This paper provide a profound study on optimum allocation of two stage multivariate stratified Warner’s randomized response (RR) model with linear and non linear cost function. The multi-objective problem is formulated as a Geometric Programming Problem (GPP). The fuzzy programming approach is adopted to solve the formulated problem. A numerical example is given to illustrate the computational details of the suggested method.

Fuzzy Geometric Programming Approach in Multivariate Stratified Sample Surveys Under Two Stage Randomized Response Model

This article addresses the problem of estimating the population distribution function for stratified random sampling in the presence of non-response. We suggest a generalized class of estimators for estimating the finite cumulative distribution function using the auxiliary information. Expressions for bias and mean squared error are derived up to the first order of approximation. The performance of the estimators are compared both theoretically and numerically. A real data set is used to support the theoretical findings. 

Estimation of population distribution function in the presence of non-response using stratified random sampling

Problem of Compromise Allocation in Multivariate Stratified Sampling Using Intuitionistic Fuzzy Programming

 In this paper, we have formulated the problem of non-response in multivariate stratified sample surveys as a Multi-Objective Geometric Programming problem (MOGPP). The fuzzy programming approach has described for solving the formulated MOGPP. The formulated MOGPP has been solved and the solution is obtained. The obtained solution is the dual solution corresponding to the multi-objective multivariate stratified sample surveys in presence of non-response. Afterward with the help of dual solution of formulated MOGPP and primal-dual relationship theorem the optimum allocation of sample sizes of respondents and non respondents are obtained. A numerical example is given to illustrate the procedure.

Fuzzy Geometric Programming Approach in Multi-objective Multivariate Stratified Sample Surveys in Presence of Non-Response

The petroleum industry has a complex, inflexible and challenging supply chain (SC) that impacts both the national economy as well as people’s daily lives with a range of services, including transportation, heating, electricity, lubricants, as well as chemicals and petrochemicals. In the petroleum industry, supply chain management presents several challenges, especially in the logistics sector, that are not found in other industries. In addition, logistical challenges contribute significantly to the cost of oil. Uncertainty regarding customer demand and supply significantly affects SC networks. Hence, SC flexibility can be maintained by addressing uncertainty. On the other hand, in the real world, decision-making challenges are often ambiguous or vague. In some cases, measurements are incorrect owing to measurement errors, instrument faults, etc., which lead to a pentagonal fuzzy number (PFN) which is the extension of a fuzzy number. Therefore, it is necessary to develop quantitative models to optimize logistics operations and supply chain networks. This study proposed a linear programming model under an uncertain environment. The model minimizes the cost along the refineries, depots, multimode transport and demand nodes. Further developed pentagonal fuzzy optimization, an alternative approach is developed to solve the downstream supply chain using the mixed-integer linear programming (MILP) model to obtain a feasible solution to the fuzzy transportation cost problem. In this model, the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number. Furthermore, defuzzification is performed using an accuracy function. To validate the model and technique and feasibility solution, an illustrative example of the oil and gas SC is considered, providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study. 

Multimodal Fuzzy Downstream Petroleum Supply Chain: A Novel Pentagonal Fuzzy Optimization

Non-linear programming problems can be solved efficiently by geometric programming in which non-linear expressions can be expressed by an exponential or power functions. In this paper, Double Sampling Stratification (DSS) strategy is used in multivariate stratified population with unidentified strata weights, for optimum sampling design (OSD) in the presence of non-response to estimate the unidentified population means. The double sampling problem in the presence of non-response is formulated as Fuzzy Multiobjective Convex Programming Problem (FMOCPP). Then, we convert FMOCPP into Fuzzy Single Objective Convex Problem (FSOCP) by using membership function. Dual solution is obtained using LINGO Software by solving FSOCP. The optimum allocations of sample sizes of respondents and non- respondents for both the phases are obtained by applying dual solutions and primal-dual relationship theorem. The given technique is illustrated by projecting a numerical problem.

/pdf/a-new-fuzzy-multiobjective-geometric-programming-in-double-2xlrx58apb.pdf

A New Fuzzy Multiobjective Geometric Programming in Double Sampling in Presence of Non-Response

This paper deals with fuzzy goal programming (FGP) approach to stochastic multivariate stratified sampling with non linear objective function and probabilistic non linear cost constraint which is formulated as a multiobjective non linear programming problem (MONLPP). In the model formulation of the problem, we first determine the individual best solution of the objective functions subject to the system constraints and construct the non linear membership functions of each objective. The non linear membership functions are then transformed into equivalent linear membership functions by first order Taylor series at the individual best solution point. Fuzzy goal programming approach is then used to achieve maximum degree of each of the membership goals by minimizing negative deviational variables and finally obtain the compromise allocation. A numerical example is presented to illustrate the computational procedure of the proposed approach.

/pdf/a-fuzzy-goal-programming-approach-in-stochastic-multivariate-az27am1ccb.pdf

A fuzzy goal programming approach in stochastic multivariate stratified sample surveys

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A New Fuzzy Multiobjective Geometric Programming in Double Sampling in Presence of Non-Response

A fuzzy goal programming approach in stochastic multivariate stratified sample surveys