Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods

There are several methods, in literature, for finding the fuzzy optimal solution of fully fuzzy transportation problems (transportation problems in which all the parameters are represented by fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings, two new methods (based on fuzzy linear programming formulation and classical transportation methods) are proposed to find the fuzzy optimal solution of unbalanced fuzzy transportation problems by representing all the parameters as trapezoidal fuzzy numbers. The advantages of the proposed methods over existing methods are also discussed. To illustrate the proposed methods a fuzzy transportation problem (FTP) is solved by using the proposed methods and the obtained results are discussed. The proposed methods are easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems occurring in real life situations.

Measuring the Effect of the Rules and Regulations on Global Malmquist Index

The circle-type or global Malmquist index, which is based on Data Envelopment Analysis (DEA) models, is an important index that is widely used for measuring the relative productivity change of decision-making units (DMUs) in multiple time periods. This index, similar to the standard approach of measuring the productivity change using the standard Malmquist index, breaks down into various components, which can then be used to measure the impact of the efficiency, technology, and scale on productivity changes over time. However, empirical studies show that there are some rules and regulations that can affect the result of the productivity changes. Therefore, this paper presents new insight into the global Malmquist index for measuring the effect of the rules and regulations on productivity changes that come from imposing some trade-offs to the production possibility set of the problem, and provides a new decomposition of this index.

Sequential Test for Arbitrary Ratio of Mean Times Between Failures

This paper describes a planning methodology and tools for a truncated SPRT (sequential probability ratio test) for checking the means ratio of the times between failures (assumed to be exponentially distributed) of two items. The problem is considered for the situation in which the ratio may differ from unity, whereby the results are applicable for any specified ratio, or wherever multiple copies of each item are tested simultaneously (group test). The authors present a methodology for optimal test choice and dependences for determining the acceptance/rejection boundaries of such a test with given characteristics. Planning and implementation of a group test are illustrated in an example, including substantiation of the choice of the number of new-item copies.

Information in Fleeting Opportunities

This paper focuses on the study of information in fleeting opportunities. An application example is the evaluation of business proposals by venture capitalists. The authors formulate the generic problem as a dynamic program where the decision maker can either accept a given deal directly, reject it directly, or seek further information on its potential and then decide whether to accept it or not. Results show well behaved characteristics of the optimal policy, deal flow value, and the value of information over time and capacity. It is presumed that the risk preference of the decision maker follows a linear or an exponential utility function. This approach is illustrated through several examples.

Data Envelopment Analysis with Fuzzy Parameters

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. In the conventional DEA, all the data assume the form of specific numerical values. However, the observed values of the input and output data in real-life problems are sometimes imprecise or vague. Previous methods have not considered the preferences of the decision makers (DMs) in the evaluation process. This paper proposes an interactive evaluation process for measuring the relative efficiencies of a set of DMUs in fuzzy DEA with consideration of the DMs’ preferences. The authors construct a linear programming (LP) model with fuzzy parameters and calculate the fuzzy efficiency of the DMUs for different a levels. Then, the DM identifies his or her most preferred fuzzy goal for each DMU under consideration. A modified Yager index is used to develop a ranking order of the DMUs. This study allows the DMs to use their preferences or value judgments when evaluating the performance of the DMUs.

Optimizing Series Repairable Systems with Imperfect Repair

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

Local Perturbation Analysis of Linear Programming with Functional Relation Among Parameters

In this paper, the authors study the sensitivity analysis for a class of linear programming (LP) problems with a functional relation among the objective function parameters or those of the right-hand side (RHS). The classical methods and standard sensitivity analysis software packages fail to function when a functional relation among the LP parameters prevail. In order to overcome this deficiency, the authors derive a series of sensitivity analysis formulae and devise corresponding algorithms for different groups of homogenous LP parameters. The validity of the derived formulae and devised algorithms is corroborated by open literature examples having linear as well as nonlinear functional relations between their vector b or vector c components.

An Integrated Vendor-Buyer Model with Uncertain Lead Time, Life Time under Inflation and Variable Holding Cost

This study considers the problem of a vendor which supplies an item to the buyer with imprecise partial backlogging rate of unsatisfied demand and non instantaneous deterioration rate considering variable holding cost, the effect of inflation and time value of money. The supplier’s lead time is a stochastic function of his managing cost. The extra costs incurred by the retailer due to the uncertain lead time in terms of shortage costs or lost sales costs should be owed by the supplier. A numerical example is cited to illustrate the results and its significant features. Finally, to study the effect of changes of demand parameters, deterioration, inflation and managing cost on supplier and the retailer’s profit, a sensitivity analysis is presented numerically.

Highway Alignment Optimization Using Cost-Benefit Analysis Under User Equilibrium

Usually, selection of a highway alignment depends on an economical route that minimizes alignment sensitive costs, such as construction cost, user cost, right-of-way cost, and earthwork cost. Most of the available highway alignment optimization algorithms do not consider traffic assignment and distribution of traffic as a result of the new road network consisting of the new alignment as well as other pre-existing alignments. Constructing a new highway will ease the traffic in the existing road network. Based on Wardrop’s principle, the users will choose a route that will minimize their travel-time. Users will unilaterally shift to the available routes for their benefit and thus, traffic flow will attain equilibrium. Theoretically, the equilibrium of traffic flow between the existing highway and the newly designed highway alternative can be achieved by a user equilibrium model. A new methodology is developed in this paper to optimize a new three-dimensional highway alignment based on the existing highway alignment system information using a cost-benefit analysis approach. The results are quite promising for new road design and bypass construction since benefit maximization and cost minimization is performed simultaneously while attaining user equilibrium.