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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 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]

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.

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 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]

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]

Abstract: Goal programming as a well known technique has been widely used for solving multi objective decision making problems. However, in some practical cases, there may exist situations where the decision maker is interested in setting multi aspiration levels for objectives that may not be expressed in a precise manner. In this paper, a novel formulation of fuzzy multi-choice goal programming (FMCGP) is presented. The proposed approach not only improves the applicability of goal programming in real world situations but also provides useful insight about the solution of a new class of problems. To illustrate and clarify the proposed approach, a numerical example is presented. [Copyright &y& Elsevier]

Abstract: In this paper, assuming cooperative behavior of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are considered. To deal with the formulated two-level linear programming problems involving fuzzy random variables, -level sets of fuzzy random variables are introduced and an -stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account the vagueness of judgments of decision makers, fuzzy goals are introduced and the -stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through the use of the fractile criterion optimization model, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. It is shown that all of the problems to be solved in the proposed interactive fuzzy programming can be easily solved by the simplex method, the sequential quadratic programming or the combined use of the bisection method and the sequential quadratic programming. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Risk management is an inherent part of supplier selection. While companies are enjoying the benefits of outsourcing, risks brought by this practice should be taken into account in the process of decision making. This paper presents a multiobjective stochastic sequential supplier allocation model to help in supplier selection under uncertainty. Demand for products, capacities at suppliers as well as transportation and other variable costs are the main sources of uncertainty and are modeled using probability distributions. Disruptions are exogenous events and the model provides proactive mitigation strategies against disruptions by assigning backup suppliers who can be used in case of a default at a primary supplier. When there is no disruption, the model’s solution is an optimal supplier order assignment, considering operational risks. [Copyright &y& Elsevier]

Abstract: Two-stage DEA (data envelopment analysis) models show the performance of individual processes, and thus are more informative than the conventional one-stage models for making decisions. This paper extends this approach from deterministic to uncertain situations, where the observations are represented by fuzzy numbers. The extension principle is utilized to develop a pair of two-level mathematical programs to calculate the lower and upper bounds of the -cut of the fuzzy efficiency. By enumerating various values of , the membership functions of fuzzy efficiencies are constructed numerically. It is found that the property of the system efficiency being equal to the product of the two process efficiencies, which holds for the deterministic case, also holds for the fuzzy case. This property can be generalized to series systems with more than two processes. An example of non-life insurance companies in Taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy. [Copyright &y& Elsevier]

Summary: This paper provides an empirical test of whether the Asian Development Bank (ADB) adjusts allocation decisions about environmentally risky projects to reflect borrower environmental performance in previous projects. This type of performance-based decision-making has been repeatedly highlighted as key to achieving favorable development assistance outcomes in a variety of programming areas. I collect recipient environmental performance information from all available post-project evaluations since 1990 and create an indicator of environmental reputation using a Bayesian updating model. I use this environmental reputation indicator to demonstrate that the ADB responds to previous borrower environmental performance when approving environmentally risky projects, but that past environmental performance does not positively influence the allocation of projects with no environmental risks. These results demonstrate that performance-based allocation decisions are possible for development organizations within specific programmatic areas when low performance is a significant risk to the core functions of the organization, which in this case is the ability to approve and disburse lending projects. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a systematic methodology is presented for the simultaneous optimal selection of raw materials, fossil fuels and alternative fuels in cement production. The aim is to offer a generic mathematical formulation that can be used as the basis for developing case specific mathematical formulations that can assist the strategic decision-making process. The mathematical model presented takes into consideration the essential elements of a cement plant operation. The final formulation is a mixed integer linear programming problem that aims at minimizing the overall operating cost. A realistic case study is presented which demonstrates the usefulness of the proposed mathematical programming methodology. [Copyright &y& Elsevier]

Abstract: Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods. [ABSTRACT FROM AUTHOR]

Abstract: Alirezaee and Afsharian have proposed a new index, namely, Balance Index, to rank DMUs. In this paper, we will use their examples to illustrate that the proposed index is not stable. As a result, the corresponding rankings are also unstable. Then we analyze where an error occurs in the new method for complete ranking of decision making units and amend it by introducing the Maximal Balance Index. The numeral example reports the reasonability of our methods. [ABSTRACT FROM AUTHOR]

This paper is primarily concerned with data envelopment analysis (DEA) of systems where negative outputs and negative inputs arise naturally. Examples of situations in which both negative inputs and negative outputs occur are given. More attention has been paid, in the literature, to the former type of problem. Most available DEA software does not solve this type of problem or copes with negative outputs and possibly negative inputs by assigning zero weights to them. A modified slacks-based measure (MSBM) model is presented, in which both negative outputs and negative inputs occur. The MSBM model overcomes the lack of translation invariance in the slacks-based measure model by drawing on the ideas from the range directional model (RDM). The MSBM model takes into account individual input and output slacks, which provides more precise evaluation of inefficient decision-making units (DMUs). It therefore, generally leads to lower efficiencies for inefficient DMUs than the RDM. [ABSTRACT FROM AUTHOR]

This paper investigates the improvements in manufacturing performance that can be realized by broadening the scope of the production scheduling function to include both job sequencing and processing-time control through the deployment of a flexible resource. We consider an environment in which a set of jobs must be scheduled over a set of parallel manufacturing cells, each consisting of a single machine, where the processing time of each job depends on the amount of resource allocated to the associated cell. Two versions of the problem are introduced: a static problem in which a single resource-allocation decision is made and maintained throughout the production horizon, and a dynamic problem in which resource can be reassigned among the production cells as local bottlenecks shift. We provide mathematical formulations for each version of the problem, establish problem complexity, identify important characteristics of optimal solutions, develop optimal and heuristic solution approaches, and report the results of a set of computational experiments. The computational results demonstrate that substantial improvements in operational performance can be achieved through effective utilization of resource flexibility. [ABSTRACT FROM AUTHOR]