is provided to compare our proposed models with the basic model. [ABSTRACT FROM AUTHOR]

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [ABSTRACT FROM AUTHOR]

In this paper we consider a transportation system consisting of a carrier with capacity Q ≤ ∞, operating between two terminals. Passengers arrive at these terminals according to independent Poisson processes and are transported by the carrier from one terminal to the other terminal. Under a fairly general cost structure we show that the optimal operating policy which minimizes the expected average cost is a monotone decreasing function of the number of customers waiting at each terminal. Bounds are derived for the optimal average cost policy and a method to compute these optimal policies using linear programming is presented. [ABSTRACT FROM AUTHOR]

Pure processing network problems are minimum cost flow problems in which the flow entering or leaving a node may be constrained to do so in given proportions. In this paper, new theoretical results concerning pure processing networks are developed, and, based on these results, two new primal simplex variants are presented. One of these variants has been implemented and tested against a general purpose linear programming code. A large class of problems is identified for which the specialized code is an order of magnitude faster than the general purpose code. [ABSTRACT FROM AUTHOR]

Single objective cost minimization linear programming models are used as computerized decision-aids in sausage manufacturing (hot dogs, bologna, salami, etc.). However, sausage blending is clearly a problem with multiple conflicting criteria (cost, color, fat, protein, moisture, etc.) Presented in this paper is a vector-maximum/filtering MOLP (multiple objective linear programming) methodology for use as an improved decision-making approach with single formula sausage blending problems. [ABSTRACT FROM AUTHOR]

The extensions, new developments and new interpretations for DEA covered in this paper include: (1) new measures of efficiency, (2) new models and (3) new ways of implementing established models with new results and interpretations presented that include treatments of ‘congestion’, ‘returns-to-scale’ and ‘mix’ and ‘technical’ inefficiencies and measures of efficiency that can be used to reflect all pertinent properties. Previously used models, such as those used to identify ‘allocative inefficiencies’, are extended by means of ‘assurance region’ approaches which are less demanding in their information requirements and underlying assumptions. New opportunities for research are identified in each section of this chapter. Sources of further developments and possible sources for further help are also suggested with references supplied to other papers that appear in this volume and which are summarily described in this introductory chapter. [ABSTRACT FROM AUTHOR]

This paper presents a parallelization of the simplex method for linear programming. Current implementations of the simplex method on sequential computers are based on a triangular factorization of the inverse of the current basis. An alternative decomposition designed for parallel computation, called the quadrant interlocking factorization, has previously been proposed for solving linear systems of equations. This research presents the theoretical justification and algorithms required to implement this new factorization in a simplex-based linear programming system. [ABSTRACT FROM AUTHOR]

This paper considers the block-coded modulation system in the multipath fading environment and derives the upper bound expression for the bit error rate considering the effects of the interleaving size and the space diversity. Here a signal design is proposed. Here, the set of signals minimizing the upper bound expression is sought using the quasi-Newton method, which is known as an iterative solution method for the nonlinear programming problem. The bit error rate for the signal sequence derived by the proposed signal design is evaluated by a computer simulation, and the effectiveness of the proposed signal design is demonstrated. [ABSTRACT FROM AUTHOR]

Linear programming is applied to measurement of whole life insurance to obtain a functional relationship between interest adjusted cost of insurance protection and rate of return on policy equity. For comparative purposes, policy differences related to premium rates, dividends and cash-values are controlled by maintaining identical insurance requirements and constant levels of wealth for the insured. Marginal discount factors, obtained from the dual variables for the wealth constraints, demonstrate the importance of policy holder wealth. The interest adjusted cost measure currently used by the insurance industry is shown to be a special case when the linear programming approach is used. The method used in this paper is sufficiently flexible to incorporate different patterns of time preference for insurance. Finally, it is demonstrated that the trade-off between interest adjusted cost of insurance and rate of return on policy equity is sensitive to the external rate of return. [ABSTRACT FROM AUTHOR]

In this paper we consider a certain aggregate production planning model. This model permits regular and overtime production and allows for backordering of goods for a number of periods. Although the discussed model can be formulated as a linear programming problem a special (noniterative) method is developed. First the optimal level of each mode of production is determined for each period. Then the complete solution is immediately constructed. This procedure is so simple that it can be also implemented via pencil and paper. Several computational improvements as well as problem variations are discussed. [ABSTRACT FROM AUTHOR]

More than twenty years after the publication of the Linear Decision Rule (LDR) of Holt, Modigliani, Muth, and Simon (HMMS), the LDR remains an implementation failure. No company is reported to be using it. This paper hypothesizes that the reason for this failure may be a very simple one: the incremental benefit of aggregate planning (i.e., the coordinated optimization of aggregate work force, production, and inventory) over improved aggregate inventory management alone may be quite small. To demonstrate our hypothesis we reexamine the original paint company cost comparisons presented by HMMS, and show that virtually all of the LDR' s reported saving over paint company management could have been obtained with a one time adjustment in management's aggregate buffer inventory level. We conclude that although the LDR might provide significantly larger savings than improved aggregate inventory management alone, published empirical results fail to demonstrate that potential. The implications of our hypothesis and conclusions are discussed. [ABSTRACT FROM AUTHOR]

This paper examines the performance of three heuristic methods (Senju-Toyoda, Kochenberger et al., and Hillier) when applied to the 0-1 linear programming problem with nonnegative coefficients. Their effectiveness, measured in terms of computing time, error and relative error, is evaluated on a set of problems from the literature and randomly generated 0-1 test problems with nonnegative coefficients. Analysis of variance and stepwise regressions are employed to study the effect of the number of variables, number of constraints and degree of constraint slackness. The methods exhibited some similarities but also marked differences in their behavior. Interestingly enough, the larger the number of variables the better the accuracy of each method. Error differences among the three methods were significant (1:0.8:0.2) yet small (less than 2% on the average) for many practical situations. Hillier's algorithm was the most accurate but much slower and more core demanding than the other two, which makes it difficult or impossible to use for solving large 0-1 problems. Kochenberger's et al. heuristic was the fastest (most accurate) of the three in tightly (loosely) constrained problems. In general the Senju-Toyoda algorithm was the fastest, but least accurate on small and medium size problems. Suggestions are made for selecting the "best" heuristic based on the problem characteristics. [ABSTRACT FROM AUTHOR]

There are numerous situations in management and elsewhere in which an individual decision maker chooses subsets of multiattributed items. The specification of a measure of goodness for selecting subsets may differ from one situation to the next. In this paper, a model is developed for evaluating subsets where the choice criterion is one of balance among the attributes of items in the subset chosen. A method for determining the parameters of the model from a small number of judgments on subsets using linear programming is discussed, The model is applied to the problem of evaluating subsets of television shows and of choosing the most balanced subset of shows. Several extensions of the model and potential applications are also given. [ABSTRACT FROM AUTHOR]

The rim multiparametric linear programming problem (RMPLP) is a parametric problem with a vector-parameter in both the right-hand side and objective function (i.e. in the "rim"). The RMPLP determines the region K&lowest; ⊂ E &lowest; such that the problem, maximize z(λ) = c T(λ)x, subject to Ax = b(λ), x ≥ 0, has a finite optimal solution for all λ ∈ K&lowest;. Let Bi be an optimal basis to the given problem, and let Ri&lowest; be a region assigned to Bi such that for all λ ∈ Ri&lowest; the basis Bi is optimal. The goal of the RMPLP problem is to cover K&lowest; by the Ri&lowest; such that the various Ri&lowest; do not overlap. The purpose of this paper is to present a solution method for finding all regions Ri&lowest; that cover K&lowest; and do not overlap. This method is based upon an algorithm for a multiparametric problem described in an earlier paper by Gal and Nedoma. [ABSTRACT FROM AUTHOR]

Continuous location models generally use the Euclidean or rectangular norm to approximate travel in a transportation network. This paper considers a new and more accurate distance measure, termed the weighted one-two norm, which is a positive linear combination of the preceding norms. A directional bias function is introduced to show the equivalence of this distance measure to the well known l[sub p] norm. We then formulate a simple linear regression model to fit the parameters of our distance function to a given data set. Some novel applications based on standard statistical tests are derived which provide practical insights into the nature of networks with rectangular bias. The results are readily extended to other types of networks. [ABSTRACT FROM AUTHOR]

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as "master" problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that "subproblems" arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it (see Part II of this paper) to rederive a representative selection of algorithms. The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled "Problem Manipulation: Source of 'Master' Problems" covers the subjects of projection, inner linearization and outer linearization. The third section, "Solution Strategies: Source of 'Subproblems'," discusses piecewise strategy, restriction and relaxation. The fourth section is entitled "Synthesizing Known Algorithms from Manipulations and Strategies," and is followed by a concluding section and an extensive bibliography. [ABSTRACT FROM AUTHOR]

The article focuses attention on the problems encountered in formulating and using process mathematical models in an industrial environment. A model of an actual lime factory is used for descriptive purposes. The linear programming technique is employed to illustrate the simulation of the plant. The paper does not try to explain the mathematics of linear programming or any other technique used to simulate the activities of a plant. The aim of the writers is rather to outline the steps taken in formulating a plant model and what can be done with it. This paper is mainly concerned, therefore, with the managerial, engineering and cost accounting problems encountered. The linear programming technique is applied here mainly because of its wide range of applications. Much of what is described may be of value to persons using other methods. [ABSTRACT FROM AUTHOR]

This paper demonstrates the equivalence of several published algorithms for solving the so-called linear fractional programming problem. [ABSTRACT FROM AUTHOR]

In linear programming under uncertainty the two-stage problem is handled by assuming that one chooses a first set of constrained decision variables; this is followed by observations of certain random variables after which another set of decisions must be made to adjust for any constraint violations. The objective is to optimize an expected value functional defined relative to the indicated choices. This paper shows how such problems may always be replaced with either constrained generalized medians or hypermedians in which all random elements appear only in the functional. The resulting problem is called a deterministic equivalent for the original problem since (a) the originally defined objective replaces all random variables by corresponding expected values and (b) the remaining constraints do not contain any random terms. Significant classes of cases are singled out and special attention is devoted to the structure of the constraint matrices for these purposes. Numerical examples are supplied and related to the previous literature. Other properties of these models are also examined and related to types of problems which are often of interest. For instance the hypermedian and generalized median formulations involve minimizations over absolute value terms in the functional. These, in turn, are developed for their possible pertinence in problems where minimizations are to be over the maximum of a set of functions under inequality constraints. Utilizing Moore-Penrose (generalized) inverses, other characterizations are also secured in which all relevant weights and coefficients are stated explicitly in terms of original data. [ABSTRACT FROM AUTHOR]

This paper shows in a hypothetical and illustrative manner, how a linear programming model of moderate size can be used in selecting projects for a national development program, without requiring the construction of a model that covers the whole of the economy in detail. [ABSTRACT FROM AUTHOR]

As interest grows rapidly in industry on the potentialities of mathematical programming techniques, it appears worthwhile to have a paper devoted to some of the more promoting developments which may speed up the transition from interest to use. Three topics have been selected (in three sections that follow) which have recently come into prominence: uncertainty, combinatorial problems, and large scale systems. The reader will find in the course of their dissensions that a survey--though perhaps not a systematic survey--has been made of current techniques in the linear programming field. [ABSTRACT FROM AUTHOR]