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In the context of project management, the attention given to project portfolio management has increased in recent years. The use of mathematical programming for portfolio management is also on the rise, because it integrates the project interactions with the multiple objectives of portfolio management into a single model. Among the possible objectives, recent studies have paid special attention to the emerging objective of future preparedness, which has not yet been incorporated into the existing mathematical models. This paper presents a mixed-integer nonlinear optimization model for portfolio selection that considers four main performance measures for project management, namely, value maximization, strategic alignment, balance, and future preparedness. Given the importance of the last measure, the purpose of this paper is to provide a more complete model that provides the marginal contribution and the best combination of projects according to the needs of the company. The model is tested using real data from two companies, one in Brazil and one in Canada, and the results obtained are coherent with their respective practices. [ABSTRACT FROM AUTHOR]

In public policy decision making and in capital planning fractional criterion functions occur. For a given set of desirable target values (goals) τi, this paper develops an algorithm for solving a nonconvex programming problem of the type: Minx∈S Maxi{&phii(fi(x)/gi(x) - τi), i = 1,..., m} where fi are convex functions, gi, are concave functions over the convex subset S of Rn and φi are nondecreasing gauge functions. Here φi(&middot) is the penalty incurred whenever the fractional objective fi/gi deviates from the target value τi, the problem is then to choose an x that minimizes the maximum penalty incurred. [ABSTRACT FROM AUTHOR]

This paper provides a methodology to assist a strategic producer in making informed decisions on generation investment. A single target year is considered with demand variations modeled through blocks. The strategic behavior of the producer is represented through a bilevel model: the upper-level considers both investment decisions and strategic production actions and the lower-level corresponds to market clearing. Prices are obtained as dual variables of power balance equations. Rival uncertainties (on offering and investment) are characterized through scenarios. The resulting model is a large-scale mixed-integer LP problem solvable using currently available branch-and-cut techniques. Results pertaining to an illustrative example and a case study are reported and discussed. [ABSTRACT FROM PUBLISHER]

This note demonstrates that Freeland's (1976) modification of Ruefli's (1971) Generalized Goal Decomposition model can generate nonoptimal solutions and shows how these difficulties can be corrected. In several papers on multi-level planning, it has been suggested that extending the hierarchical levels of the models from two to three or more levels is a straightforward process. This paper shows that this assertion is generally not true. The note points out that in Freeland's (1976) three-level model, the interactions between the two lowest levels of the hierarchy must be strictly controlled before information is passed to the highest level of the organization. [ABSTRACT FROM AUTHOR]

The bond portfolio problem is viewed as a multistage decision problem in which buy, sell, and hold decisions are made at successive (discrete) points in time. Normative models of this decision problem tend to become very large, particularly when its dynamic structure and the uncertainty of future interest rates and cash flows are incorporated in the model. In this paper we present a multiple period bond portfolio model and suggest a new approach for efficiently solving problems which are large enough to make use of as much information as portfolio managers can reasonably provide. The procedure utilizes the decomposition algorithm of mathematical programming and an efficient technique developed for solving subproblems of the overall portfolio model. The key to the procedure is the definition of subproblems which are easily solved via a simple recursive relationship. [ABSTRACT FROM AUTHOR]

This paper is concerned with characterizing decision rules for the sequential E-model of chance-constrained programming. A key feature of our characterization will be a detailed discussion of various interpretations of the probability operator in the chance constraints. Specifically we define two new classes of decision rules by exhibiting those sets of constraints which locally support the corresponding probability requirements. The question of how the probabilistic constraints for future periods are affected by previous decisions and realizations of the random variables is considered in detail. Since we are primarily concerned with the feasibility of decision rules, we deal mainly with the constraints of the model. The procedure for selecting the optimum rule from among a particular class of feasible rules depends on the objective function and is briefly discussed in the final section along with some implications concerning the form of the optimum rule. The application of our proposed rules to a two-period example previously appearing in the literature concludes the paper. [ABSTRACT FROM AUTHOR]

The objective of assembly line balancing (ALB) is the allocation of tasks to workstations of continuous production lines in order to minimise operating cost or other cycle time-related management criteria. As a consequence of the development of computer technology, mathematical programming models of practical-sized ALB problems can be solved by commercial optimisation software very efficiently. Therefore, the focus of research in ALB can be shifted to practice-driven model formulation and to the investigation of new areas of application. The objective of this paper is to show how cycle-time related operations management decisions can be supported with quick solution of ALB models through the case of a bicycle assembly process. Practical ALB problems related to workforce skill and to production quantity changes are presented and management implications of the results are explained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a new Atanassov's intuitionistic fuzzy (A-IF) programming method to solve heterogeneous multiattribute group decision-making problems with A-IF truth degrees in which there are several types of attribute values such as A-IF sets (A-IFSs), trapezoidal fuzzy numbers, intervals, and real numbers. In this method, preference relations in comparisons of alternatives with hesitancy degrees are expressed by A-IFSs. Hereby, A-IF group consistency and inconsistency indices are defined on the basis of preference relations between alternatives. To estimate the fuzzy ideal solution (IS) and weights, a new A-IF programming model is constructed on the concept that the A-IF group inconsistency index should be minimized and must be not larger than the A-IF group consistency index by some fixed A-IFS. An effective method is developed to solve the new derived model. The distances of the alternatives to the fuzzy IS are calculated to determine their ranking order. Moreover, some generalizations or specializations of the derived model are discussed. Applicability of the proposed methodology is illustrated with a real supplier selection example. [ABSTRACT FROM PUBLISHER]

Purpose -- The strategic importance of sourcing is inherent in the positioning of the purchasing operation in a supply chain and supplier evaluation -- a crucial step in sourcing -- is a complex multicriteria decision making (MCDM) problem. The purpose of this paper is to provide a meta-model for supplier evaluation and order quantity allocation, based on a MCDM method, namely the Analytic Network Process (ANP) and a multiobjective mathematical programming method (MOMP), the AUGMECON. Design/methodology/approach -- The proposed approach consists of two parts. The former develops and applies the ANP method in order to evaluate the suppliers in qualitative terms. The latter implements the AUGMECON method in order to find the Pareto optimal solutions for the allocation of order quantities in a multiple sourcing environment. The integrated meta-model is exposed through an illustrative case concerning the parapharmaceutical enterprise cluster in Greece. Findings -- The proposed meta-model constitutes an efficient method that enables managers to actively participate in the decision making process and exploit the "qualitative value" of their suppliers, while minimizing the costs and the mean delivery times. In addition, it is proved to be suitable for the enterprise clusters, as it adapts a multiple sourcing strategy and enhances the partnership among the members. Research limitations/implications -- The outcome of the model is highly dependent on the inputs provided by the decision maker. Moreover, the ANP method is computational intensive, but this limitation can be alleviated by appropriate software tools. Originality/value -- The proposed meta-model is an innovative approach for decision making in the area of multiple sourcing and order allocation. [ABSTRACT FROM AUTHOR]

In non-cooperative models of coalition formation, players have to decide whether or not to participate in a coalition (alliance). Game theoretic analyses of the formation of alliances in games with externalities, stress the difficulties in designing self-enforcing treaties because of free-riding. The presence of a strong free-rider incentive prevents most alliances of being stable and/or effective. This paper focuses on computing stability in a game on multiple coalition formation with membership rules and different transfer schemes. A new mathematical programming notation for game theory concepts is outlined. To compute stability, the new notation is used for implementation into computer coding. Implementation and computation aspects are discussed. Numerical illustration of the algorithm shows that stability varies with the applied membership rules and transfer schemes. An application of coalition formation to International Environmental Agreements (lEAs) is provided. [ABSTRACT FROM AUTHOR]

The article features the author's comments on the research paper "A New Product Analysis and Decision Model." The author acknowledges the important applications of the paper for sequential decision theory in the field of management science, but expresses concern as to generalizations made in the text. It is suggested that the demand function component of the mathematical analysis discussed in the paper. The author proposes that the functional analysis overlooks some main difficulties associated with the featured decision making variables. The industrial product development process is discussed. A heuristic programming approach is also examined.

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference "values" to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo 1983). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture. [ABSTRACT FROM AUTHOR]

This paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory. &sect2;1-3 present four fundamental situations of preferences, their combinations and the concept of relational system of preferences. In §4, a particular case of relational system of preference is studied. It is associated with the concept of pseudo-criterion derived from the classical concept of criterion by adjunction of two thresholds. Some results are given, generalizing the properties of such well-known structures as complete preorders and semiorders. &sect2;5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions, irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account. [ABSTRACT FROM AUTHOR]

A Steiner tree problem on the plane is that of finding a minimum length Steiner tree connecting a given set K of terminals and lying within a given region R of the Euclidean plane; it includes as special cases the Euclidean Steiner minimal tree problem (ESMT), the rectilinear Steiner tree problem (RST), and the Steiner tree problem on graphs (STG). A Steiner hull for K in R generically refers to any subregion of R known to contain a Steiner tree. This paper gives a survey of the role of Steiner hulls in the Steiner tree problem. The significance of Steiner hulls in the efficient solution of Steiner tree problems is outlined, and then a compendium is given of the known Steiner hull constructions for ESMT, RST, and STG problems. [ABSTRACT FROM AUTHOR]

This paper deals with the development of an interactive goal programming model to handle the problems of multiple goals. With a goal programming model, the manager can handle decision problems which deal with a single goal and multiple subgoals, as well as problems with multiple goals and multiple subgoals. Unlike linear programming, an arbitrary conversion of other value measures to a single objective function is unnecessary in goal programming. A goal is a target that the decision maker is attempting to accomplish. For example, the decision maker's goal may be a specific amount of profit, sales, cost or full utilization of the plant capacity or manpower expressed in terms of hours worked. Linear goal programming problems also have duality but in a little different fashion from that showing in linear programming. The dual of a linear goal programming problem is a linear programming problem with multiple, prioritized right-hand side values. For example, one can interpret a dual price associated with a particular goal as the level of preference per unit of that goal. One popular cost estimation method is the least square regression method with the assumption of symmetric quadratic loss function. For capital budgeting decisions, there are three commonly used criteria: net present value of cash flows, accounting earnings, and payback.

This paper develops a model to study the stay/leave decisions of Air Force officers. The model includes the most important institutional factors affecting an officer's career: promotion probabilities and timing, regular force integration probabilities, and mandatory separation and retirement probabilities. The model considers the officer's income for each potential combination of future grade and year of service and his civilian income opportunities. The model studies the incentives to retire for the current nondisability retirement system and the recent proposal by the President's Commission on Military Compensation. Numerical results are presented using actual data from Fiscal Year 1970 for nonrated officers who entered the Air Force through ROTC. On average, the officers' stay/leave behavior conforms with the model's predictions. Dynamic programming is the methodology used to construct the stay/leave model. Two versions of the dynamic programming model are considered. First, a sequential decision model for a risk-neutral agent is developed. The second version of the dynamic programming model generalizes the risk-neutral case to encompass risk-aversion. A functional equation is developed in which there is temporal resolution of uncertainty with respect to both military and civilian incomes. [ABSTRACT FROM AUTHOR]

Within the context of the U.K. background (public expenditure is being severely curtailed, at a local level health services and social services arc controlled by separate organisations and there are many groups of the population for whom a number of acceptable treatments, or methods of caring, exist), the paper describes the development of a resource allocation model and its use in a local planning situation. Although based on the techniques of mathematical programming, the model does not purport to indicate a single optimum allocation of health and social services resources, but rather to calculate the resource consequences of possible alternative courses of action. As such, its use is seen as iterative, in that health and social services decision makers can review and update their assumptions in the light of the results from successive runs of model. [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]

In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply l-stage contraction. The verification of the conditions of this note is somewhat easier. [ABSTRACT FROM AUTHOR]

Determining intercriteria relations is an important issue in MCDA. In order to handle this problem, this paper presents a new approach to the concept of compensation in multicriteria analysis, named PACMAN (Passive and Active Compensability Multicriteria ANalysis). The notion of compensability introduced here is decision maker oriented, relying only on information provided by him. In PACMAN compensability is analysed by taking into consideration two criteria at a time and distinguishing the compensating criterion from the compensated one. Separating active and passive effects of compensation allows one to point out a possible asymmetry of the notion of compensability. A valued binary relation of compensated preference is introduced. Compensated preference can be used for a modelization of the preference structure. [ABSTRACT FROM AUTHOR]

This research paper provides an example of a method which can be used to aid a decision maker while taking into account the multidimensional factors that must be considered. The method, called "policy capturing," requires little sophistication on the part of the decision-maker yet provides the analyst with a mathematical description of the tradeoffs faced by the decision-maker. Several alternative ways of using this method in a goal programming context are discussed. The policy capturing methodology seems to have the potential to capture loan decision policies of experts, use these policy functions to routinely perform screening activities for loans, and use these policy functions for routine goal programming determinations of loan mix decisions.

The paper describes a method of representing and analysing the multi-stage, dynamic nature of many types of research and development projects. The method makes use of a number of well-known techniques, decision trees, mathematical programming and simulation in combination. Each project which could form part of a laboratory portfolio is represented in a modified decision tree format called a "project tree", and the project trees are then considered in one analysis based on heuristics. The approach is demonstrated using a small illustrative example, and an industrial case study is described, giving attention to computational problems of size. [ABSTRACT FROM AUTHOR]

This survey examines eight mathematical programming models of pattern classification. The paper determines the range of applicability and computational merits of each model. The flexibility and large sample properties of the models are also discussed. We find that six of the models produce decision rules that maximize a function we call the quality of a decision rule. The remaining two models minimize a weighted sum of errors. [ABSTRACT FROM AUTHOR]

A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm for the solution of mathematical programming problems having a linear objective function and non-linear constraints. The algorithm is basically an adaptation of the simplex method to the case of non-linear constraints. Certain complications are, however, introduced through non-linearity in the constraints, and it is shown how these can be overcome. [ABSTRACT FROM AUTHOR]

A multi-depot Chinese postman problem (MDCP) arises from a network (e.g. cityplan) in which several depots are located wherefrom edges (e.g. streets) have to be served. Since costs are involved with each visit to an edge, the objective is to find a minimum cost tour in the network that visits all edges of the network. Such a minimum cost tour consists of a collection of subtours such that the subtours originate from different depots, and each subtour starts and ends at the same depot. This typical OR problem turns into a multi decision maker problem if agents are assigned to the streets. In this new setting the cost of a minimum cost tour that visits all edges have to be paid by the agents. However, now each group of agents (coalition) has the opportunity to find its own minimum cost tour, i.e. a minimum cost tour that only visits the edges owned by the group of agents. Therefore, the main objective is to find allocations of the cost of a minimum tour that visits all agents in such a way that no coalition has higher costs than the costs incurred by its own minimum tour. We will use cooperative game theory to investigate whether these so-called core allocations exist. Therefore, we consider a cooperative Chinese postman (CP) game that is induced by an MDCP by associating every edge of the network with a different agent. In this paper, we characterize classes of networks that ensure the existence of core allocations, the so-called CP balanced graphs, and the existence of specific core allocations, the so-called CP submodular graphs. [ABSTRACT FROM AUTHOR]

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. [ABSTRACT FROM AUTHOR]

Numerous analytical methods ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve supplier selection and order allocation problems. However, the traditional methods too often fail to consider: (1) situations in which goods are transported from a supplier to a receiver using different transportation alternatives (TAs) and (2) a finite planning horizon consisting of multiple discrete time periods. We present a structured framework with two separate but dependent phases. In the selection phase, we use a data envelopment analysis model to determine the relative efficiency of the suppliers and the TAs. In the allocation phase, we use a multi-objective mixed integer programming model with two objectives for minimizing the total costs and maximizing the overall efficiencies. The contribution of this paper is threefold: (1) It provides a comprehensive and systematic framework that embraces both quantitative and qualitative criteria; (2) it addresses the need in the supplier evaluation literature for methods that considers different TAs in the supplier selection and order allocation decisions encompassing multiple discrete time periods; and (3) it uses a real-world case study to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms. [ABSTRACT FROM AUTHOR]

While data envelopment analysis (DEA) models are very sensitive to possible data errors, in many real applications, the data of production processes cannot be precisely measured. Fuzzy DEA is asuccessful method that allows to deal with imprecise data in DEA. In this paper, we develop fuzzy version of the input relaxation model introduced in Jahahshahloo and Khodabakhshi [15] by using some ranking methods based on the comparison of α-cuts. The resulting auxiliary crisp problems can be solved by the usual DEA software. It is shown that, using a numerical example, how the proposed model become specially useful for detecting sensitive decision-making units. [ABSTRACT FROM AUTHOR]

This paper presents a fuzzy goal programming (FGP) procedure for solving bilevel multiobjective linear fractional programming (BL-MOLFP) problems. It makes an extension work of Moitra and Pal (2002) and Pal et al. (2003). In the proposed procedure, the membership functions for the defined fuzzy goals of the decision makers (DMs) objective functions at both levels as well as the membership functions for vector of fuzzy goals of the decision variables controlled by first-level decision maker are developed first in the model formulation of the problem. Then a fuzzy goal programming model to minimize the group regret of degree of satisfactions of both the decision makers is developed to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both decision makers. The method of variable change on the under- and over-deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. Illustrative numerical example is given to demonstrate the procedure. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal constrained pruning of decision trees. We present a novel 0-1 programming model for pruning the tree to minimize some general penalty function based on the resulting leaf nodes, and show that this model possesses a totally unimodular structure that enables it to be solved as a shortest-path problem on an acyclic graph. Moreover, we prove that this problem can be solved in strongly polynomial time while incorporating an additional constraint on the number of residual leaf nodes. Furthermore, the framework of the proposed modeling approach renders it suitable to accommodate different (multiple) objective functions and side-constraints, and we identify various such modeling options that can be applied in practice. The developed methodology is illustrated using a numerical example to provide insights, and some computational results are presented to demonstrate the efficacy of solving generically constrained problems of this type. We also apply this technique to a large-scale transportation analysis and simulation system (TRANSIMS), and present related computational results using real data to exhibit the flexibility and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In a recent paper, Petersen (1990) proposed to relax the convexity assumptions invoked in JL traditional Data Envelopment Analysis (DEA). Unfortunately, the new approach is not consistent with the relaxed assumptions. Also, the efficiency evaluations in input and output spaces are based on different technological assumptions. The aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent. In effect, a family of DEA methods based on relaxed convexity assumptions is identified. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for evaluating and selecting R&D projects in a collective decision setting, especially useful at sectorial and national levels. It consists of two major phases: Evaluation and Selection. The evaluation process repeatedly uses mathematical programming models to determine the "relative values" of a given R&D project from the viewpoint of the other R&D projects. The selection process of R&D projects is based on these "relative values" and is done through a model-based outranking method. The salient features of the methodology developed are its ability to (1) permit the evaluation of an R&D project from the viewpoint of the other R&D projects without at first imposing a uniform evaluation scheme, and (2) maximize the level of consensus as to which projects should not be retained in the R&D Program being funded, thus minimizing the level of possible resentment in those organizations or departments whose projects are not included in the R&D Program. Also discussed in this paper is an application of the methodology to evaluate and select major R&D projects in the iron and steel industry of Turkey. [ABSTRACT FROM AUTHOR]

Distributional equity is a particularly salient objective in public sector decision making, in general, and decision making concerning the delivery of public services such as education, libraries, sanitation, and public safety, in particular. In this paper two related bicriteria mathematical programming models are developed for identifying the trade-offs between overall output (effectiveness) and equity that result from alternative allocations of service resources among different service delivery sites (branches). The models developed here incorporate equity in a more satisfactory manner than have previous efforts. An illustrative application of the models to the allocation of new books among the branches of a public library system is presented. [ABSTRACT FROM AUTHOR]

The radio frequency communication environment, for example, in large vessels, aircraft, space vehicles, and satellites, has become increasingly complex as more and more transmitters, receivers, and corresponding communication nets are being added to perform multiple functions. This paper discusses some of the problems faced by a decision maker in managing a communication network. A particular and important problem worth investigating occurs when different frequencies are simultaneously active in a network. This may cause various types of interference creating a disturbance in communication. One interesting and important type of interference, which may be expressed mathematically, is intermodulation. A typical problem scenario is thus to assign frequencies to the different nets of the network so that intermodulation interference is within desirable limits. A second problem is to add a net to an existing network, with previously assigned frequencies, so that the new net produces an acceptable level of intermodulation interference. Besides these, other related problems may be defined. For many problem scenarios, related integer nonlinear programming models may be derived. These models, corresponding algorithms and related software are discussed. [ABSTRACT FROM AUTHOR]

This paper provides a survey of model management literature within the mathematical modeling domain. The first part of the survey is a review and a summary of the literature. After giving some basic definitions of modeling, modeling life cycle, and model management, two representative algebraic modeling languages followed by three approaches to modeling are introduced. These approaches are database, graph-based, and knowledge-based. The discussion is followed by a review of two specialized model management systems. The second part of the survey is a categorization of various modeling systems based on the modeling functions they provide and some of their features. These functions include life cycle support and model base administration. The degree of model independence provided by model management systems and the implemented environment systems is also summarized. The last part of the paper provides directions for future research. [ABSTRACT FROM AUTHOR]

This paper deals with a mathematical model designed to provide guidelines for managing a land resource over an extended period of time. We develop a framework which permits sequences of management decisions to be conveniently formulated, and their associated costs and benefits specified. This takes the form of a network. Each path in the network represents a possible decision sequence. We study how to select suitable decision sequences and what proportion of the resource to manage with each selected sequence, so as to optimize some specified objective and meet the constraints imposed on management of the resource. An L.P. model is formulated. The solution strategy decomposes the L.P. matrix using Dantzig-Wolfe decomposition and solves the subproblems efficiently by dynamic programming or a network flow algorithm. Computational aspects are discussed and the concepts and procedures are illustrated in the Appendix, for forest management. [ABSTRACT FROM AUTHOR]

This paper considers a stationary discrete dynamic programming model that is a generalization of the finite state and finite action Markov programming problem. We specify conditions under which an optimal stationary linear decision rule exists and show how this optimal policy can be calculated using linear programming, policy iteration, or value iteration. In addition we allow the parameters of the problem to be random variables and indicate when the expected values or these random variables are certainty equivalents. [ABSTRACT FROM AUTHOR]

This paper discusses means of introducing decision maker input into the goal programming model in order to produce more satisfactory solutions. Both formal interactive methods and informal trial-and-error approaches are discussed. The design criteria for the choice of the initial test solution and the stopping criteria for the final solution are detailed. The area of presentation of results to, and elicitation of preferences from, the decision maker is dealt with. Practical suggestions for means of parameter alteration to produce alternative solutions are given. Finally, the integration of the above issues into an integrated framework is discussed. [ABSTRACT FROM AUTHOR]

The value of mathematical modeling and analysis in the decision support context is well recognized. However, the complex and evolutionary nature of the modeling process has limited its widespread use. In this paper, we describe our work on knowledge-based tools which support the formulation and revision of mathematical programming models. in contrast to previous work on this topic, we base our work on an indepth empirical investigation of experienced modelers and present three results: (a) a model of the modeling process of experienced modelers derived using concurrent verbal protocol analysis. Our analysis indicates that modeling is a synthetic process that relates specific features found in the problem to its mathematical model. These relationships. which are seldom articulated by modelers, are also used to revise models. (b) an implementation of a modeling support system called MODFORM based on this observationally derived model, and (c) the results of a preliminary experiment which indicates that users of MODFORM build models comparable to those formulated by experts. We use the formulation of mathematical programming models of production planning problems illustratively throughout the paper. [ABSTRACT FROM AUTHOR]

Variants of Markovian decision models are many. Of those concerned with the estimation of transition probabilities, few deal with the case of limited information in which only data on market shares are available. Where such investigations have been undertaken, the assumption of constant transition probabilities has been insurmountable. This paper offers a simple heuristic technique to estimate nonstationary transition probabilities, especially in the case where fluctuations in market shares are felt to reflect the effects of secondary considerations external to the transition probabilities as well as effects of the probabilities themselves. Dynamic and quadratic programming are the suggested tools of analysis. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with imposing constraints directly on the admissible majority decisions so as to insure transitivity without restricting individual preference orderings. We demonstrate that this corresponds to requiring that majority decisions be confined to the extreme points of a convex polyhedron. Thus, transitive majority decisions can be characterized as basic solutions of a set of linear inequalities. Through the use of a majority decision function (which is not restricted to be linear) it is shown that constrained majority rule is equivalent to an integer programming problem. Some special forms of majority decision functions are studied ineluding the generalized lp norm and an indicator function. Implications of an integer programming solution, including alternate optima and post optimality analysis, are also discussed. [ABSTRACT FROM AUTHOR]

This paper treats a Markov decision problem with an infinite planning horizon and no discounting. This model is analyzed by application, perhaps repeated, of a simple linear program. [ABSTRACT FROM AUTHOR]

Triangular fuzzy reciprocal preference relations (TFRPRs) are good choices to denote the decision makers' fuzzy preferences. Consistency analysis is a very important topic to preference relations that can avoid the illogical ranking order. However, all previous multiplicative consistency concepts for TFRPRs cannot well address this type of preference relations. To address this issue, this paper introduces a new multiplicative consistency concept for TFRPRs, which can be seen as a natural extension of Tanino's multiplicative consistency concept for reciprocal preference relations. Based on the new consistency concept, 0–1 mixed programming models for judging the multiplicative consistency of TFRPRs are constructed, and an approach for deriving multiplicative consistent TFRPRs is provided. Considering the incomplete case, programming models to determine missing values are constructed. Subsequently, a multiplicative consistency based method for decision making with TFRPRs is presented that can address the inconsistent and incomplete cases. Meanwhile, illustrative examples are provided to show the concrete application of the proposed procedure, and comparison analysis is also made. [ABSTRACT FROM AUTHOR]

Consistency analysis is very important to ensure the reasonable ranking order. However, all previous consistency concepts for interval multiplicative preference relations (IMPRs) are insufficient to address this type of preference relations. This paper introduces a new consistency concept for IMPRs that is a natural extension of the Saaty’s consistency concept for multiplicative preference relations. Several desirable properties are discussed, and the relationship between the new concept and two previous ones is studied. Then, a method to judge the consistency of IMPRs is proposed. Considering the inconsistent case, a 0–1 mixed programming model to derive consistent IMPRs from inconsistent ones is established. To determine missing values in incomplete HFPRs, 0–1 mixed programming models are constructed that can address the situation where ignore objects exist. Meanwhile, illustrative examples are offered to show the feasibility and efficiency of the developed theoretical results, and comparison analysis is provided. Finally, a consistency analysis based algorithm to decision making with IMPRs is developed that can address inconsistent and incomplete cases. [ABSTRACT FROM AUTHOR]

This paper focuses on a multidemand multisource order quantity allocation problem with multiple transportation alternatives. To solve this problem, a bilevel multiobjective programming model under a mixed uncertain environment is proposed. Two levels of decision makers are considered in the model. On the upper level, the purchaser aims to allocate order quantity to multiple suppliers for each demand node with the consideration of three objectives: total purchase cost minimization, total delay risk minimization, and total defect risk minimization. On the lower level, each supplier attempts to optimize the transportation alternatives with total transportation and penalty costs minimization as the objective. In contrast to prior studies, considering the information asymmetry in the bilevel decision, random and fuzzy random variables are used to model uncertain parameters of the construction company and the suppliers. To solve the bilevel model, a solution method based on Kuhn-Tucker conditions, sectional genetic algorithm, and fuzzy random simulation is proposed. Finally, the applicability of the proposed model and algorithm is evaluated through a practical case from a large scale construction project. The results show that the proposed model and algorithm are efficient in dealing with practical order quantity allocation problems. [ABSTRACT FROM AUTHOR]

Best-worst method (BWM) has attracted increasing attention. It has been generalized to different fuzzy environments and applied to various real-life decision problems. This article develops a new intuitionistic fuzzy (IF) BWM (IFBWM) for multicriteria decision-making. When a decision maker (DM) makes comparisons, there may be some hesitancies. Thus, the reference comparisons are represented as intuitionistic fuzzy values (IFVs), the Best-to-Others vector and the Others-to-Worst vector are IF vectors. According to the multiplicative consistency of intuitionistic fuzzy preference relation, this article gives the consistency equations and views them as IF equations. The derivation of optimal IF weights of criteria is formulated as an IF decision-making problem. Thereby, a mathematical programming model is constructed to assure that the derived optimal IF weights of criteria is a normalized IF weight vector. Depending on the risk preference of DM, four linear programming models are presented to obtain the optimal IF weights based on the constructed mathematical programming model for the optimistic DM, the pessimistic DM, and the neutral DM, respectively. Furthermore, this article investigates the process of improving the consistency. Several examples are demonstrated to show the application and effectiveness of the proposed IFBWM. [ABSTRACT FROM AUTHOR]

Abstract: The optimal placement of turbines in a wind farm is critical to the maximization of power production. In this paper, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen's wake decay model to represent multi-turbine wake effects. We develop mixed integer linear and quadratic optimization formulations and apply them to several example layout cases in the literature. Compared to previous approaches, our models produce layouts that tend to be more symmetric and that generate slightly more power. Our formulations solve quickly, allowing a decision maker to efficiently explore the impact of different turbine densities in a wind farm. [Copyright &y& Elsevier]

Abstract: This paper deals with a minimum spanning tree problem where each edge cost includes uncertainty and importance measure. In risk management to avoid adverse impacts derived from uncertainty, a d-confidence interval for the total cost derived from robustness is introduced. Then, by maximizing the considerable region as well as minimizing the cost-importance ratio, a biobjective minimum spanning tree problem is proposed. Furthermore, in order to satisfy the objects of the decision maker and to solve the proposed model in mathematical programming, fuzzy goals for the objects are introduced as satisfaction functions, and an exact solution algorithm is developed using interactive decision making and deterministic equivalent transformations. Numerical examples are provided to compare our proposed model with some previous models. [Copyright &y& Elsevier]