Real Case Problem Research Articles

PROBLEM-BASED LEARNING AT AHMAD IBRAHIM KULLIYYAH OF LAWS

Problem-based learning (PBL) serves as an alternative tool in the teaching of law at the International Islamic University Malaysia (IIUM). IIUM emphasises on producing well-rounded graduates who are professionally qualified and who practice Islamic values. Problem-based learning has proven to be a very effective complementary tool in achieving this educational aim. The main elements of problem-based earning (PBL) are the study of real case problems, team work, time management, reflective journal writing and peer evaluation. All of these elements form essential parts of the Islamic education system. This paper discusses the Islamic values existing in problem-based learning and evaluates to what extent Ahmad Ibrahim Kulliyyah of Laws (AIKOL) in general, and the course Equity and Trust in particular, has successfully harmonized and integrated problem-based learning with Islamic values.

Worst-case global optimization of black-box functions through Kriging and relaxation

A new algorithm is proposed to deal with the worst-case optimization of black-box functions evaluated through costly computer simulations. The input variables of these computer experiments are assumed to be of two types. Control variables must be tuned while environmental variables have an undesirable effect, to which the design of the control variables should be robust. The algorithm to be proposed searches for a minimax solution, i.e., values of the control variables that minimize the maximum of the objective function with respect to the environmental variables. The problem is particularly difficult when the control and environmental variables live in continuous spaces. Combining a relaxation procedure with Kriging-based optimization makes it possible to deal with the continuity of the variables and the fact that no analytical expression of the objective function is available in most real-case problems. Numerical experiments are conducted to assess the accuracy and efficiency of the algorithm, both on analytical test functions with known results and on an engineering application.

Liner ship route schedule design with sea contingency time and port time uncertainty

This paper deals with a tactical-level liner ship route schedule design problem which aims to determine the arrival time of a ship at each portcall on a ship route and the sailing speed function on each voyage leg by taking into account time uncertainties at sea and at port. It first derives the optimality condition for the sailing speed function with sea contingency and subsequently demonstrates the convexity of the bunker consumption function. A mixed-integer non-linear stochastic programming model is developed for the proposed liner ship route schedule design problem by minimizing the ship cost and expected bunker cost while maintaining a required transit time service level. In view of the special structure of the model, an exact cutting-plane based solution algorithm is proposed. Numerical experiments on real data provided by a global liner shipping company demonstrate that the proposed algorithm can efficiently solve real-case problems.

Generalized linear mixed model for monitoring autocorrelated logistic regression profiles

Profile monitoring is used to monitor the regression relationship between a response variable and one or more explanatory variables over time. Many researches have been done in this area, but in most of them, the distribution of the response variable is assumed to be normal. However, this assumption is violated in many real case problems. In these instances, classic methods cannot be used for monitoring the profiles. For example, when the response variable is binary, logistic regression methods should be used rather than ordinary least square or other classic regression methods. There are some methods for monitoring logistic profiles in the literature, but the basic assumption of these methods is the independency of the consecutive observations, while this assumption is violated in some instances for example when the successive samples are taken in short intervals. This paper considers the effect of autocorrelation presence between the observations in different levels of the independent variable in a logistic regression profile on the monitoring procedure (T2 control chart) and proposes two remedies to account for the autocorrelation within logistic profiles. In one of the remedies, upper control limit of the traditional T2 control chart is modified. In the second one, we use a generalized linear mixed model (GLMM) to estimate the regression parameters and then use the T2 control chart for monitoring autocorrelated logistic regression profiles. Simulation studies show the better performance of T2 control chart when the regression parameters are estimated by the GLMM method under both step shifts and drifts.

A HYBRID TABU SEARCH FOR A VEHICLE ROUTING PROBLEM WITH DOUBLE TIME WINDOWS FOR THE DEPOT AND MULTIPLE USE OF VEHICLES: CASE OF FUEL DELIVERY

We address in this paper a distribution real case problem facing the fuel supplying companies. The cost of acquiring vehicles is often more significant than the routing cost. The goal is to minimise the number of required vehicles. We deal with a vehicle routing problem with double time windows for the depot and multiple use of vehicles (VRPDM). There is a single depot with double time windows, the first window is for travelling and the second one (smaller) is for loading vehicles. The problem consists of designing and assigning routes to vehicles while considering time windows and capacity constraints. To solve this problem a hybrid tabu search based approach is proposed with a new heuristic for scheduling and assignment routes to vehicles. The computational results are reported for a set of 70 instances with 100 clients, and compared to those of evolutionary approach.

Liner shipping service network design with empty container repositioning

This paper proposes a liner shipping service network design problem with combined hub-and-spoke and multi-port-calling operations and empty container repositioning. It first introduces a novel concept – segment – defined as a pair of ordered ports served by one shipping line and subsequently develops a mixed-integer linear programming model for the proposed problem. Extensive numerical experiments based on realistic Asia–Europe–Oceania shipping operations show that the proposed model can be efficiently solved by CPLEX for real-case problems. They also demonstrate the potential for large cost-savings over pure hub-and-spoke or pure multi-port-calling network, or network without considering empty container repositioning.

Combined forecasts in portfolio optimization: A generalized approach

In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean–variance–skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized.

A Goal Programming model for Aggregate Production Planning problem

Aggregate Production Planning (APP) involves the simultaneous determination of company's production, inventory and employment levels over a finite time horizon to minimise the total costs while meeting the forecasted demand. Other objectives can be to minimise the fluctuation on the employment levels, the inventory levels or to reach some standard on the performance levels. The objective of this paper is to propose an effective method to elaborate an aggregate plan which takes into account the manager's preferences. We propose a Goal Programming (GP) approach, with satisfaction functions. This latter has not been used in the field of APP. Applied to a real case problem, weighted GP has initially been used; the results were not satisfactory for the manager. Our GP with satisfaction function gives, very satisfactory results for the manager.

Selection of 3PL service providers: a combined approach of AHP and Graph theory

3PL service provider helps the shippers in achieving their strategic objectives hence becoming vital in the logistics outsourcing. Shippers need to have a careful evaluation and selection before offering an important outsourcing contract. The selection process involves the identification of potential criteria and performance assessment of 3PL service providers with reference to selected criteria thus necessitates systematic methodology. The present work, proposes a methodology based on combined approach of Analytic Hierarchy Process (AHP) and Graph theory. A LSP selection index which evaluates and ranks the 3PL service providers have been derived to help shippers. The paper also proposes coefficients of similarity, coefficients of dissimilarity and the identification sets for further comparison of 3PL service providers. A real case problem of a MNC has been illustrated to help the logistics managers for their logistics outsourcing assignments.

Dynamic penalty function method for the side constrained traffic assignment problem

The traffic assignment problem (TAP) is traditionally defined without side constraints. Although introducing side constraints into the TAP is used as a way of refining applied assignment models, it brings some computational difficulties that prevent the refined model from being applicable in real-case problems. In this paper an iterative solution algorithm is developed for TAP with linear side constraints. This method is based on implicitly considering the side constraints by means of adding a dynamic penalty function (DPF) to the link travel times. Each of the iterations of the algorithm is reduced to an unconstrained assignment followed by updating the penalty functions. The unconstrained assignment is carried out using the linearization method that has been derived from the complementarity formulation of TAP. The implementation of the algorithm and computational experiments on some well-known networks are also presented for two types of side constraint, i.e. link and node capacity constraints. For the link-type side constraint, compared to the reported results of the existing alternative approaches, a DPF algorithm finds feasible solutions with better Beckmann’s objective functions in less number of iterations. For the node-type constraints, the algorithm also shows good performance.

Detecting Causes of Variances in Operational Outputs of Manufacturing Organizations: A Forensic Accounting Investigation Approach

With the introduction of the International Standard on Auditing number 240 (ISA240) there has been a paradigm shift in auditing as auditors are now required to identify and assess the risks of material misstatements due to fraud at the financial statement level and to evaluate the sufficiency, implementation and the effectiveness of the controls related to those assessed prone to fraud. This, of course, implies that statutory audit must now take the garb of forensic investigations. The problem with the present system of forensic investigation is that it is focused more on financial transactions than on the totality of the entity’s operations and often time neglects areas where there have been constant leakages of other organizational resources that are of financial consequences but which are not easily detected with a normal analysis of the financial statement. This paper attempts to offer suggestions using real case problem on how to apply forensic accounting in investigating variances and suspected fraudulent activities in manufacturing processes. It employs both empirical and supervised experimental modules integrated with the normal audit tools in unearthing fraudulent acts perpetrated over many accounting periods.

A PLATFORM APPROACH FOR HARDWARE/SOFTWARE CO-DESIGN WITH SUPPORT FOR RTOS-BASED SYSTEMS

We propose a new flow for hardware/software co-design, based on the platform-based design, which forms a base for further automation attempts of the co-design process. We prove the applicability of the proposed flow on co-designing generic systems as well as RTOS-based systems. Our proposed flow starts with a software-only solution in which all system functionality is described as embedded software targeting a selected platform. Then, the flow iterates through co-verification, profiling, partitioning, and co-synthesis until the design criteria are met. We present four test cases to show the effectiveness of our proposed methodology. The main contribution added by the proposed methodology is incorporating the target application platform at the first stage of the flow then applying our iterative co-design algorithm without altering the main platform. This opposes other co-design methodologies that let the platform details be synthesized at later stages, widening the exploration space to be unrealistic and producing platforms that may vary to a large extent compared to the pre-verified application platform. The other contribution is the study provided on the effect of co-design on the behavior of RTOS-based platforms, which brings the flow closer to real-case problems, where most embedded systems utilize RTOS in their software stack.

On the equivalence of extrapolation and Richardson’s iteration and its applications

Sometime ago two articles [G. Opfer, G. Schober, Richardson’s Iteration for Nonsymmetric Matrices, Linear Algebra Appl. 58 (1984) 343–361; A. Hadjidimos, The Optimal Solution to the Problem of Complex Extrapolation of a First Order Scheme, Linear Algebra Appl. 62 (1984) 241–261] appeared the same year in this journal solving the problem of optimizing the convergence factor of the stationary Richardson’s iteration (i.e., x ( m+1) = x ( m) − a( Ax ( m) − b), m = 0,1,2, …) for the solution of the system Ax = b, A ∈ C n , n , det( A) ≠ 0, b ∈ C n . In Opfer and Schober [G. Opfer, G. Schober, Richardson’s Iteration for Nonsymmetric Matrices, Linear Algebra Appl. 58 (1984) 343–361], when the spectrum of A was contained in a certain compact set S 1 not including the origin, the optimal parameter a was determined. In Hadjidimos [A. Hadjidimos, The Optimal Solution to the Problem of Complex Extrapolation of a First Order Scheme, Linear Algebra All. 62 (1984) 241–261], for the solution of Ax = b, the consistent linear scheme x ( m+1) = Tx ( m) + c, m = 0,1,2, … , for which the spectrum of T was contained in a certain compact convex set S 2 not including the point 1, was considered and the optimal extrapolation parameter ω of its extrapolation scheme (i.e., x ( m+1) = ((1 − ω) I + ωT) x ( m) + ωc, m = 0,1,2, …) was determined. Because the approach in obtaining the optimal parameters in the two articles was quite different it seems it was difficult for any one to notice their equivalence and, therefore, to use them even in trivial cases. In this article we show the equivalence of the optimal results in Opfer and Schober [G. Opfer, G. Schober, Richardson’s Iteration for Nonsymmetric Matrices, Linear Algebra Appl. 58 (1984) 343–361] and Hadjidimos [A. Hadjidimos, The Optimal Solution to the Problem of Complex Extrapolation of a First Order Scheme, Linear Algebra All. 62 (1984) 241–261], explore them further, obtain new results and give applications for cases which may occur in practice. Finally, based on observations regarding the optimal two-cyclic successive overrelaxation (SOR) and accelerated overrelaxation (AOR) methods in two real case problems we solve the problem of “optimal” two-cyclic AOR in the more general complex case.

Symplectic Integrators: Rotations and Roundoff Errors

We investigate the numerical implementation of a symplectic integrator combined with a rotation (as in the case of an elongated rotating primary). We show that a straightforward implementation of the rotation as a matrix multiplication destroys the conservative property of the global integrator, due to roundoff errors. According to Blank et al. (1997), there exists a KAM-like theorem for twist maps, where the angle of rotation is a function of the radius. This theorem proves the existence of invariant tori which confine the orbit and prevent shifts in radius. We replace the rotation by a twist map or a combination of shears that display the same kind of behaviour and show that we are able not only to recover the conservative properties of the rotation, but also make it more efficient in term of computing time. Next we test the shear combination together with symplectic integrator of order 2, 4, and 6 on a Keplerian orbit. The resulting integrator is conservative down to the roundoff errors. No linear drift of the energy remains, only a divergence as the square root of the number of iterations is to be seen, as in a random walk. We finally test the three symplectic integrators on a real case problem of the orbit of a satellite around an elongated irregular fast rotating primary. We compare these integrators to the well-known general purpose, self-adaptative Bulirsch–Stoer integrator. The sixth order symplectic integrator is more accurate and faster than the Bulirsch–Stoer integrator. The second- and fourth- order integrators are faster, but of interest only when extreme speed is mandatory.