This thesis project will attempt to answer the question if it is possible to gain performance by using SIMD instructions when generating code for scalar computation. The current trend in processor architecture is to equip the processors with multi-way SIMD units to form so-called throughput cores. This project uses the CELL SPE processor for a concrete implementation. To get good code quality the thesis project continues work on the code generator by Mattias Eriksson and Andrzej Bednarski based on integer linear programming. The code generator is extended to handle generation of SIMD code for 32bit operands. The result show for some basic blocks, positive impact in execution time of the generated schedule. However, further work has to be done to get a feasable run time of the code generator.

Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed-integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose-volume constraints. In this study, we incorporated dose-volume constraints in an MIP model to generate treatment plans for IMPT. Methods: We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method while the other plan was derived with our MIP model with dose-volume constraints. We then compared these two plans by dose-volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose-volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results: The MIP model with dose-volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial-and-error process. Some notable reduction in the mean doses of OARs is observed. Conclusions: The treatment plans from our MIP model with dose-volume constraints can meetall dose-volume constraints for OARs and targets without any tedious trial-and-error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

This thesis proposes and verifies a number of optimization models for re-designing a master surgery schedule with minimized peak inpatient load at the ward. All models include limitations on Operating Rooms and surgeons availability. Surgeons` preference is included with regards to a consistent weekly schedule over a cycle. The uncertain in patients` length of stay was incorporated using discrete probability distributions unique to each surgeon. Furthermore, robust optimization was utilized to protect against the uncertainty in the number of inpatients a surgeon may send to the ward per block. Different scenarios were developed that explore the impact of varying the availability of operating rooms on each day of the week. The models were solved using Cplex and were verified by an Arena simulation model.

Almost every medium and large company has to deal with an optimal placing of administrative workers. This thesis focuses on solving a problem of dislocation of employees of the Ministry of Finance of the Czech Republic (MFCR) and it proposes a possible solution of the current situation. The basis for finding the optimal solutions are integer programming tasks. The structure of the MFCR and the description of the current/future state of dislocations has been defined in cooperation with the MFCR. Therefore, the solution fully meets the MFCR specifications. The thesis also outlines another optional solution for dislocations within MFCR. Finally, there are summarized other aspects of optimal dislocation of employees that can further improve the solution given in this thesis, especially in terms of efficiency, satisfaction and health of the employees.

The management of large-scale transportation infrastructure is becoming a very complex task for the urban areas of this century which are covering bigger geographic spaces and facing the inclusion of connected and self-controlled vehicles. This new system paradigm can leverage many forms of sensing and interaction, including a high-scale mobile sensing approach. To obtain a high penetration sensing system on urban areas more practical and scalable platforms are needed, combined with estimation algorithms suitable to the computational capabilities of these platforms. The purpose of this work was to develop a transportation framework that is able to handle different kinds of sensing data (e.g., connected vehicles, loop detectors) and optimize the traffic state on a defined traffic network. The framework estimates the traffic on road networks modeled by a family of Lighthill-Whitham-Richards equations. Based on an equivalent formulation of the problem using a Hamilton-Jacobi equation and using a semi-analytic formula, I will show that the model constraints resulting from the Hamilton-Jacobi equation are linear, albeit with unknown integer variables. This general framework solve exactly a variety of problems arising in transportation networks: traffic estimation, traffic control (including robust control), cybersecurity and sensor fault detection, or privacy analysis of users in probe-based traffic monitoring systems. This framework is very flexible, fast, and yields exact results. The recent advances in sensors (GPS, inertial measurement units) and microprocessors enable the development low-cost dedicated devices for traffic sensing in cities, 5 which are highly scalable, providing a feasible solution to cover large urban areas. However, one of the main problems to address is the privacy of the users of the transportation system, the framework presented here is a viable option to guarantee the privacy of the users by design.

The purpose of this thesis is to provide a new scheduling model of a large constellation of imaging satellites that does not use a heuristic solving method. The objective is to create a mixed-integer linear model that would be competitive in speed and in its closeness to reality against a current model using simulated annealing, while trying to improve both models. Each satellite has the choice between a number of possible events, each event having a utility and a cost, and the chosen schedule must take into account numerous time-related constraints. The main difficulties appeared in modeling realistically a battery level and in handling infeasible configurations due to inaccurate parameters. The obtained linear model has enabled a better understanding of the performance of the simulated annealing solver, and could also be adapted to different real-world scheduling problems.

The goal of this project is to implement and verify an optimization model for finding a min-cost selection of switches and train paths at railway stations. The selected train paths must satisfy traffic requirements that commonly apply to regular railway traffic. The requirements include different combinations of simultaneous and overtaking train movements. The model does not rely on timetables but does instead utilize different path sets that are produced via algorithms based on a network representation of the station layout. The model has been verified on a small test station and also on the real station layout at Katrineholm. These tests show that the model can solve the problem for mid size stations with through traffic. In addition, we have performed a literature study regarding maintenance problems for switches and crossings. We have also looked at articles regarding the scheduling and routing of trains through railway stations. Finally we present some possible ways to further improve the model for more realistic experiments.

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The goal of this dissertation is to study optimization models that integrate location, production, inventory and transportation decisions for industrial products and apply the knowledge gained to develop supply chains for agricultural products (biomass). We estimate unit cost for the whole biomass-to-biofuels’ supply chain which is the per gallon cost for biofuels up till it reaches the markets. The unit cost estimated is the summation of location, production, inventory holding, and transportation costs. In this dissertation, we focus on building mathematical models for designing and managing the biomass-to-biofuels’ supply chains. The computational complexity of the developed models makes it advisable to use heuristic solution procedures. We develop a Lagrangean decomposition heuristic. In our heuristic, we divide the problem into two sub-problems, sub-problem 1 is a transportation problem and sub-problem 2 is a combination of a capacitated facility location and production planning problem. Subproblem 2 is further divided by commodities. The algorithm is tested for a number of different scenarios. We also develop a decision support system (DSS) for the biomass-to-biofuels’ supply chain. In our DSS, the main problem is divided into four easy-to-solve supply chain problems. These problems were determined based on our knowledge of supply chain and discussions with the experts from the biomass and biofuels’ sector. The DSS is coded using visual basic applications (VBA) for Excel and has a simple user interface which assists the user in running different types of supply chain problems and provides results in form of reports which are easy to understand.