Traditionally, aircraft routing and crew pairing problems are solved sequentially with the aircraft routing problem solved first followed by the crew pairing problem. But in some cases, the results are suboptimal. In order to overcome this problem, both problems will be composed in one model. Although the integration model is challenging to solve but it is practically useful in airlines operations for getting the optimal solutions. In this study, we proposed the constructive heuristic method and the genetic algorithm (GA) in producing the feasible paths. After that, we will solve those two types of feasible paths in the integrated model by using three approaches which are the integer linear programming (ILP), Dantzig Wolfe decomposition method and Benders decomposition method. Computational results show that the obtained feasible path from the constructive heuristic method and solved by the Dantzig Wolfe decomposition method is more effective while the paths from the GA and solved by the Dantzig Wolfe decomposition method is good in finding the minimum computational time. From the results obtained, all the flight legs and crew pairing are used only once. There are four type of aircrafts are used in testing the performance of the approaches which based on local flights in Malaysia for seven days. The solutions of the feasible paths from GA is more advantageous in term of the computational times compare to the solutions by using the feasible paths from constructive heuristic method.

In airline operations planning, there are four problems which are schedule design, fleet assignment, aircraft routing and crew pairing problem. Those problems are sequentially and interdependent. Aircraft routing and crew pairing problem are hard to solve and normally crew pairing problem dependent to the aircraft routing problem which gives the suboptimal solutions. As minimizing the costs is important in the airline system, so in order to tackle suboptimal solutions, aircraft routing problem and crew pairing problem are being integrated in one model. For solving the integrated model, the feasible aircraft routes and crew pairs are required. Because of that, a method is being proposed in this work for generating the feasible aircraft routes and crew pairs which is the constructive heuristic method. By using the generic aircraft routes and crew pairs, the integrated model then being solve by two approaches. The first approach is the exact method called the integer linear programming (ILP) while the second approach is from the heuristic method called particle swarm optimization. Encouraging results are encountered by testing on four types of aircrafts for one week flight cycle from local flights in Malaysia.

In this paper, we present the numerical results of the Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet problem for an elliptic type Partial Differential Equation (PDE) with a variable coefficient. The numerical constructions are based on discretizing the boundary of the problem region by utilizing continuous linear iso-parametric elements while the domain of the problem region is meshed by using iso-parametric quadrilateral bilinear domain elements. We also use a semi-analytic method to handle the integration that exhibits logarithmic singularity instead of using Gauss-Laguare quadrature formula. The numerical results that employed the semi-analytic method give better accuracy as compared to those when we use Gauss-Laguerre quadrature formula. The system of equations that obtained by the discretized BDIDE is solved by an iterative method (Neumann series expansion) as well as a direct method (LU decomposition method). From our numerical experiments on all test domains, the relative errors of the solutions when applying semi-analytic method are smaller than when we use Gauss-Laguerre quadrature formula for the integration with logarithmic singularity. Unlike Dirichlet Boundary Integral Equation (BIE), the spectral properties of the Dirichlet BDIDE is not known. The Neumann iterations will converge to the solution if and only if the spectral radius of matrix operator is less than 1. In our numerical experiment on all the test domains, the Neumann series does converge. It gives some conclusions for the spectral properties of the Dirichlet BDIDE even though more experiments on the general Dirichlet problems need to be carried out.

In this paper, we show that we have two approaches in implementing of Boundary-Domain Integro-Differential Equation (BDIDE) associated to Dirichlet Boundary Value Problem (BVP) for an elliptic Partial Differential Equation (PDE) with a variable coefficient. One way is by choosing the collocation points at all nodes i.e. on the boundary and interior domain. The other approach is choosing the collocation points for the interior nodes only. We present the numerical implementation of the BDIDE associated to Dirichlet BVP for an elliptic PDE with a variable coefficient by using the second approach. The BDIDE is consisting of several integrals that exhibit singularities. Generally, the integrals are evaluated by using Gauss- Legendre quadrature formula. Our numerical results show that the use of semi-analytic method gives high accuracy results. The discretized BDIDE yields a system of equations. We then apply by a direct method i.e. LU decomposition method to solve the systems of equations. In all the test domains, we present the relative errors of the solutions and the relative error for the gradient.

ABSTRACT This research is a case study to identify the best criteria that a person should have as the leader of Malaysia School Youth Cadet Corps (Kadet Remaja Sekolah (KRS)) at SMK Ahmad Boestamam, Sitiawan in order to select the most appropriate person to hold the position. The approach used in this study is Analytical Hierarchy Process (AHP) which include pairwise comparison to compare the criteria and also the candidates. There are four criteria namely charisma, interpersonal communication, personality and physical. Four candidates (1, 2, 3 and 4) are being considered in this study. Purposive sampling and questionnaires are used as instruments to obtain the data which are then analyzed by using the AHP method. The final output indicates that Candidate 1 has the highest score, followed by Candidate 2, Candidate 4 and Candidate 3. It shows that this method is very helpful in the multi-criteria decision making when there are several options available.