S. K. Bhatt

Assessment of reliability in water distribution networks using entropy based measures

Entropy based expressions for measurement of reliability and redundancy have recently been reported. These measures approach assessment of the reliability of the distribution network from the intrinsic redundancy of the network layout. The paper extends earlier work on entropy functions by including a more explicit statement of the alternate paths available in the network and by recognizing that under certain circumstances, e.g., failure of some part of the network work, an outflow link from a node under normal working condition may become an inflow link to the same node. The measures are assessed by comparison with parameters measuring Nodal Pair Reliability and percentage of flow supplied at adequate pressure for a range of networks and link failure conditions in this networks. The entropy measures are shown to reflect changes in the network reliability, as measured by these two comparative parameters, very well.

Application of possibility theory to investment decisions

Carlson and Fuller (2001, Fuzzy Sets and Systems, 122, 315–326) introduced the concept of possibilistic mean, variance and covariance of fuzzy numbers. In this paper, we extend some of these results to a nonlinear type of fuzzy numbers called adaptive fuzzy numbers (see Bodjanova (2005, Information Science, 172, 73–89) for detail). We then discuss the application of these results to decision making problems in which the parameters may involve uncertainty and vagueness. As an application, we develop expression for fuzzy net present value (FNPV) of future cash flows involving adaptive fuzzy numbers by using their possibilistic moments. An illustrative numerical example is given to illustrate the results.

AN INTEGER PROGRAMMING MODEL FOR LAYOUT DESIGN OF WATER DISTRIBUTION NETWORKS

Abstract A model for the layout optimization of water distribution networks under single loadings is presented. The model uses zero-one integer programming to select the links that should form the network, while still satisfying looping, redundancy, and hydraulic requirements. This solution constitutes a starting solution to any network component optimization model. A network component optimization step, using well established design models, is then applied to this solution to refine the pipe sizes and pressure heads, thus giving a layout and component optimal solution. The model is demonstrated by application to an example.

Equivalence of various linearization algorithms for linear fractional programming

ZusammenfassungIn dieser Arbeit werden vier Algorithmen zur linearen Quotientenoptimierung betrachtet und es wird gezeigt, daß alle vier Linearisierungsverfahren vom Frank Wolfe-Typ sind. Die betrachteten Algorithmen wurden von Isbell und Marlow, Mangasarian, Bitran and Novaes sowie von Bhatt vorgeschlagen. Es wird gezeigt, daß diese Verfahren alle im wesentlichen dieselbe Folge von linearen Programmen erzeugen und damit dieselbe Folge von zulässigen Punkten, die zur Optimallösung führt.AbstractThis paper considers four algorithms for linear fractional programming and show that they are all Frank Wolfe type linearization algorithms. These algorithms are those proposed by Isbell and Marlow, Mangasarian, Bitran and Novaes; and Bhatt. It is shown that these algorithms all use essentially the same sequence of l.p.s to generate the same sequence of feasible points that leads to the optimal solution.

Sufficient optimality criteria in non-linear programming in the presence of convex equality and inequality constraints

SummarySufficient optimality criteria are derived for mathematical programs in which non-linear inequality and equality constraints are present. These are similar to those ofKuhn-Tucker andFritz John optimality criteria.ZusammenfassungFür mathematische Optimierungsprobleme mit nichtlinearen Nebenbedingungen in Ungleichungs- und Gleichungsform werden hinreichende Optimalitätskriterien entwickelt, die denen vonKuhn-Tucker undFritz John gleichen.

An existence theorem for a fractional control problem

Computational algorithms in mathematical programming have been much in use in the theory of optimal control (see, for example Refs. 1–2). In the present work, we use the algorithm devised by Dinkelback (Ref. 3) for a nonlinear fractional programming problem to prove an existence theorem for a control problem with the cost functional having a fractional form which subsumes the control problem considered by Lee and Marcus (Ref. 4) as a particular case.

RESERVOIR OPERATING POLICIES CONSIDERING RELEASE CHANGE

Abstract Optimization models have been used in reservoir management problems to facilitate the satisfaction of various demands. One frequently ignored problem is the reservoir operation quality. The resulting operation curves may have sharp changes in the storage level of the reservoir or in the release to the downstream channel, which has potentially negative impact on the quality of reservoir operation. A Goal Programming model involving a min-max objective has been developed herein to determine operating policies, which attempts to remedy such problems. The results show a significant improvement in the reservoir operation.

Fuzzy EOQ model using possibilistic approach

Purpose – The purpose of this paper is to derive an economic order quantity (EOQ) for an inventory control problem where the inventory carrying cost and the order cost are uncertain, represented by fuzzy numbers. The fuzzy numbers used herein are most general so far, represented by adaptive trapezoidal fuzzy numbers. This paper attempts to use the most general form of fuzziness to represent the uncertainty of the parameters in the inventory model.Design/methodology/approach – The fuzzy EOQ formula derivation is analytical. Given the inventory cost Cc and the order cost Co as fuzzy numbers and the demand, a crisp number and instant replenishment of inventory, a fuzzy EOQ is derived. This is done by using the possibilistic mean and the possibilistic variance of the fuzzy total inventory cost. Then for practical implementation, this quantity is defuzzyfied using the middle of the maxima (MOM) of the fuzzy EOQ, in order to get the crisp value of the EOQ that minimizes the (fuzzy) total inventory cost.Findings...

A mixed solution strategy for group multi-attribute TOPSIS model with application to supplier selection problem

Abstract In this paper we introduce a concept called (φ, λ) -mixed solution strategy for the group fuzzy TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) model using possibility concepts, objective entropy weights derived exclusively from the decision matrix, and a group decision methodology to compute criteria weights. This approach reflects both the subjective considerations of a group of decision makers and the objective information in the decision matrix. An application to the supplier selection problem illustrates the application of the proposed method.

Possibilistic characterization of (m,n) -Trapezoidal fuzzy numbers with applications

Abstract In this paper, we derive possibilistic mean, possibilistic variance, and possibilistic covariance of (m, n)-trapezoidal fuzzy numbers. Results for ordinary trapezoidal and triangular fuzzy numbers (both non-symmetric and symmetric) are derived as special cases. Furthermore, examples are provided through which we discuss weighted possibilistic moments for (m, n)-trapezoidal fuzzy numbers, using some specific weighting function.