a b s t r a c tIn this paper, we introduce the possibilistic mean value and variance of continuous distribution, rather than probability distributions. We propose a multi-objective Portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation. For quantifying any potential return and risk, portfolio liquidity is taken into account and a multi-objective non-linear programming model for portfolio rebalancing with transaction cost is proposed. The models are illustrated with numerical examples.

This article investigates the effects of lost sales reduction and quality improvement in an imperfect production process under imprecise environment with simultaneously optimizing reorder point, order quantity, and lead time. This study assumes that the demand during lead time follows a mixture of normal distributions and the cost components are imprecise and vague. Under these assumptions, the aim is to study the lost sales reduction and the quality improvement in an uncertainty environment. The objective function in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method (MGMIRM). For the defuzzified objective function, theoretical results are developed to establish optimal policies. Finally, some numerical examples and sensitivity analysis are provided to examine the effects of non-stochastic uncertainty.

This study investigates an economic order quantity model of deteriorating items, where demand is fuzzy in nature and depends on promotional effort with full backorder for a given time horizon. The learning effect in the fuzzy environment is added in this model. A constant deterioration rate is assumed. Under these circumstances, a mathematical model is developed to curtail the total cost over a finite time horizon by determining the replenishment order quantity, number of replenishments, and the fraction of the replenishment cycle when inventory is positive. A solution algorithm is developed to find the optimal solutions. The applicability of the proposed model is illustrated through numerical examples. To get further insights, sensitivity analysis is carried out for the main parameters in crisp, fuzzy, and fuzzy-learning environments.

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A gravity model for trip distribution describes the number of trips between two zones, as a product of three factors, one of the factors is separation or deterrence factor. The deterrence factor is usually a decreasing function of the generalized cost of traveling between the zones, where generalized cost is usually some combination of the travel, the distance traveled, and the actual monetary costs. If the deterrence factor is of the power form and if the total number of origins and destination in each zone is known, then the resulting trip matrix depends solely on parameter, which is generally estimated from data. In this paper, it is shown that as parameter tends to infinity, the trip matrix tends to a limit in which the total cost of trips is the least possible allowed by the given origin and destination totals. If the transportation problem has many cost-minimizing solutions, then it is shown that the limit is one particular solution in which each nonzero flow from an origin to a destination is a product of two strictly positive factors, one associated with the origin and other with the destination. A numerical example is given to illustrate the problem.

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The paper presents an information-theoretic algorithm for solving constrained non-linear programming problems based upon the principle of minimum cross-entropy and surrogate mathematical programming. It is an alternative to the earlier work by Templeman and Li [4-61 based on the maximum entropy principleand so far as the rate ofconvergence of the solution is concerned it is an improvement upon it. The merit of the present technique is illustrated with two numerical examples.

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