Algoritma Criss-crosss dan Branch and Bound dalam Pemrograman Linier Integer, Studi Kasus: Produksi Pangan

Dalam laporan analisis situasi pangan dan gizi tahun 2014 oleh badan ketahanan pangan dan penyuluhan Daerah Istimewa Yogyakarta terdapat 16 desa yang resiko pangan dan gisi tergolong waspada dan 26 desa yang resiko pangan dan gisi tergolong rawan, efisiensi penggunaan bahan baku pangan menjadi sangat penting peranannya. Efisiensi bahan baku bisa digunakan juga untuk mencapai keuntungan dalam industry makanan.Dalam penelitian ini masalah pangan tersebut dipandan dan diformulasikan dengan menggunakan pemrograman linier yang diselesaikan dengan model integer. Algoritma criss-crosss yang dikombinasikan dengan algoritma branch and bound diusulkan dalam penyelesaian masalah integer linier programming. Penelitian ini berfokus pada penerapan kedua algoritma tersebut dalam studi kasus produksi makanan dan pencarian kondisi batasan yang sesuai.Penelitian ini berhasil menerapkan penggabungan algoritma criss-crosss dan branch and bound. Penelitian ini mendefinisikan 4 batasan yang dapat diperhatikan untuk mengurangi pencabangan dalam pencarian nilai intege

A FUZZY BI-LEVEL PROJECT PORTFOLIO PLANNING CONSIDERING THE DECENTRALIZED STRUCTURE OF PHARMACY HOLDINGS

Research and development (R&D) in the pharmaceutical industry requires proper and optimal planning and management because of its critical role in public health. Taking into account a decentralized decision-making structure in R&D management in pharmaceutical holding companies, this study introduces a new fuzzy bi-level multi-follower mathematical optimization model to address budget allocation and project portfolio planning. Specifically, the holding company's head office, as the leader, and the subsidiaries, as followers, make strategic and operational decisions concerning important issues such as budget allocation and portfolio selection and scheduling. Since the lower level represents multiple mixed-integer programming problems with uncooperative reference relationships between followers, solving the resulting bi-level model is challenging. Therefore, our model is based on an effective hybrid solution methodology, which converts the bi-level model, including multiple followers, into a single-level model. In order to validate the proposed model, we conducted a case study and analyzed the strategies of each actor within the conglomerate. Based on the results of experiments, it is evident that a strategy that focuses on one level of operations profoundly affects decisions at the other level

Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control

Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance

Advanced multiparametric optimization and control studies for anaesthesia

Anaesthesia is a reversible pharmacological state of the patient where hypnosis, analgesia and muscle relaxation are guaranteed and maintained throughout the surgery. Analgesics block the sensation of pain; hypnotics produce unconsciousness, while muscle relaxants prevent unwanted movement of muscle tone. Controlling the depth of anaesthesia is a very challenging task, as one has to deal with nonlinearity, inter- and intra-patient variability, multivariable characteristics, variable time delays, dynamics dependent on the hypnotic agent, model analysis variability, agent and stability issues. The modelling and automatic control of anaesthesia is believed to (i) benefit the safety of the patient undergoing surgery as side-effects may be reduced by optimizing the drug infusion rates, and (ii) support anaesthetists during critical situations by automating the drug delivery systems. In this work we have developed several advanced explicit/multi-parametric model predictive (mp-MPC) control strategies for the control of depth of anaesthesia. State estimation techniques are developed and used simultaneously with mp-MPC strategies to estimate the state of each individual patient, in an attempt to overcome the challenges of inter- and intra- patient variability, and deal with possible unmeasurable noisy outputs. Strategies to deal with the nonlinearity have been also developed including local linearization, exact linearization as well as a piece-wise linearization of the Hill curve leading to a hybrid formulation of the patient model and thereby the development of multiparametric hybrid model predictive control methodology. To deal with the inter- and intra- patient variability, as well as the noise on the process output, several robust techniques and a multiparametric moving horizon estimation technique have been design and implemented. All the studies described in the thesis are performed on clinical data for a set of 12 patients who underwent general anaesthesia.Open Acces

Advancing Multiparametric Programming for Model Predictive Control

Model predictive control provides the optimal operation for chemical processes by explicitly accounting for the system, constraints, and costs. In an online setting, developing the implicit optimal control action under time consideration is non-trivial. Over a decade ago, it was demonstrated through multiparametric programming that the implicit control law defining the model predictive controller can be determined explicitly, once and offline. The benefit of such an approach is the (i) improved online computational time, (ii) the development of the offline map of solution \textit{a priori}, and (iii) the derivation of the optimal control laws under any state variation. In recent years there has been a significant push for the development of novel algorithms and theoretical advancements for multiparametric model predictive control. These algorithms and theoretical underpinnings have expanded the problem classes that are solvable and improved the computational efficiency. However, there is still a need to provide analysis for formulations based on different surrogate models, and to tackle large scale multiparametric model predictive control problems. In this dissertation, the research focus is (i) the inclusion of a new surrogate modeling technique from the machine learning community, (ii) developing a criterion to compare multiparametric model predictive control formulations based on different surrogate models, (iii) the development of an algorithm to solve large scale multiparametric optimization problems, and (iv) improving the online computational performance of online solvers via multiparametric programming. To this end, tools from data science, computational geometry, and the operations research community contributed greatly to the results presented in this work. This research is verified via the optimal operation of chemical engineering processes and the efficacy of the developed algorithms is demonstrated on computational studies