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Determining the economic lot size has always represented one of the most important issues in production planning. This problem has long attracted the attention of researchers, and several models have been developed to meet requirements at minimum cost. In this paper we explore and discuss the evolution of these models during one hundred years of history, starting from the basic model developed by Harris in 1913, up to today. Following Harris׳s work, a number of researchers have devised extensions that incorporate additional considerations. The evolution of EOQ theory strongly reflects the development of industrial systems over the past century. Here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the EOQ problem. Finally, a new research agenda is proposed and discussed.

Process industries has for long been important for the development of Swedish industry and society. All industries face different conditions that affect how to best run their operations. This thesis aims to describe some of the conditions that characterize process industries compared to other industries. Further one of these characteristics has been studied more closely. One of the traits of process industries is that they are positioned at the start of the transformation process close to the raw material mixing, separating or forming it into products often used for further transformation. Process industries hence become dependent on the properties of these materials. One of the most prominent characteristics inherent from the raw material properties is the divergent bill of material. The divergent bill of material originates from the fact that a given raw material is made up of different components that will yield several products with different characteristics when processed. When splitting the raw material into the desired products the yielded products from a certain raw material usually have different value to the producer, some more desired than others. These multiple products generated poses a challenge from a planning perspective raising questions like “How should we balance the supply and demand of all the products produced?”, “What shall we do with the excess products produced?”. The first paper in this thesis describe the production planning in four Swedish process industries with the ultimate aim to connect their planning to the supply chain characteristics they face as process industries. The study concludes that the industry specific conditions mainly affect planning at short time ranges when planning becomes more detailed. In general the use of planning or decision support systems is low, stemming from a, warranted or not, belief that general decision support systems do not fit process industries. Another finding is that the case companies mainly operate in niche markets. This study also highlighted that the planning complexity arising from characteristic of co- and by-product generation in combination with the lack of decision support systems requires further studies. The subsequent two papers focus on supply chain planning and coordination with a divergent bill of material. They present a mathematical model over the supply chain planning in a real case company in the specialty oils industry. The second paper investigates transfer pricing as a coordination tool by comparing decentralised supply chain planning with centralized planning in an integrated model. Transfer pricing is found to have a potential positive effect on supply chain planning while simultaneously creating problems in terms of uneven distribution of the contribution margin among supply chain partners. Finally the third paper more closely investigates different ways to set transfer prices and comparing them to the optimal transfer prices. Setting optimal transfer prices with a divergent bill of material has proven to be less straightforward than the case with no dependencies between products. Some optimal transfer prices could even be set lower than the marginal cost for producing them due to the dependency between the products in the divergent bill of material. This indicates that there is an opportunity cost for a product that is dependent on the demand of other products. Processindustrier har länge varit viktiga för utvecklingen av svensk industri och det svenska samhället. Alla branscher möter olika förutsättningar som påverkar hur verksamheten bäst skall drivas. Avhandlingen syftar till att beskriva några av de villkor som kännetecknar processindustrin jämfört med andra branscher. Slutligen har en av dessa kännetecknande egenskaper studerats närmare. En av de egenskaper som utmärker processindustrier är att de är positionerade vid början av omvandlingsprocessen nära råvaran och blandar, separerar eller formar den till produkter som ofta används för ytterligare förädling. Processindustrin blir därmed beroende av egenskaperna hos råmaterialet som används. En av de mest framträdande egenskaperna härrörande från dessa råmaterialegenskaper är det divergenta materialflödet. Det divergerande materialflödet har sitt ursprung i att ett visst råmaterial består av olika komponenter som ger flera produkter med olika egenskaper. När råmaterialet separeras i sina komponenter erhålls flera produkter som kan ha väldigt olika värde för producenten. Efterfrågan på de produkter som erhålls ur separeringen kan vara vitt skild från vad som erhålls ur produktionsprocessen. Denna obalans mellan efterfrågan och försörjning är en utmaning ur ett planeringsperspektiv och väcker frågor som " Hur ska efterfrågan och försörjning av de produkter som produceras balanseras?", "Hur skall överskottet på vissa produkter hanteras? ". Den första artikeln i denna avhandling beskriver produktionsplaneringen i fyra svenska processindustriföretag inom områdena pappersmassa, specialkemi, specialoljor samt papper och pappersmassa. Målet med studien var att jämföra planeringen av försörjningskedjan med de förutsättningar som processindustrin ställs inför. I studien dras slutsatsen att de branschspecifika förhållandena främst påverkar den kortsiktiga planeringen med mer detaljer. I allmänhet verkar användningen av planerings- eller beslutsstödsystem vara låg, som härrör från en, befogat eller inte, tro att generella beslutsstödssystem inte passar processindustri. Fallföretagen förefaller också huvudsakligen vara verksamma på nischmarknader. Denna studie betonar också vikten av djupare studier av energiplanering samt den planeringskomplexitet som uppkommer till följd av divergerande materialflöden. De två efterföljande artiklarna fokuserar på planering och koordinering av försörjningskedjan vid ett divergerande materialflöde. De presenterar en matematisk modell över försörjningskedjan i ett fallföretag som tillverkar specialoljor. Den andra artikeln undersöker effekter av att använda internprissättning som verktyg för koordinering av försörjningskedjor genom att jämföra decentraliserad försörjningskedjeplanering med en fullt integrerad centraliserad planering. Internprissättning visar sig ha potentiellt positiva effekter på planeringen av försörjningskedjan men skapar samtidigt problem i form av att täckningsbidraget kan fördelas väldigt ojämnt mellan partner i försörjningskedjan. Slutligen behandlar den tredje artikeln olika sätt att bestämma internpriser och utvärderar deras koordineringseffekter på försörjningskedjan genom att jämföra med optimal satta internpriser. Att bestämma optimala internpriser med ett divergerande materialflöde har visat sig bli komplicerat i och med det beroende som finns mellan produkterna som kommer från samma råmaterial. Optimala internpriser har visat sig kunna vara både avsevärt högre och avsevärt lägre än marginalkostanden för att producera dem. Detta indikerar att alternativkostnaden för en produkt kan påverkas starkt av efterfrågan på andra produkter den har en koppling till via råmaterialet de båda produceras från.

The overall purpose of the PhD project is to develop a framework for making optimal decisions on the equity derivatives markets. Making optimal decisions refers e.g. to how to optimally hedge an options portfolio or how to make optimal investments on the equity derivatives markets. The framework for making optimal decisions will be based on stochastic programming (SP) models, which means that it is necessary to generate high-quality scenarios of market prices at some future date as input to the models. This leads to a situation where the traditional methods, described in the literature, for modeling market prices do not provide scenarios of sufficiently high quality as input to the SP model. Thus, the main focus of this thesis is to develop methods that improve the estimation of option implied surfaces from a cross-section of observed option prices compared to the traditional methods described in the literature. The estimation is complicated by the fact that observed option prices contain a lot of noise and possibly also arbitrage. This means that in order to be able to estimate option implied surfaces which are free of arbitrage and of high quality, the noise in the input data has to be adequately handled by the estimation method. The first two papers of this thesis develop a non-parametric optimization based framework for the estimation of high-quality arbitrage-free option implied surfaces. The first paper covers the estimation of the risk-neutral density (RND) surface and the second paper the local volatility surface. Both methods provide smooth and realistic surfaces for market data. Estimation of the RND is a convex optimization problem, but the result is sensitive to the parameter choice. When the local volatility is estimated the parameter choice is much easier but the optimization problem is non-convex, even though the algorithm does not seem to get stuck in local optima. The SP models used to make optimal decisions on the equity derivatives markets also need generated scenarios for the underlying stock prices or index levels as input. The third paper of this thesis deals with the estimation and evaluation of existing equity market models. The third paper gives preliminary results which show that, out of the compared models, a GARCH(1,1) model with Poisson jumps provides a better fit compared to more complex models with stochastic volatility for the Swedish OMXS30 index. Det övergripande syftet med doktorandprojektet är att utveckla ett ramverk för att fatta optimala beslut på aktiederivatmarknaderna. Att fatta optimala beslut syftar till exempel på hur man optimalt ska hedga en optionsportfölj, eller hur man ska göra optimala investeringar på aktiederivatmarknaderna. Ramverket för att fatta optimala beslut kommer att baseras på stokastisk programmerings-modeller (SP-modeller), vilket betyder att det är nödvändigt att generera högkvalitativa scenarier för marknadspriser för en framtida tidpunkt som indata till SP-modellen. Detta leder till en situation där de traditionella metoderna, som finns beskrivna i litteraturen, för att modellera marknadspriser inte ger scenarier av tillräckligt hög kvalitet för att fungera som indata till SP-modellen. Följaktligen är huvudfokus för denna avhandling att utveckla metoder som, jämfört med de traditionella metoderna som finns beskrivna i litteraturen, förbättrar estimeringen av ytor som impliceras av en given mängd observerade optionspriser. Estimeringen kompliceras av att observerade optionspriser innehåller mycket brus och möjligen också arbitrage. Det betyder att för att kunna estimera optionsimplicerade ytor som är arbitragefria och av hög kvalitet, så behöver estimeringsmetoden hantera bruset i indata på ett adekvat sätt. De första två artiklarna i avhandlingen utvecklar ett icke-parametriskt optimeringsbaserat ramverk för estimering av högkvalitativa och arbitragefria options-implicerade ytor. Den första artikeln behandlar estimeringen av den risk-neutrala täthetsytan (RND-ytan) och den andra artikeln estimeringen av den lokala volatilitetsytan. Båda metoderna ger upphov till jämna och realistiska ytor för marknadsdata. Estimeringen av RND-ytan är ett konvext optimeringsproblem men resultatet är känsligt för valet av parametrar. När den lokala volatilitetsytan estimeras är parametervalet mycket enklare men optimeringsproblemet är icke-konvext, även om algoritmen inte verkar fastna i lokala optima. SP-modellerna som används för att fatta optimala beslut på aktiederivatmarknaderna behöver också indata i form av genererade scenarier för de underliggande aktiepriserna eller indexnivåerna. Den tredje artikeln i avhandlingen behandlar estimering och evaluering av existerande modeller för aktiemarknaden. Den tredje artikeln tillhandahåller preliminära resultat som visar att, av de jämförda modellerna, ger en GARCH(1,1)-modell med Poissonhopp en bättre beskrivning av dynamiken för det svenska aktieindexet OMXS30 jämfört med mer komplicerade modeller som innehåller stokastisk volatilitet.

This paper suggests a modularized sales and operations planning (S&OP) framework, consisting of content and process. The framework’s content is based on a typology of decoupling points in which the effect of decoupling points on the decision variables in S&OP is studied. The framework’s process takes a step back and addresses the need for a more elaborate design to precede the operational use of S&OP content for different production contexts. The framework supports both process industries (PIs) and discrete manufacturing industries (DIs), and recognizes their specific requirements and reflects them in their S&OP. The differentiating characteristics of PIs and DIs are emphasized through three different decoupling points, namely: discretization decoupling point, control mode decoupling point, and customer order decoupling point. The suggested framework aims to fill the gap in the literature regarding the lack of aggregate planning processes that match the PIs’ specific requirements by reflecting the differentiating characteristics of PIs in S&OP.

This dissertation is centered around two comprehensive themes: the extraction of information embedded in equity index option prices, and how to use this information in order to be able to make optimal decisions in the equity index option markets. These problems are important for decision makers in the equity index options markets, since they are continuously faced with making decisions under uncertainty given observed market prices. The methods developed in this dissertation provide robust tools that can be used by practitioners in order to improve the quality of the decisions that they make. In order to be able to extract information embedded in option prices, the dissertation develops two different methods for estimation of stable option implied surfaces which are consistent with observed market prices. This is a difficult and ill-posed inverse problem which is complicated by the fact that observed option prices contain a large amount of noise stemming from market micro structure effects. Producing estimated surfaces that are stable over time is important since otherwise risk measurement of derivatives portfolios, pricing of exotic options and calculation of hedge parameters will be prone to include significant errors. The first method that we develop leads to an optimization problem which is formulated as a convex quadratic program with linear constraints which can be solved very efficiently. The second estimation method that we develop in the dissertation makes it possible to produce local volatility surfaces of high quality, which are consistent with market prices and stable over time. The high quality of the surfaces estimated with the second method is the crucial input to the research which has resulted in the last three papers of the dissertation. The stability of the estimated local volatility surfaces makes it possible to build a realistic dynamic model for the equity index derivatives market. This model forms the basis for the stochastic programming (SP) model for option hedging that we develop in the dissertation. We show that the SP model, which uses generated scenarios for the squared local volatility surface as input, outperforms the traditional hedging methods that are described in the literature. Apart from having an accurate view of the variance of relevant risk factors, it is when building a dynamic model also important to have a good estimate of the expected values, and thereby risk premia, of those factors. We use a result from recently published research which lets us recover the real-world density from only a cross-section of observed option prices via a local volatility model. The recovered real-world densities are then used in order to identify and estimate liquidity premia that are embedded in option prices. We also use the recovered real-world densities in order to test how well the option market predicts the realized statistical characteristics of the underlying index. We compare the results with the performance of commonly used models for the underlying index. The results show that option prices contain a premium in the tails of the distribution. By removing the estimated premia from the tails, the resulting density predicts future realizations of the underlying index very well.

To make a difference among the energy intensive process industries, this dissertation addresses production planning and supply chain planning problems related to industrial energy management issues. The energy issue is turning more and more important from different angles, involving price as well as environmental problems due to climate change leading to political pressure on all energy users. The process industry sector is one of the largest users of energy, and thus important to analyse. Process industries are also capital intensive and operate on large and expensive process equipment, making it imperative to plan their production well in order to reach preferable capacity utilisation. Therefore this dissertation strives to locate the most important energy management issues for the long term profitability of process industries, and investigates the symbiotic effects of including energy issues in production and supply chain planning. Three different studies at three case companies are carried out, analysed, and presented in five papers. The cases represent the process industry sectors: chemicals, pulp, and steel. Both qualitative case study methodologies as well as quantitative mathematical modelling and optimisation approaches have been practiced. The research questions are analysed from both an energy system and from a production process point of view, separately as well as combined. Energy is somewhat considered to be the main workforce for process industries and this dissertation exemplifies some of its most important dimensions in this context. Several prerequisites for putting energy management on the strategic agenda are located in a specialty chemical industry where the importance of introducing a strategic perspective on energy, the way energy is used, and the possibilities of increasing alternative revenue from utilising by- and/or co-products differently are pinpointed. Approaches for including energy issues in planning processes are also suggested in terms of a MILP model for the entire supply chain of a pulp company, including decisions on purchase and transportation of raw maerials, production allocation, energy mix, and distribution. Another example is presented based on the perspectives of economics of scale and lot sizing through economic order quantity principles in a steel company. By using real company data, energy smart approaches in planning and scheduling are developed with respect to the most important intersections between the production processes and their supporting energy system. The accumulated resource intensity and embedded energy could, and probably should, hence be more fairly reflected in the product price. The research finally shows some possible impact with including energy issues in a production and supply chain planning model. By planning differently, production prioritisations can be done, and it is not only possible without any large investments, but also prosperous with savings on both energy and money within reach. To conclude, planning of production and supply chain has either a direct or an indirect impact on the energy cost-effectiveness of a company. This dissertation argues that such impact also exists in its mutual form, and is very important when the energy issues are large enough, as they often are in the energy intensive process industry sector. Decision makers should thus beware of the short end of the stick that might be devastating in the long run, but also aware of all the possibilities that can bring success and prosperity when the future begins.