Feature selection is an important step in data preprocessing, which helps  reducing the dimensionality of data and simplifying the models. This process not only reduces the computational complexity of models, but also improves their accuracy by eliminating irrelevant features and noise. The three most widely used approaches for feature selection are filter, wrapper and embedded methods.  In this paper, first we review some support vector machine based Mixed-integer Linear programming (MILP) models and Supervised Infinite Feature Selection (Inf-FS$_s$) method.  Then, we propose three hybrid approaches based on them. The first approach involves solving the relaxed linear model of the underlying  MILP model and then solving the MILP model for those features with nonzero weights, namely a smaller MILP. In the second approach, first the Inf-FS$_s$ method is applied to rank the features. Then depending on the features costs, either chooses the top features from the ranked features until budget parameter is reached  or solves a knapsack problem to select cost effective features. The third approach applies the first approach to the top $20\%$ of features ranked by Inf-FS$_s$ method. To evaluate the proposed approaches' performance, experiments are conducted on four high-dimensional benchmark datasets for fixed and random features costs. Results demonstrate that using either of the proposed approaches can significantly reduce running time of MILP models with comparable accuracies with the original MILP models.

modelled by mathematical programming and genetic algorithm. Since green supply chain issues become important and new legislations are taken into account, carbon emissions costs are included in the total costs of the supply chain. The optimisation model has the ability to minimise the total costs and provides the best solutions, which are both cost-effective and environmentally friendly.Moreover, a mathematical model and genetic algorithm are used to simulate the developments when carbon emission costs are changed and when companies are committed penalty charge. Finally, the result is shown the genetic algorithm technique is feasible in transportation network planning.

Here, we consider single vendor-buyer model with multi-product and multi-customer and multi-facility location-production-distribution problem. It is assumed that the players of the supply chain are coordinated by sharing information. Vendor manufactures produce different products at different plants with limited capacities and then distribute the products to the consumers according to deterministic demands. A Mixed integer linear fractional programming (MILFP) model is formulated and a solution approach for MILFP is discussed. Product distribution and allocation of different customers along with sensitivity of the key parameters and performance of the model are discussed through a numerical example. The results illustrate that profit achieved by the MILFP model is slightly higher than Mixed integer programming (MIP) model. It is observed that increase in the opening cost decreases the profit obtained by both MILFP and MIP models. If the opening cost of a location decreases or increases, the demand and capacity of the location changes accordingly. The opening cost dramatically changes the demand rather than the capacity of the product. Finally, a conclusion is drawn in favor of the MILFP model as a relevant approach in a logistic model searching for the optimum solution.

Data Envelopment Analysis (DEA) cannot provide adequate discrimination among efficient decision making units (DMUs). To discriminate these efficient DMUs is an interesting research subject. The purpose of this paper is to develop the mix integer linear model which was proposed by Foroughi (Foroughi A.A. A new Mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers & Industrial Engineering 60 (2011) 550-554) to present new alternative mix integer programming DEA (MIP-DEA) models which can be used to improve discrimination power of DEA and select the most BCC- efficient decision making unit (DMU). We will demonstrate that proposed model is able to select DMU throughout the real data sets.