Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts

Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.publishedVersio

Optimal Investments in PV Sources for Grid-Connected Distribution Networks: An Application of the Discrete–Continuous Genetic Algorithm

The problem of the optimal siting and sizing of photovoltaic (PV) sources in grid connected distribution networks is addressed in this study with a master–slave optimization approach. In the master optimization stage, a discrete–continuous version of the Chu and Beasley genetic algorithm (DCCBGA) is employed, which defines the optimal locations and sizes for the PV sources. In the slave stage, the successive approximation method is used to evaluate the fitness function value for each individual provided by the master stage. The objective function simultaneously minimizes the energy purchasing costs in the substation bus, and the investment and operating costs for PV sources for a planning period of 20 years. The numerical results of the IEEE 33-bus and 69-bus systems demonstrate that with the proposed optimization methodology, it is possible to eliminate about 27% of the annual operation costs in both systems with optimal locations for the three PV sources. After 100 consecutive evaluations of the DCCBGA, it was observed that 44% of the solutions found by the IEEE 33-bus system were better than those found by the BONMIN solver in the General Algebraic Modeling System (GAMS optimization package). In the case of the IEEE 69-bus system, the DCCBGA ensured, with 55% probability, that solutions with better objective function values than the mean solution value of the GAMS were found. Power generation curves for the slack source confirmed that the optimal siting and sizing of PV sources create the duck curve for the power required to the main grid; in addition, the voltage profile curves for both systems show that voltage regulation was always maintained between ±10% in all the time periods under analysis. All the numerical validations were carried out in the MATLAB programming environment with the GAMS optimization package

Collective opinion formation in a business climate survey

A large body of literature has proposed models inspired by particle physics as formalizations of collective processes in the economic and social spheres of human societies [1, 2, 3, 4]. However, attempts at empirical validation of such models have been very sparse so far. This paper develops a broadly applicable methodology for estimating the parameters of microscopic models of social interactions. Its application to a popular business climate survey indicates that the collective behaviour of the survey respondents is well explained by a simple ‘particle’ model of social interactions. This result also lends support to the view that the large fluctuations of investors’ and consumers’ confidence are mostly due to ‘animal spirits’ rather than new information

Optimal GENCO bidding strategy

Electricity industries worldwide are undergoing a period of profound upheaval. The conventional vertically integrated mechanism is being replaced by a competitive market environment. Generation companies have incentives to apply novel technologies to lower production costs, for example: Combined Cycle units. Economic dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary Algorithms share a common mechanism, stochastic searching per generation. The stochastic property makes evolutionary algorithms robust and adaptive enough to solve a non-convex optimization problem. This research implements GA, EP, and PS algorithms for economic dispatch with Combined Cycle units, and makes a comparison with classical Mixed Integer Linear Programming.;The electricity market equilibrium model not only helps Independent System Operator/Regulator analyze market performance and market power, but also provides Market Participants the ability to build optimal bidding strategies based on Microeconomics analysis. Supply Function Equilibrium (SFE) is attractive compared to traditional models. This research identifies a proper SFE model, which can be applied to a multiple period situation. The equilibrium condition using discrete time optimal control is then developed for fuel resource constraints. Finally, the research discusses the issues of multiple equilibria and mixed strategies, which are caused by the transmission network. Additionally, an advantage of the proposed model for merchant transmission planning is discussed.;A market simulator is a valuable training and evaluation tool to assist sellers, buyers, and regulators to understand market performance and make better decisions. A traditional optimization model may not be enough to consider the distributed, large-scale, and complex energy market. This research compares the performance and searching paths of different artificial life techniques such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Particle Swarm (PS), and look for a proper method to emulate Generation Companies\u27 (GENCOs) bidding strategies.;After deregulation, GENCOs face risk and uncertainty associated with the fast-changing market environment. A profit-based bidding decision support system is critical for GENCOs to keep a competitive position in the new environment. Most past research do not pay special attention to the piecewise staircase characteristic of generator offer curves. This research proposes an optimal bidding strategy based on Parametric Linear Programming. The proposed algorithm is able to handle actual piecewise staircase energy offer curves. The proposed method is then extended to incorporate incomplete information based on Decision Analysis. Finally, the author develops an optimal bidding tool (GenBidding) and applies it to the RTS96 test system

Climate change and agricultural structural change : the relevance for machinery use and acquisition in Germany

This thesis is a contribution to the research project Regional Climate Change, funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG Forschergruppe 1695 Regionaler Klimawandel). The projects objective was to learn about the vulnerability and sensitivity of typical land systems in Southwest Germany and identify suitable strategies for adaptation. The doctoral work contributes with empirical and methodological insights of farmers likely management adaptations in light of the farm managerial challenges arising from climate and structural change in Germany. The agricultural structure in Germany has strongly changed in the last 60 years. Where before numerous small-scale and labor-intensive farms were observed, it is now the place where fewer and highly mechanized farms contribute to agricultural production. The ongoing agricultural structural change in Germany is characterized by a trend in which many farms exit the agricultural sector, and the remaining --growth-oriented-- farmers take over the land, reorganize their farm business, and expand their operations. Nevertheless, this trend of farm growth, which is expected to continue in the future, poses significant challenges at the farm management level: Decisions on machinery use and acquisition play a crucial role in shaping the farm cost structure, and represent a critical element for maintaining competitiveness. Particularly for the expansion efforts, farm managers face a highly complex decision-making process to acquire the proper machinery capacities for field operations. Moreover, an additional factor will need to be considered for adequate decision-making: Climate change developments and the uncertainties associated with this process will likely increase the complexity of the farmers decision-making regarding the best reorganizational strategies towards farms expansion. Changes in the natural conditions for crop growth and development will likely result in management adaptations, e.g., changing the timing for fieldwork operations or changing land-use patterns. An analysis of the complex interactions and interdependencies between the environment and the farm system, on the one hand, and the resources and production possibilities available to the farm manager in the course of farm expansion on the other hand, require adequate tools of analysis. This work analyzes three dimensions of farm machinery management in the context of climate change and agricultural structural change. The first element of analysis corresponds to an examination of the sensibility of land-use and machinery investment decisions to climate change scenarios with the agent-based MPMAS model constructed for Central Swabian Jura in Southwest Germany. The Central Swabian Jura MPMAS model is a constitutive part of the bioeconomic modeling system MPMAS_XN. The MPMAS_XN system integrates the agricultural economic agent-based software MPMAS and the plant-soil modeling software Expert-N (XN) into a fully coupled system. The assessment of the sensibility and responsiveness of the MPMAS component revealed complex adaptation responses of land-use and machinery investment decisions as a result of shifted timing in fieldwork operations (e.g., harvesting or fertilization tasks). The second element of analysis corresponds to an examination of economies of size arising from farm machinery use and acquisition decisions in arable farms that follow a typical crop rotation practiced in Germany. For the analysis, a whole-farm multiperiod mathematical program implemented in the agent-based software MPMAS was employed. Optimizations were run and evaluated at a broad range of farm sizes and two distinctive distributions of availability of fieldwork days estimated for Southwest Germany. The results allowed observing patterns of optimal farm machinery demand and cost curves for several evaluated farm sizes and distributions of available fieldwork days distributions. The third main element of this work corresponds to a methodological contribution to the MPMAS_XN model system. Within this element, the implementation, functioning, and potential of an external theory-based MPMAS module are presented. The external module represents dynamics for joint machinery investments among simulated farm agents and serves as an enhancing methodological contribution for analyzing and representing farm machinery management in the agent-based software MPMAS.Diese Arbeit ist ein Beitrag zum von der Deutschen Forschungsgemeinschaft geförderten Projekt Regionaler Klimawandel, dessen Ziel es war die Verwundbarkeit und Sensitivität typischer Landsysteme in Südwestdeutschland zu untersuchen und geeignete Anpassungsstrategien zu identifizieren. Diese Doktorarbeit liefert empirische und methodische Erkenntnisse über die wahrscheinlichen Managementanpassungen der Landwirte und Landwirtinnen angesichts der Herausforderungen der Betriebsführung, die sich aus dem Klima- und Strukturwandel in Deutschland ergeben. Die Agrarstruktur in Deutschland hat sich in den letzten 60 Jahren stark verändert. Wo früher zahlreiche kleine und arbeitsintensive Betriebe beobachtet wurden, tragen heute weniger, dafür aber hochmechanisierte Betriebe zur landwirtschaftlichen Produktion bei. Dieser anhaltende landwirtschaftliche Strukturwandel in Deutschland kennzeichnet sich dadurch, dass viele Betriebe den Agrarsektor verlassen und die verbleibenden, wachstumsorientierten Landwirte und Landwirtinnen die Produktion übernehmen, ihre Betriebe neu organisieren und ihre Tätigkeiten ausweiten. Dieser Wachstumstrend, der sich voraussichtlich in Zukunft fortsetzen wird,hat erhebliche Herausforderungen auf der Ebene des Betriebsmanagements zur Folge: Entscheidungen über den Einsatz und die Anschaffung von Maschinen spielen eine entscheidende Rolle bei der Gestaltung der Betriebskostenstruktur und sind daher ein zentrales Element für die Aufrechterhaltung der Wettbewerbsfähigkeit. Insbesondere bei den Expansionsbemühungen stehen die BetriebsleiterInnen vor einem hochkomplexen Entscheidungsprozess, um die passenden Maschinenkapazitäten für den Feldeinsatz zu erwerben. Neben dem Erwerb und der optimalen Nutzung von Maschinen muss ein zusätzlicher Faktor für eine angemessene Entscheidungsfindung berücksichtigt werden: Die Entwicklung des Klimawandels und die mit diesem Prozess einhergehenden Unsicherheiten werden die Komplexität der Entscheidungsfindung hinsichtlich der besten Umstrukturierungsstrategien für die Expansion der landwirtschaftlichen Betriebe vermutlich weiter erhöhen. Dadurch entstehenden Änderungen der natürlichen Bedingungen für Pflanzenwachstum und -entwicklung wird wahrscheinlich mit Anpassungen des Managements begegnet, z.B. durch Verschiebung derFeldarbeitszeitpunkte oder durch Veränderung der Landnutzungsmuster. Eine Analyse der geschilderten komplexen Wechselwirkungen und Abhängigkeiten, einerseits zwischen Umwelt und landwirtschaftlichen Systemen, andererseits zwischen Ressourcen und Produktionsmöglichkeiten, die den Verantwortlichen zur Betriebserweiterung zur Verfügung stehen, erfordert geeignete Analysewerkzeuge. Diese Arbeit analysiert drei Dimensionen des Landmaschinenmanagements im Kontext des Klimawandels und des landwirtschaftlichen Strukturwandels. Im ersten Analyseelement wird die Sensibilität von Landnutzungs- und Maschineninvestitionsentscheidungen in Bezug auf verschiedene Klimawandelszenarien untersucht. Diese Analyse wird mit dem agentenbasierten MPMAS Modell durchgeführt, das für die mittlere Schwäbischen Alb in Südwestdeutschland erstellt wurde. Das MPMAS- Modell ist ein wesentlicher Bestandteil des bioökonomischen Modellierungssystems MPMAS_XN. Das MPMAS_XN Modellierungssystem integriert die agrarökonomische, agentenbasierte MPMAS Software und die Pflanzen-Boden-Modellierungssoftware Expert-N (XN) in ein vollständig gekoppeltes System. Die Bewertung der Sensibilität und Reaktionsfähigkeit der MPMAS Komponente zeigt komplexe Anpassungsreaktionen von Landnutzungs- und Maschineninvestitionsentscheidungen als Ergebnis eines verschobenen Zeitplans bei Feldarbeiten (z. B. Ernte- oder Düngungsaufgaben). Im zweiten Schritt befasst sich die vorliegende Arbeit mit einer Untersuchung der Skaleneffekte, die sich aus den Kaufentscheidungen und dem Einsatz von Landmaschinen in Ackerbetrieben ergeben, in denen eine für Deutschland übliche Fruchtfolge angebaut wird. Für die Analyse wird ein in der agentenbasierten Software MPMAS implementiertes mathematisches Mehrperiodenprogramm für den gesamten landwirtschaftlichen Betrieb verwendet. Optimierungen werden in einem breiten Spektrum von Betriebsgrößen und zwei unterschiedlichen Verteilungen der Verfügbarkeit von Feldarbeitstagen, die für Südwestdeutschland geschätzt werden, durchgeführt und bewertet. Die Ergebnisse ermöglichen die Beobachtung von Mustern der optimalen Nachfrage nach landwirtschaftlichen Maschinen sowie der Kostenkurven für die betrachteten Betriebsgrößen und Verteilungen der verfügbaren Feldarbeitstage. Der dritte Hauptteil dieser Arbeit stellt einen methodischen Beitrag zum MPMAS_XN Modellsystem dar. In diesem Element werden die Implementierung, Funktionsweise und das Potenzial eines externen und theoretisch aufgebauten MPMAS-Moduls vorgestellt. Dieses externe Modul repräsentiert die Dynamik, die sich aus gemeinsamen Maschineninvestitionen zwischen simulierten Computer-Agenten ergibt und dient als verbesserter methodischer Beitrag zur Analyse und Darstellung des Landmaschinenmanagements in der Agentenbasierte Software MPMAS

Should network structure matter in agent-based finance?

We derive microscopic foundations for a well-known probabilistic herding model in the agent-based finance literature. Lo and behold, the model is quite robust with respect to behavioral heterogeneity, yet structural heterogeneity, in the sense of an underlying network structure that describes the very feasibility of agent interaction, has a crucial and non-trivial impact on the macroscopic properties of the model

Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation

This paper provides what we believe to be the first empirical test of whether investors in the foreign exchange market are uncertainty averse. We do this using a heterogeneous agents model in which fundamentalist and chartist beliefs of the exchange rate co-exist and are allowed to be either uncertainty neutral or uncertainty averse. Uncertainty aversion is modelled using the maxmin expected utility approach. We find significant evidence of uncertainty aversion in the FX market where in particular fundamentalists are found to be largely uncertainty neutral while chartists are mainly uncertainty averse. Inclusion of uncertainty averse agents significantly improves the performance of the model

Rational forecasts or social opinion dynamics? Identification of interaction effects in a business climate survey

This paper develops a methodology for estimating the parameters of dynamic opinion or expectation formation processes with social interactions. We study a simple stochastic framework of a collective process of opinion formation by a group of agents who face a binary decision problem. The aggregate dynamics of the individuals’ decisions can be analyzed via the stochastic process governing the ensemble average of choices. Numerical approximations to the transient density for this ensemble average allow the evaluation of the likelihood function on the base of discrete observations of the social dynamics. This approach can be used to estimate the parameters of the opinion formation process from aggregate data on its average realization. Our application to a well-known business climate index provides strong indication of social interaction as an important element in respondents’ assessment of the business climate