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In recent decades, due to reduction in precipitation, groundwater resource management has become one of the most important issues considered to prevent loss of water. Many solutions are concerned with the investigation of groundwater flow behavior. In this regard, development of meshless methods for solving the groundwater flow system equations in both complex and simple aquifers' geometry make them useful tools for such investigations. The independency of these methods to meshing and remeshing, as well as its capability in both reducing the computation requirement and presenting accurate results, make them receive more attention than other numerical methods. In this study, meshless local Petrov–Galerkin (MLPG) is used to simulate groundwater flow in Birjand unconfined aquifer located in Iran in a transient state for 1 year with a monthly time step. Moving least squares and cubic spline are employed as approximation and weight functions respectively and the simulated head from MLPG is compared to the observation results and finite difference solutions. The results clearly reveal the capability and accuracy of MLPG in groundwater simulation as the acquired root mean square error is 0.757. Also, with using this method there is no need to change the geometry of aquifer in order to construct shape function.

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This paper proposes a multi-objective mathematical formulation and a hybrid approach to solve buffer sizing and machine allocation problems simultaneously in unreliable production and assembly lines. This paper unlike prior researches assumes that time-dependent parameters of production systems are generally distributed (e.g., uniform, normal, gamma, etc.) and not only deterministic or exponential. This paper proposes a multi-objective mixed binary integer nonlinear mathematical model to solve the problem of buffer sizing and machine allocation. The proposed mathematical model is capable of purchasing new machines (candidate) and also selling old machines (current available). In other words, this model compares the candidate machines to current available machines in each station based on different aspects and is capable to replace the current machines with candidate machines or to sell some of the current machines without replacement. To solve the mentioned problem, a new formulation for dealing with multi-objectiveness of the problem is proposed. This formulation generates a series of nondominated solutions, and also, it is capable of generating a non-dominated solution between two adjacent non-dominated solutions determined by decision maker. A hybrid genetic algorithm (HGA) with a new dynamic mutation probability is proposed to solve the model. Since the proposed mathematical model and the proposed solution method are novel, the proposed HGA is compared to simple genetic algorithm and non-dominated sorting genetic algorithm (NSGA-II). The computational results indicate the effectiveness of the proposed HGA.

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