The Best-Worst Method (BWM) is one of the latest methods in Multiple Attribute Decision Making (MADM) problems. The mentioned method determines the optimal solution by forming and solving a Non-Linear programming model (NLPM). In respect to the difficulties of solving the relevant NLPM, some attempts have been made to provide Linear programming models (LPM) or Equivalent Mixed Linear programming models. But there are some deficiencies in each of the proposed models. In this paper, by removing the mentioned deficiencies, an algorithm was proposed to estimate the solution of BWM NLPM with an acceptable error by forming and solving Mixed Integer Linear programming models (MILPMs). In the suggested algorithm, first, the equivalent model of NLPM (ENLPM) was formed. Then by Piecewise Linear Approximation (PLA) using the SOS2 method, the non-Linear sentences of ENLPM were approximated and the first MILP model was formed and solved. If the error of solution is not acceptable, improving the PLA of the ENLPM nonLinear sentences, the forming of new MILPMs, and its solving continues until a solution with acceptable error obtained. To investigate the reliability of the algorithm, a new method for generating samples was proposed. Then using this method, 128 samples with three and five attributes were generated. The results of implementing the proposed algorithm to solve generated samples showed the performance and efficiency of the proposed algorithm. In this regard by forming and solving a maximum of three MILPMs of the samples, an estimation of the solution with 1% error was obtained.

In this study, the strategy of effective asset allocation under uncertainty with the capability of risk control, transaction cost reduction and favorable return realization is investigated. In order to implement this strategy and to overcome the shortfalls of classic portfolio optimization models in dealing with uncertainty, the formation of an index fund using a robust approach and considering cardinality constraint became the agenda. Accordingly, in order to solve the index tracking problem, a Linear programming model as minimizing the absolute deviation between the expected return of the index fund and that of the benchmark is presented. Considering the dimension of the solution space, a Meta heuristic genetic algorithm was implemented to solve the robust counterpart of the problem. The results of the analysis imply on the selection of 20 stocks as the index fund composition and indicate good performance of the index tracking funds based on criteria such as correlation, root mean square error and the excess return using out of sample data.

Quality of products and services is considered as a key factor for customer satisfaction. Quality function deployment (QFD) is known as a critical tool for translating voice of customers to prioritize technical requirements of a production. The level of this satisfaction depends on the number of fulfilled requirements. It should be noted that this level varies according to the possible constraints.This paper aims to maximize customer satisfaction based on the possible limitations by using a fuzzy Linear programming model. In this regard, customer requirements are prioritized by using fuzzy Delphi method and then the problem is changed to a Linear programming model considering to the possible relationships in QFD.The proposed model is used as a case study for construction industry.After running the model, the percentage of optimal performance for each of the technical production requirements is defined.

We consider interval Linear programming (ILP) problems in the current paper. Best-worst case (BWC) is one of the methods for solving ILP models. BWC determines the values of the target function, but some of the solutions obtained through BWC may result in an infeasible space. To guarantee that solution is completely feasible (i.e. avoid constraints violation), improved twostep method (ITSM) has been proposed. Many solutions are lost in this method. By using an algorithm, we introduce closed ball method (namely, CBM) as a new method for solving ILP models. In this method, feasibility test ensures that solution space is feasible. To demonstrate the effectiveness of the proposed approach, we solve two numeric examples and we compare the results obtained through BWC, ITSM, and CBM.