This thesis is concerned with the Resident Scheduling Problem (RSP) in which a good schedule is desired that will meet both departmental requirements and residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with this specific problem. The problem is modeled as a mixed-integer program (MIP) and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEX-MIP package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time with less scheduling flexibility. / Master of Science

The work presented in this dissertation was carried out at the Division ofMechanics, Department of Management and Engineering at Link¨oping University,between 2003 and 2008. It was supervised by Prof. Anders Klarbring,head of the division, and financially supported by the National GraduateSchool of Scientific Computing (NGSSC) and the Swedish Research Council(VR). There are many people to whom I would like to express my gratitude: firstand foremost I would like to thank my supervisor Prof. Anders Klarbring forhis help, support and endless patience during our discussions, and for alwayshaving time to read and comment on the numerous drafts that eventually ledto the research manuscripts presented in this thesis. I would also like to thankmy co–supervisor Dr. Thomas Borrvall for all his help regarding numericalissues, especially with the implementation of the models. Moreover, I wouldlike to thank present and former colleagues for their inspiration and assistanceduring my time as a graduate student at the division. Last but not least, I am very grateful for having a family that has alwaysbeen there to support me, and for all my friends who enrich my life outsidethe office walls in more ways then I can say.

Norrmejerier står inför förändringar vad gäller både mjölkkonsumtion och flytt av produktionen från Luleå mejeri till Umeå mejeri inom en snar framtid. Det har gett behov av ett verktyg för att snabbt kunna fatta beslut om systemet kan hantera en ökad mängd volym och antal produktkategorier. För att ta fram ett sådant verktyg skapades en matematisk optimeringsmodell uppbyggd i programvaran Python som gör det möjligt att köra programmet för olika scenarion. Modellen använder optimeringslösaren Pulp för att hitta en lösning på problemet. Den matematiska modellen baseras på Multi Commodity Flow Problem med tidsvariabel i kombination med Flow-shop scheduling och har modifierats efter systemet på Umeå mejeri. Det är en pessimistisk modell baserat på de antaganden som gjorts i rapporten. Programmet baseras på ett dygns produktion och avgör, genom att minimera den totala tiden det tar för flödet genom processen, om det finns kapacitet för en ökad produktion. Systemet i projektet är uppdelat i två subnätverk på grund av tidskomplexiteten och resultaten visar att implementering av en ytterligare produktkategori kan hanteras av båda subnätverken. En ökad volym med 10% av den befintliga kan endast hanteras av den första delen av nätverket. Det betyder att det finns tekniska begränsningar i det andra subnätverket. Genom tillägg av extra noder som kan användas till en viss straffkostnad kunde flaskhalsar identifieras och det visade sig att pastör 2P1 är en uppenbar flaskhals i systemet. Om man ökar produktionen ytterligare kan även silosarna behöva utökas för att hantera flödet. / Norrmejerier is facing changes in terms of both milk consumption and a move of the production from Luleå dairy to Umeå dairy in the near future. This has given rise to the need of a tool that quickly can make descisions about whether the system can handle an increased amount of volume and number of product categories. To produce such a tool a mathematical optimization model was created in Python which makes it possible to run the program for different scenarios. The model uses the optimization solver Pulp. The mathematical model is based on Multi Commodity Flow Problem with time variable combined with Flow-shop scheduling and has been modified according to the system at Umeå dairy. Based on the assumptions made in the report it is a pessimistic model. The program is based on one day's production and determines by minimizing the total time it takes for the flow to pass through the system, to see if there is enough capacity for increased production. The system in the project is divided into two subnetworks due to the time complexity and the results show that implementation of an additional product category can be handled by both subnetworks. An increased volume of 10% of the existing volume can only be handled by the first part of the network. This means that there are technical limitations in the second subnetwork. By adding extra nodes that can be used for a certain penalty cost, bottlenecks could be identified and it turned out that Pasteur 2P1 is an obvious bottleneck in the system. If the production increases further the silos may also need to be expanded to handle the flow in the system.

One of the biggest threats to the power systems as critical infrastructures is large-scale blackouts resulting from cascading failures (CF) in the grid. The ongoing shift in energy portfolio due to ever-increasing penetration of renewable energy sources (RES) may drive the electric grid closer to its operational limits and introduce a large amount of uncertainty coming from their stochastic nature. One worrisome change is the increase in CFs. The CF simulation models in the literature do not allow consideration of RES penetration in studying the grid vulnerability. In this dissertation, we have developed tools and models to evaluate the impact of RE penetration on grid vulnerability to CF. We modeled uncertainty injected from different sources by analyzing actual high-resolution data from North American utilities. Next, we proposed two CF simulation models based on simplified DC power flow and full AC power flow to investigate system behavior under different operating conditions. Simulations show a dramatic improvement in the line flow uncertainty estimation based on the proposed model compared to the simplified DC OPF model. Furthermore, realistic assumptions on the integration of RE resources have been made to enhance our simulation technique. The proposed model is benchmarked against the historical blackout data and widely used models in the literature showing similar statistical patterns of blackout size.

Automated Guided Vehicle (AGV) Container-Job deployment is essentially a vehicle-dispatching problem. In this problem, the impact of vehicle dispatching polices on the ship makespan for discharging and/or loading operations is analyzed. In particular, given a storage location for each container to be discharged from the ship and given the current location of each container to be loaded onto the ship, the problem is to propose an efficient deployment scheme to dispatch vehicles to containers so as to minimize the makespan of the ship so as to increase the throughput. The makespan of the ship refers to the time a ship spends at the port for loading and unloading operations. In this paper, we will compare the performance of current deployment scheme used with the new proposed deployment scheme, both with deadlock prediction & avoidance algorithm done in previous study [1]. The prediction & avoidance algorithm predicts and avoids cyclic deadlock. The current deployment scheme, namely pmds makes use of a greedy heuristics which dispatches the available vehicle that will reach the quay with the minimum amount of time the vehicle has to spend waiting for the crane to discharge/load the container from/onto the ship. The new deployment scheme, namely mcf aims to formulate the problem as a minimum cost flow problem, which will then be solved by network simplex code. The two simulation models are implemented using discrete-event simulation software, AutoMod, and the performances of both deployment schemes are analyzed. The simulation results show that the new deployment scheme will result in a higher throughput and lower ship makespan than the current deployment scheme. / Singapore-MIT Alliance (SMA)

As structure and size of electric power distribution systems are getting more complex, distribution automation schemes become more attractive. One of the features that is desirable in an automated system is feeder reconfiguration for loss reduction. Loss reduction can make considerable savings for a utility and results in released system capacity. There is also improved voltage regulation in the system as a result of reduced feeder voltage drop. In this thesis, multi branch exchange algorithm is introduced to solve the network reconfiguration for loss reduction problem. The proposed technique is based on heuristic techniques applied to constraint satisfaction optimization problems. A critical review of earlier methods related with feeder reconfiguration is presented. A computer program was developed using Matlab to simulate this algorithm and results of simulations demonstrate its advantages over single branch exchange method. Moreover, the results show that the final configuration is independent of the initial configuration and give assurance that any solution offered will have a radial configuration with all loads connected.

In this thesis, we proposed a delay limited routing scheme in wireless ad hoc networks. When nodes transmit packets in wireless ad hoc networks, most people think the one-hop way is better than the multi-hop way in reducing the delay time. Since most cases in wireless ad hoc networks are not single sources, we should consider at least two sources transmitting packets at the same time and then use the multi-hop way in order to reduce the energy consumption. We want to maximize the throughput with limited delay. Our contribution is to transform the optimal scheduling problem in wireless ad hoc networks to the classic maximum flow problem. The maximum flow approach does maximize the throughput and can get the optimal solution.

In this thesis, we consider how to reduce the communication cost of the key exchange procedures as many as possible, while the secure group communication can still be achieved. Due to the energy consumption is usually proportional to the distance, we use the shortest paths algorithm to find the shortest communication paths between any pair of the secure group members. We first propose a straightforward heuristic named Minimum-Energy First-Selected ( MEFS ). MEFS tries to select the pair of group members which has less communication cost than all other pairs have at every time. Though MEFS performs better than random selecting, it still has some weakness in solving the energy-aware key management problem. So we use the concept of the minimum cost flow problem, and by appropriate transformation, then we get the optimal solution of the energy-aware key management problem under some constraints. At last, the simulation results proves that the minimum cost flow approach actually works better than MEFS does.

This thesis considers three separate but connected problems regarding energy networks: the load flow problem, the optimal power flow problem, and the islanding problem. All three problems are non-convex non linear problems, and so have the potential of returning local solutions. The goal of this thesis is to find solution methods to each of these problems that will minimize the chances of returning a local solution. The thesis first considers the load ow problem and looks into a novel approach to solving load flows, the Holomorphic Embedding Load Flow Method (HELM). The current literature does not provide any HELM models that can accurately handle general power networks containing PV and PQ buses of realistic sizes. This thesis expands upon previous work to present models of HELM capable of solving general networks efficiently, with computational results for the standard IEEE test cases provided for comparison. The thesis next considers the optimal power flow problem, and creates a framework for a load flow-based OPF solver. The OPF solver is designed with incorporating HELM as the load flow solver in mind, and is tested on IEEE test cases to compare it with other available OPF solvers. The OPF solvers are also tested with modified test cases known to have local solutions to show how a LF-OPF solver using HELM is more likely to find the global optimal solution than the other available OPF solvers. The thesis finally investigates solving a full AC-islanding problem, which can be considered as an extension of the transmission switching problem, using a standard MINLP solver and comparing the results to solutions obtained from approximations to the AC problem. Analysing in detail the results of the AC-islanding problem, alterations are made to the standard MINLP solver to allow better results to be obtained, all the while considering the trade-off between results and elapsed time.

The purpose of this paper is to develop a general method for using Finite Elements in the Steepest Descent Method. The main application is to a partial differential equation for a Transonic Flow Problem. It is also applied to Burger's equation, Laplace's equation and the minimal surface equation. The entire method is tested by computer runs which give satisfactory results. The validity of certain of the procedures used are proved theoretically. The way that the writer handles finite elements is quite different from traditional finite element methods. The variational principle is not needed. The theory is based upon the calculation of a matrix representation of operators in the gradient of a certain functional. Systematic use is made of local interpolation functions.