Studien genomfördes på industriföretaget Gränges Finspång AB som är en producent av valsade aluminiumprodukter för värmeväxlare vilka används som komponenter främst inom bilindustrin och värme, ventilation och luftkonditionering. Aluminium är en miljöeffektiv råvara tack vare materialets naturliga egenskaper samt dess återanvändbarhet vilket har lett till att allt fler företag vill ta vara på dessa egenskaper vid tillverkning av klimatsmarta produkter. För Gränges Finspång AB har materialets aktualitet på marknaden inneburit en ökad efterfrågan på företagets produkter vilket i sin tur har satt ökad press på företagets produktionseffektivitet. Den produktionsprocess som studerades på företaget var en uppsättning maskiner – även kallade kallvalsverk – vilka kan liknas med en funktionell verkstad. Syftet med studien var att, med hjälp av optimeringsmetoder, ta fram en modell som kan användas som beslutsunderlag för sekvensering av produkter i företagets kallvalsverk. Utifrån intervjuer, granskning av interna dokument och en kvantitativ dataanalys genomfördes en kartläggning av Gränges Finspång AB:s hela produktionsflöde såväl som de processer unika för kallvalsprocessen. För sekvensering av företagets produkter tillämpades en linjär heltalsmodell vilken anger optimum för maximalt 14 produkter. Studien bekräftar att företagets kallvalsning är ett komplext produktionssystem ur ett schemaläggningsperspektiv. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

Is battery energy storage a feasible solution for lowering the operational costs of electric vehicle fast charging and reducing its impact on local grids? The thesis project aims at answering this question for the Swedish scenario. The proposed solution (fast charging station coupled with storage) is modelled in MATLAB, and its performance is tested in the framework provided by Swedish regulation and electricity tariff structure. The analysis is centred on the economic performance of the system. Its cost-effectiveness is assessed by means of an optimisation algorithm, designed for delivering the optimal control strategy and the required equipment sizing. A mixed-integer linear programming (MILP) formulation is utilised. The configuration and operative costs of conventional fast charging stations are used as a benchmark for the output of the optimisation. Sensitivity analysis is conducted on most relevant parameters: charging load, battery price and tariff structure. The modelling of the charging demand is based on statistics from currently implemented 50 kW DC chargers in Sweden. Overall, results show that with current figures the system may be an economically viable solution for both reducing costs and lowering the impact on the local distribution grid, at least during peak-period pricing. However, sensitivity analysis illustrates how system design and performance are highly dependent on input parameters. Among these, electricity tariff was identified as the most important. Consequently, detailed discussion on the influence of this parameter is conducted. Finally, the study shows how the system is in line with most recent directives proposed by the European Commission.

Swedish home care industry has been facing both external and internal problems, such as ageing population, varying quality and unsatisfactory continuity. Accordingly, workforce scheduling system, as one of the most common and useful software within home care planning nowadays, is in need of constant improvement and upgrading. This master’s thesis aimed to explore and analyze improvement potential of an established workforce scheduling system for an IT-company. The thesis was divided into two phases, of which a pre-study in Phase I tried to understand the planning process for planners and identify the perceived problems and shortcomings of the current system from a planner’s perspective. Based on the analysis from the pre-study, the caregiver continuity was chosen as the research area for Phase II. The current system was re-implemented and was modelled as an optimization problem. Furthermore, the system mainly consisted of two key parts, mixed integer linear programming (MILP) and heuristics. Different approaches in terms of modifications in both MILP and heuristics were applied to the re-implemented system. The performance of the modifications was measured by multiple evaluation indicators. The test results showed that there was a potential to improve caregiver continuity with 1.2% to almost 13% depending on the modification type. The modifications were lastly suggested for further examination regarding their practical appropriateness by applying them to the current running algorithm. / Den svenska hemtjänsten möter både yttre och inre problem såsom åldrande befolkning, varierande kvalitet och bristande kontinuitet. Schemaläggningssystemet som är en av de vanligaste och användbaraste programvarorna inom hemtjänsten behöver därmed en ständig förbättring och uppgradering som bemöter de existerande utmaningarna. Detta examensarbete hade som syfte att utforska och analysera förbättringspotentialen av ett etablerat schemaläggningssystem för ett ITföretag. Arbetet var indelat i två faser, varav förstudien i Fas I försökte förstå planerarnas planeringsprocesser och identifiera upplevda problem och brister i det nuvarande systemet utifrån ett planerares perspektiv. Baserat på analysen från förstudien, personalkontinuitet valdes som ett forskningsområde för Fas II. Nuvarande systemet implementerades om och det modellerades som ett optimeringsproblem. Systemet bestod huvudsakligen av två nyckeldelar, blandat heltalslinjärprogrammering (MILP) och heuristik. Olika metoder i form av modifieringar i både MILP och heuristik tillämpades på det omimplementerade systemet. Modifieringarnas prestanda mättes sedan med flera utvärderingsindikatorer. Testresultaten visade att, beroende på vilken modifiering det gäller, fanns det en potential att förbättra personalkontinuiteten med 1,2% till nästan 13%. Det föreslogs slutligen att modifieringarnas praktiska lämplighet behövs undersökas ytterligare genom att applicera det på det nuvarande systemet som är i drift.

With increasing shares of variable renewable energy sources in the power mix, the need for energy storage solutions is projected to increase as well. Storage can in such combined systems help mitigate the issues with relying on intermittent sources by time-shifting the supply and smoothing out frequency fluctuations, to name some examples. This thesis has focused on Azelio ABs flagship product, the TES.POD, which is a long-duration thermal energy storage technology. When integrated with, for example, solar PV power, the TES.POD can store excess energy and dispatch it during times of low supply or when during the evening/night. The aim of the thesis has been the development of a day-ahead dispatch optimization tool for systems that include multiple TES.PODs, combined into a Cluster, and solar PV. The model was to be built using the Python programming language and based on Mixed-Integer-Linear-Programming (MILP) methods. The PV+storage system was then allowed to be connected to supplementary power sources such as a larger electric grid, or diesel generators in off-grid locations. The purpose of the optimization model is to find the most economic way to operate the individual TES.PODs while also keeping track of other system components, using a cost-based objective function (minimize costs). A focus has been on using high time resolution (small time step) in order to investigate the impact that the TES.PODs dynamic constraints has on operation. Another strength compared to pre-existing models was the ability to operate individual units indifferent to each other, as opposed to having them all operated in unison. Final results from benchmarking tests and two case studies indicated that using the optimization tool with smaller time steps had an effect on key indicators, and could lead to improved economy in the system. It was observed in both cases that the cost of electricity was reduced by running the optimization tool with time steps of either two or three minutes when compared with using an hourly resolution. Furthermore, several usage parameters for the TES.PODs, notably the total amount of operated hours and energy output per cycle, saw improvements which could lead to reduced cost of operation and maintenance. While not the main intent, testing different Cluster sizes and amount of installed PV capacity with the model, it could also be used in strategic decisions for system sizing. However, due to rapidly growing computational times in systems with large TES.POD clusters and using smaller time steps, the possibility of adding more complexity to the model in future work must be done with caution. To combat this issue, either improvements to the model formulation could be attempted, or by using more powerful hardware or optimizer (imported software algorithm that handles solving the model).

There is an ever-increasing usage of mobile data with global traffic having reached 115 exabytes per month at the end of 2022 for mobile data traffic including fixed wireless access. This is projected to grow up to 453 exabytes at the end of 2028, according to Ericssons 2022 mobile data traffic outlook report. To meet the increasing demand radio access networks (RAN) used for mobile communication are continuously being improved with the current generation enabling larger virtualization of the network through the Cloud RAN (C-RAN) architecture. This facilitates the usage of commercial off-the-shelf servers (COTS) in the network replacing specialized hardware servers and making it easier to scale up or down the network capacity after traffic demand. This thesis looks at how we can efficiently identify servers needed to meet traffic demand in a network consisting of both COTS servers and specialized hardware servers while trying to reduce the energy consumption of the network. We model the problem as a network where the antennas and radio heads are connectedto the core network through a C-RAN and a specialized hardware layer. The network is then represented using a graph where the nodes represent servers in the network. Using this problem model as a base we then generate problem instances with varying topologies, server profiles, and traffic demands. To find out how the traffic should be passed through the network we test two different methods: A mixed integer linear programming (MILP) method focused on energy minimization and a graph attention network (GAT) predictor combined with the energy minimization MILP. To help evaluate the results we also create three other methods: a MILP model that tries to spread the traffic as evenly as possible, a random predictor combined with the energy minimization MILP and a greedy method. Our results show that the energy optimization MILP method can be used to create optimal solutions, but it suffer from a slow computation time compared to the other methods. The GAT model shows promising results in making predictions regarding what servers should be included in a network making it possible to reduce the problem size and solve it faster with MILP. The mean energy cost of the solutions created using the combined GAT/MILP method was 4% more than just using MILP but the time gain was substantial for problems of similar size as the GAT was trained on. With regards to computation time the combined GAT/MILP method used was 85% faster than using only MILP. For networks of almost double the size than the ones that the GAT model was trained on the solutions of the combined GAT and MILP methods had a mean energy cost increase of 7% while still showing a strong speedup, being 93% faster than when only using MILP.

There is growing interest in commercial aircraft formation flight as a means of reducing both airspace congestion and the carbon footprint of air transportation. Wake vortex surfing has been researched extensively and proven to have significant fuel-saving benefits, however, commercial air transportation has yet to take advantage of these formation benefits due to understandable safety concerns. The realization of these formations requires serious consideration of formation contingencies and safety during closer-in maneuvering of large commercial aircraft. Formation contingency scenarios are much more complex than those of individual aircraft and have not yet been studied in depth. This thesis investigates the utility of optimization modeling in providing insight into generation of aircraft escape paths for formation contingency planning. Three high-altitude commercial aircraft formation scenarios are presented; formation join, formation emergency exit, and formation escape. The model-generated paths are compared with pilot-generated escape plans using the author’s pilot expertise. The model results compare well with pilot intuition and are useful in presenting solutions not previously considered, in evaluating separation requirements for improvement of escape path planning and in confirming the viability of the pilot-generated plans. The novel optimization model formulation presented in this thesis is the first model shown to be capable of generating escape paths comparable to pilot- generated escape plans and is also the first to incorporate avoidance of persistent and drifting wake turbulence within the formation.

High electricity prices have become the title of several news articles recently in Sweden and the prices have experienced large sudden fluctuations during certain periods. In this thesis work, a smart control model for the electricity usage in three different households has been developed with the main purpose to minimize the electricity cost. This has been implemented by using mixed-integer linear programming (MILP) to optimize the cost 24 hours ahead, and by forecasting two of the main inputs; the load and the electricity spot prices for bidding zone three (SE3) in Sweden. The units included in the model are the photovoltaic system, the batteries, the electricity consumption in the house and the electric vehicles. However, the main task of the smart control was to determine when and in which amount the energy should flow from one unit to another, or to/from the grid. In other words, it decides the charging/discharging of the batteries, the selling/buying of electricity and the charging of the electric vehicle (EV). Different amounts of cost savings/profits have been obtained when applying the smart control on the three houses, which have different annual consumption, capacities of the components, heating systems and more. The results showed that it is most optimal to run the model between the time interval 13.00-00.00, when the spot prices for the next day are known, in order to avoid the remarkable impact accompanied with the use of forecasted electricity prices as input to the model. The forecasting of the load is, on the other hand, required to run the model, but this thesis showed that the effect of the uncertainties in this forecast is relatively small. Three types of machine learning methods were implemented to perform the forecasts, namely linear regression (LR), decision tree regression and random forest regression. After measuring especially the mean absolute error (MAE) to validate the results, the random forest regression showed the least error and the other methods showed close results when looking at the electric load prognosis.

This paper presents the development and mathematical implementation of a production scheduling model utilizing mixed-integer linear programming (MILP). A simplified model of a real-world multi-product batch plant constitutes the basis. The paper shows practical extensions to the model, resulting in a digital twin of the plant. Apart from sequential arrangement, the final model contains maintenance periods, campaign planning and storage constraints to a limited extend. To tackle weak computational performance and missing model features, a condensed mathematical formulation is introduced at first. After stating that these measures do not suffice for applicability in a restrained time period, a novel solution strategy is proposed. The overall non-iterative algorithm comprises a multi-step decomposition approach, which starts with a reduced scope and incrementally complements the schedule in multiple subproblem stages. Each of those optimizations holds less decision variables and makes use of warmstart information obtained from the predecessor model. That way, a first feasible solution accelerates the subsequent improvement process. Furthermore, the optimization focus can be shifted beneficially leveraging the Gurobi solver parameters. Findings suggest that correlation may exist between certain characteristics of the scheduling scope and ideal parameter settings, which yield potential for further investigation. Another promising area for future research addresses the concurrent multi-processing of independent MILPs on a single machine. First observations indicate that significant performance gains can be achieved in some cases, though sound dependencies were not discovered yet.

Nous nous intéressons au Problème de Dimensionnement de Lots mono-produit (PDL) dans une chaîne logistique composée d'un détaillant et d'un fournisseur en y intégrant le contrat buyback et l'approvisionnement par batch. L'objectif est de déterminer un plan d'approvisionnement pour le détaillant pour satisfaire ses demandes déterministes sur un horizon fini, tout en minimisant ses coûts d'approvisionnement et de stockage. Concernant le coût d'approvisionnement, nous supposons deux structures différentes : FTL (Full Truck Load) et OFB (Only Full Batch). Trois types de contrat buyback sont étudiés : avec des périodes de retour fixes, avec une limite de temps sur les retours, et avec des retours uniquement dans les périodes d'approvisionnement. Chaque contrat est caractérisé par un pourcentage de retour maximal qui peut être égal à 100% (retour total) ou inférieur à 100% (retour partiel). Pour le PDL sous le contrat buyback avec des périodes de retour fixes, nous supposons le cas de ventes perdues (lost sales). En outre, un autre concept ajouté dans les PDL sous les trois types de contrat buyback réside dans le fait que le détaillant peut jeter la quantité invendue et non retournée au fournisseur, appelé mise au rebut (disposal). Nous avons modélisé ces différentes extensions du PDL par des Programmes Linéaires en Nombres Entiers (PLNE). Nous avons ensuite développé des algorithmes exacts polynomiaux de programmation dynamique pour certaines extensions, et montré la NP-difficulté pour d'autres. Pour chaque problème résolu en temps polynomial, nous avons comparé l'efficacité et les limites de l'algorithme proposé avec celles des quatre formulations en PLNE. Nous avons également proposé des modèles mathématiques pour les PDL sous d'autres types de contrats de réservation de capacité dans le cas déterministe à multi-périodes. / We study the single-item Lot Sizing Problem (LSP) in a supply chain composed of a retailer and a supplier by integrating the buyback contract and the batch ordering. The purpose is to determine a replenishment planning for the retailer to satisfy his deterministic demands over a finite horizon, while minimizing the procurement and inventory costs. Regarding the procurement cost, we assume two different structures: FTL (Full Truck Load) and OFB (Only Full Batch). We consider three types of buyback contract: with fixed return periods, with a time limit on returns, and with returns permitted only in procurement periods. Each contract is characterized by the maximum return percentage being either equal to 100% (full return) or less than 100% (partial return). For the LSP under the buyback contract with fixed return periods, we assume the concept of lost sales. Another concept considered in the LSP's under the three types of buyback contract is the disposal of the unsold and unreturned quantities. We model these different LSP extensions as a Mixed Integer Linear Program (MILP). Thereafter, we develop exact polynomial time dynamic programming algorithms for some extensions and show the NP-hardness of others. For each problem solved in polynomial time, we compare the efficiency and the limits of the proposed algorithm with those of four MILP formulations by performing different tests. Finally, we propose mathematical models for the LSP's under other types of the capacity reservation contract in the deterministic and multi-period case.

Cette thèse s'intéresse au développement de stratégies de décalage de charge pouvant être appliquées à un parc de chauffe-eau Joule (CEJ).On propose une modélisation entrée-sortie du système que constitue le CEJ. L'idée est de concevoir un modèle précis et peu coûteux numériquement, qui pourrait être intégré dans un CEJ intelligent. On présente notamment un modèle phénoménologique multi-période d'évolution du profil de température dans le CEJ ainsi qu'un modèle de la demande en eau chaude. On étudie des stratégies d'optimisation pour un parc de CEJ dont la résistance peut être pilotée par un gestionnaire central. Trois cas de figures sont étudiés. Le premier concerne un petit nombre de ballons intelligents et présente une méthode de résolution d'un problème d'optimisation en temps discret. Puis, on s'intéresse à un parc de taille moyenne. Une heuristique gardant indivisibles les périodes de chauffe (pour minimiser les aléas thermo-hydrauliques) est présentée. Enfin, un modèle de comportement d'un nombre infini de ballon est présenté sous la forme d'une équation de Fokker-Planck. / This thesis focuses on the development of advanced strategies for load shifting of large groups of electric hot water tanks (EHWT).The first part of this thesis is dedicated to representing an EHWT as an input-output system. The idea is to design a simple, tractable and relatively accurate model that can be implemented inside a low-power computing unit embedded in a smart EHWT, for practical applications of optimization strategies. It includes in particular a phenomenological multi-period model of the temperature profile in the tank and a realistic domestic hot water consumption model.The second part focuses on the design of optimal control strategies for a group of tanks. Three use-cases are studied. The first one deals with a small number of smart and controllable EHWT for which we propose a discrete-time optimal resolution method. The second use-case adresses a medium-scale group of controllable tanks and proposes a heuristic which keeps the heating period undivided to minimize thermo-hydraulic hazards. Finally, we present the modelling of the behavior of a infinite population of tanks under the form of a Fokker-Planck equation.