Toni Bakhtiar

The Best Achievable ℋ2 Tracking Performances for SIMO Feedback Control Systems

This paper is concerned with the inherent ℋ2 tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.

Courses timetabling problem by minimizing the number of less preferable time slots

In an organization with large number of resources, timetabling is one of the most important factors of management strategy and the one that is most prone to errors or issues. Timetabling the perfect organization plan is quite a task, thus the aid of operations research or management strategy approaches is obligation. Timetabling in educational institutions can roughly be categorized into school timetabling, course timetabling, and examination timetabling, which differ from each other by their entities involved such as the type of events, the kind of institution, and the type and the relative influence of constraints. Education timetabling problem is generally a kind of complex combinatorial problem consisting of NP-complete sub-problems. It is required that the requested timetable fulfills a set of hard and soft constraints of various types. In this paper we consider a courses timetabling problem at university whose objective is to minimize the number of less preferable time slots. We mean by less preferable time slots are those devoted in early morning (07.00 – 07.50 AM) or those in the late afternoon (17.00 – 17.50 AM) that in fact beyond the working hour, those scheduled during the lunch break (12.00 – 12.50 AM), those scheduled in Wednesday 10.00 – 11.50 AM that coincides with Department Meeting, and those in Saturday which should be in fact devoted for day-off. In some cases, timetable with a number of activities scheduled in abovementioned time slots are commonly encountered. The courses timetabling for the Educational Program of General Competence (PPKU) students at odd semester at Bogor Agricultural University (IPB) has been modelled in the framework of the integer linear programming. We solved the optimization problem heuristically by categorizing all the groups into seven clusters.

Optimal intervention strategies for cholera outbreak by education and chlorination

This paper discusses the control of infectious diseases in the framework of optimal control approach. A case study on cholera control was studied by considering two control strategies, namely education and chlorination. We distinct the former control into one regarding person-to-person behaviour and another one concerning person-to-environment conduct. Model are divided into two interacted populations: human population which follows an SIR model and pathogen population. Pontryagin maximum principle was applied in deriving a set of differential equations which consists of dynamical and adjoin systems as optimality conditions. Then, the fourth order Runge-Kutta method was exploited to numerically solve the equation system. An illustrative example was provided to assess the effectiveness of the control strategies toward a set of control scenarios.

Sirs-Si Model of Malaria Disease with Application of Vaccines, Anti-Malarial Drugs, and Spra)'ing

Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes .It can also be transmitted from an infected mother (congenitally) or through blood transfusion. In this paper, we discussed the transmission of malaria featuring in the framework of an SIRS-SI model with treatments are given to humans and mosquitoes. We here utilized the use of vaccines, the use of anti-malarial drugs, and the use of spraying as treatment efforts. A stability analysis was then performed and numerical simulation was provided to clarify the result. It is shown that treatments affect the dynamics of human and mosquito populations. In addition, we proposed the Homotopy Analysis Method (HAM) to construct the approximate solution of the model.

Optimal Tracking Performance for SIMO Feedback Control Systems: Analytical Closed-Form Expressions and Guaranteed Accuracy Computation

This paper is concerned with the H2 optimal tracking problem under a control input penalty. Analytical closed-form expressions are derived for the best performance levels for the cases of single-input-multiple-output LTI continuous-time systems and single-input-single-output sampled-time systems, which extend previous results. Moreover a numerical algorithm is developed which, given a continuous-time plant, computes the best performance level in a manner that guarantees accuracy. The obtained results are demonstrated on some numerical examples

The nurse scheduling problem: a goal programming and nonlinear optimization approaches

Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

Optimal Control of Malaria Transmission using Insecticide Treated Nets and Spraying

In this paper, we consider a model of the transmission of malaria which was developed by Silva and Torres equipped with two control variables, namely the use of insecticide treated nets (ITN) to reduce the number of human beings infected and spraying to reduce the number of mosquitoes. Pontryagin maximum principle was applied to derive the differential equation system as optimality conditions which must be satisfied by optimal control variables. The Mangasarian sufficiency theorem shows that Pontryagin maximum principle is necessary as well as sufficient conditions for optimization problem. The 4th-order Runge Kutta method was then performed to solve the differential equations system. The numerical results show that both controls given at once can reduce the number of infected individuals as well as the number of mosquitoes which reduce the impact of malaria transmission.

Two-strain Tuberculosis Transmission Model under Three Control Strategies

In 1997, Castillo-Chavez and Feng developed a two-strain tuberculosis (TB) model, which is typical TB and resistant TB. Castillo-Chavez and Fengs model was then subsequently developed by Jung et al. (2002) by adding two control variables. In this work, Jung et al.s model was modified by introducing a new control variable so that there are three controls, namely chemoprophylaxis and two treatment strategies, with the application of three different scenarios related to the objective functional form and control application. Pontryagin maximum principle was applied to derive the differential equations system as a condition that must be satisfied by the optimal control variables. Furthermore, the fourth-order Runge-Kutta method was exploited to determine the numerical solution of the optimal control problem. In this numerical solution, it is shown that the controls treated on TB transmission model provide a good effect because latent and infected individuals are decreasing, and the number of individuals that is treated effectively is increasing.

Low-Carbon City Scenarios for DKI Jakarta Towards 2030

This study presents the results of a modelling study on greenhouse gas (GHG) mitigation actions through which the DKI Jakarta energy sector may achieve “Low-carbon City in 2030” targets. The study assesses the effect of future GHG emission levels in DKI Jakarta and ways in which the DKI Jakarta provincial government may reach reduction targets by up to 30 % below the baseline level in 2030 through the Provincial Action Plan (RAD GRK). Using a back-casting approach, an energy development path is developed based on desirable goals, and we then seek ways to employ it.

Scenarios for Fleet Assignment: A Case Study at Lion Air

Given the sets of flights and aircrafts of an airline, the fleet assignment problem consists of assigning the most profitable aircraft in every flight. In this paper, the model of fleet assignment is set up using the data from the airline company which has the largest market in Indonesia, i.e. Lion Air. Its involved the runway constraints in the model to result more realistic scenarios, where three scenarios of the fleet assignment have been analyzed. The aim of the first scenario is to assign the most appropriate fleet type to flights while minimizing the cost. The second scenario is to see what is the minimum number of aircraft required to cover all flights. The aim of the third scenario is to assign the most appropriate fleet type to flights while minimizing not only the cost but also the number of aircraft for all flights. Models have been set up under constraints of all airline operations and formulated in term of an integer linear programming. The solution of these problems generates a minimum daily cost of fleet assignment and the minimum number of aircraft for all flights.