In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.
Engineers design systems to be reliable and work to fulfil their missions without failure for a specific period. However, the system components deteriorate with time and lead to its failures. A frequent system failure increases the management costs, hence posing a challenge to decision-makers. Therefore, for the avoidance of frequent system failures, preventive maintenance is necessary. The objective of any manufacturing firm is to maximize profit and minimize costs. The interval for preventive maintenance can be optimized if the system's availability is maximized and its cost function minimized. This study evaluates the availability and cost function for a continuous operating series-parallel system under a fixed time environment. A multiobjective model is formulated to maximize the availability and minimize the cost function of the system. The study illustrated a numerical example and solved using goal programming (GP), fuzzy goal programming (FGP), genetic algorithm (GA), and particle swarm optimization (PSO) techniques. The results are compared using a robust statistical test and, the PSO proves to be better. A simulation study was carried out further to evaluate the availability and cost function using R and MATLAB packages.
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