This dissertation contributes to the theoretical foundations of systems engineering (SE) and exposes an unstudied SE area of definition of verification models. In practice, verification models are largely qualitatively defined based on heuristic assumptions rather than science-based approach. For example, we may state the desire for representativeness of a verification model in qualitative terms of low, medium, or high fidelity in early phases of a system lifecycle when verification requirements are typically defined. Given that fidelity is defined as a measure of approximation from reality and that the (real) final product does (or may) not exist in early phases, we are stating desire for and making assumptions of representative equivalence that may not be true. Therefore, this dissertation contends that verification models can and should be defined on the scientific basis of systems theoretic principles. Furthermore, the practice of SE is undergoing a digital transformation and corresponding desire to enhance SE educationally and as a discipline, which this research proposes to address through a science-based approach that is grounded in the mathematical formalism of systems theory. The maturity of engineering disciplines is reflected in their science-based approach, such as computational fluid dynamics and finite element analysis. Much of the discipline of SE remains qualitatively descriptive, which may suffer from interpretation discrepancies; rather than being grounded in, inherently analytical, theoretical foundations such as is a stated goal of the SE professional organization the International Council on Systems Engineering (INCOSE). Additionally, along with the increased complexity of modern engineered systems comes the impracticality of verification through traditional means, which has resulted in verification being described as broken and in need of theoretical foundations. The relationships used to define verification models are explored through building on the systems theoretic lineage of A. Wayne Wymore; such as computational systems theory, theory of system design, and theory of problem formulation. Core systems theoretic concepts used to frame the relationship-based definition of verification models are the notions of system morphisms that characterize equivalence between pairs, problem spaces of functions that bound the acceptability of solution systems, and hierarchy of system specification that characterizes stratification. The research inquisition was in regard to how verification models should be defined and hypothesized that verification models should be defined through a combination of systems theoretic relationships between verification artifacts; system requirements, system designs, verification requirements, and verification models. The conclusions of this research provide a science-based metamodel for defining verification models through systems theoretic principles. The verification models were shown to be indirectly defined from system requirements, through system designs and verification requirements. Verification models are expected to be morphically equivalent to corresponding system designs; however, there may exist infinite equivalence which may be reduced through defining bounding conditions. These bounding conditions were found to be defined through verification requirements that are formed as (1) verification requirement problem spaces that characterize the verification activity on the basis of morphic equivalence to the system requirements and (2) morphic conditions that specify desired equivalence between a system design and verification model. An output of this research is a system theoretic metamodel of verification artifacts, which may be used for a science-based approach to define verification models and advancement of the maturity of the SE discipline. / Doctor of Philosophy / We conduct verification to increase our confidence that the system design will do what is desired as defined in the requirements. However, it is not feasible to perform verification on the final product design within the full scope of the requirements; due to cost, schedule, and availability. As a result, we leverage surrogates, such as verification models, to conduct verification and determine our confidence in the system design. A challenge to our confidence in the system design exists in that we accept the representativeness of the surrogates based on faith alone; rather than scientific proof. This dissertation defines science-based approach to determining the representativeness of substitutes. In the discipline and practice of systems engineering, verification models serve as substitutes for the system design; and verification requirement problem spaces serve as substitutes the requirements. The research used mathematical principles to determine representative equivalence and to find that a combination of relationship framing is needed for sufficient selection of verification models. The framing includes relationships to the system being engineered and to the substitute conditions under which the verification model is examined relative to the conditions under which the engineered system is expected to operate. A comparison to the state of the discipline and practice to the research findings was conducted and resulted in confirming unique contribution of the dissertation research. In regard to framing the acceptability of verification models, this research established the foundations for a science-based method to advance the field of Systems Engineering.

Random or stochastic integral equations occur frequently in the mathematical description of random phenomena in engineering, physics, biology, and oceanography. The present study is concerned with random or stochastic integral equations of the Volterra type in the form x(t;w) = h(tiW) + fa k(t,T~w)f(T,x(Tjw»dT, t > 0, and of the Fredholm type in the form 00 x(tjw) = h(t:w) + fa ko(t,T;w)e(T,x(T;w»dT, t ~ 0, where w £ Q, the supporting set of a complete probability measure space (n,A,p). A random function x(t:w} is said to be a random solution of an equation such as those above if it satisfies the equation with probability one. It is also required that X(tiW) be a second order stochastic process. The purpose of this dissertation is to investigate the existence, uniqueness, and stochastic stability properties of a random solution of these Volterra and Fredholm stochastic integral equations using the "theory of admissibility" and probabilistic functional analysis. The techniques of successive approximations and stochastic approximation are employed to approximate the random solution of the stochastic Volterra integral equation, and the convergence of the approximations to the unique random solution in mean square and with probability one is proven. Problems in telephone traffic theory, hereditary mechanics, population growth, and stochastic control theory are formulated, and some of the results of the investigation are applied. Finally, a discrete version of the above random integral equations is given, and several theorems concerning the existence, uniqueness, and stochastic stability of a random solution of the discrete equation are proven. Approximation of the random solution of the discrete version is obtained, and its convergence to the random solution is studied. This work extends and generalizes the work done by C. P. Tsokos in Mathematical Systems Theory 3 {1969}, pages 222-231, and M. W. Anderson in his Ph.D. dissertation at the University of Tennessee, 1966, among others. Extensions:of this research to several areas of application are proposed. / Ph. D.

Recent research on working with families in which one child is suffering from a developmental disability has indicated a need for more focused clinical attention on the well sibling or neurotypical sibling experience. Research has also suggested that a systemic approach to the therapeutic process would be the most beneficial to all members of the family system, including the well sibling. Although the literature supports the use of systemic interventions in supporting the well sibling, there is a gap between what the research is suggesting and the clinical application. In an effort to fill this gap, this study sought to explore how Marriage and Family therapists are working systemically with families in which one child has a disability to incorporate the needs of the well sibling. After conducting four qualitative interviews and analyzing the data, three central themes emerged: 1) stabilization; 2) involving the well sibling; and 3) methods of support. Clinical implications as well as suggestions for future research are also addressed. / Master of Science

Yes / Purpose The research study aims to investigate green supply chain management (GSCM) elements as part of a complete system. It aims to understand the special properties of the GSCM system under the moderating effects of product complexity and purchasing structure. Design/methodology/approach A thorough literature review led to the building of the conceptual framework. Six constructs were identified using systems theory. These constructs include green supply chain technological dimensions (particularly, Artificial Intelligence (AI) based), green supply chain strategy, green supply chain process, product complexity, purchasing structure, and firm performance. The instrument was scientifically developed for gathering survey responses using complete design test methods. The conceptual model was eventually tested based on survey data collected from 250 automotive components and allied manufacturers in the emerging economy of South Africa. Findings The results indicate that GSCM technological dimensions (AI-based) positively influence GSCM strategy. Further, GSCM strategy was found to positively influence the GSCM process. The GSCM processes have significant effects on environmental performance, social performance, and financial performance. The product complexity has a significant moderation effect on the paths GSCM strategy and GSCM process. Originality/value The findings from multivariate data analysis provide a better understanding of GSCM system dynamics and are helpful to key decision-makers. This unique model has elevated GSCM theory to a new level. There are limited studies available in the existing GSCM literature using systems theory. This study will offer an advanced/comprehensive understanding to readers in this relatively new concept.

Yes / Purpose: The aim of this research is to evaluate if the Complex Adaptive Systems theory can be used to explain resilience strategies within the pharmaceutical supply chain Research Approach: An in depth review of literature surrounding resilience in the pharmaceutical supply chain. In order to pursue this study agenda, data was collected from Scopus, the largest peer review journal as well as EBSCOhost. The PRISMA guideline was adopted in the systematic review process where 34 peer reviewed papers in the field of CAS, supply chain and supply chain resilience were identified with respect to methodologies employed, location of the study and approaches. Findings and Originality: The systematic review of literature shows that there are inherent similarities between the concept of resilience and the CAS theory. The CAS theory explains that PSC’s are dynamic, have emergent behaviours complex, adaptive, interconnected as well as possess schemas that regulate their operations. Hence if resilience strategies are to be employed to mitigate disruptive events they need to be harnessed in a manner to fit this particular supply chain. This work is innovative as it provides a new insight into the contemporary discourse on resilience strategy creation and deployment, examining the use of this theory in the PSC, and thus provides original contribution. Research Impact: This study contributes to the existing literature base, by providing theoretical underpinnings in the area of resilience and the pharmaceutical supply chain. This furthers the CAS agenda, SCR agenda and also presents an innovative output which warrants more detailed analysis and feasibility testing. Practical Impact: Complexity principles are multi-scaled and multi-domain and as such the suggestions put forward in this theoretical framework can be adopted in various supply chain networks as well as disruptive events. It provides new insights with regards to structures for managers seeking to design and improve resilience supply chains, a key element of which is the adoption of a holistic analysis by SC managers when developing resilience strategies. This is critical if disruptions are to be identified and mitigated before their impact is felt.

<p>Sweden experiences heavy snowfall during the winter season and cost effective road maintenance is significantly affected by the routing of snowplows. The routing problem becomes more complex as the SwedishNational Road Administration (Vägverket) sets operational requirements such as satisfying a time window for each road segment. </p><p>This thesis focuses on route optimization for snowplows after snowfall; to develop and implement an algorithm for finding combinations of generated routes which minimize the total cost. The results are compared to those stated in the licentiate thesis by Doctoral student Nima Golbaharan (2001). </p><p>The algorithm calculates a lower bound to the problem using a Lagrangian master problem. A common subgradient approach is used to find near-optimal dual variables to be sent to a column-generation program which returns routes for the snowplows. A greedy heuristic chooses a feasible solution, which gives an upper bound to the problem. This entire process is repeated as needed. </p><p>This method for routing snowplows produces favorable results with a relatively small number of routes and are comparable to Golbaharan's results. An interesting observation involves the allocation of vehicles in which certain depots were regularly over- or under-utilized. This suggests that the quantity and/or distribution of available vehicles may not be optimal.</p>

<p>Nynas produces bitumen at two refineries in Sweden. The bitumen is shipped to seven depots along the swedish coast line, and from the depots special trucks handle the transportation to customers. Recently Nynas has transformed its supply chain and closed down a few depots. At the moment the company is considering a further reduction of the number of depots. In connection to these discussions an analyse of the companys distributionsystem and of possible changes is required. In this thesis an optimization model is developed that simulates Nynas distribution of bitumen from the depots to the customers. The model is used to investigate the required vehicle fleet size for a number of different scenarios, that is with different depots closed down. The question to be answered is, thus, what depots could be closed without any dramatic increase in the required vehicle fleet size? Scenarios where customers are allocated an increased storage capacity are also studied. </p><p>The distribution model that is developed is an inventory route planning problem. It is solved by column generation. Each column represents a route and is generated by a subproblem with restrictions on permitted working hours for the truck drivers. Integer solutions are generated heuristically. </p><p>Simulations that have been performed with the model reveals interesting differences concerning how the distribution is handled in different parts of Sweden. In western Sweden the transportation planning works well, but the distribution in the central parts of the country could be planned in a better way. Results from simulations also show that the depots in Norrköping and Västerås could be closed down without increasing the vehicle fleet. Probably, the existing vehicle fleet size will be sufficient even with the Kalmar-depot closed down. Nevertheless, Nynas transportation suppliers will have to purchase new vehicles if the Sandarne-depot is to be closed. </p><p>Another interesting conclusion that can be drawn from this thesis is that there is a potential for reducing the vehicle fleet size if the storage capacity is increased at a few chosen customers. A considerably small increase in the storage capacity at a few big customers that are located far from the depots will have a great effect.</p>

<p>We analyse several facets of bilevel decision problems under uncertainty. These problems can be interpreted as an extension of stochastic programming problems where part of the uncertainty is attributed to the behaviour of another actor.</p><p>The field of decision making under uncertainty with bilevel features is quite new and most approaches focus on the interactions and relations between the decision makers. In contrast to these studies, the approach of bilevel stochastic programming pursued here stresses the stochastic programming aspect of the problem formulation. The framework enables a direct application of stochastic programming concepts and solution methods to the bilevel relationship between the actors. Thus more complex problem structures can be studied and the aspect of uncertainty can be treated adequately.</p><p>Our analysis covers both theoretical and more practically oriented issues. We study different formulations of one and two stage bilevel stochastic programming problems and state necessary optimality conditions for each of the problem instances. Additionally we present a solution algorithm utilising a stochastic quasi-gradient method. A further study is concerned with the uniqueness of the minima of a convex stochastic programming problem with uncertainty about the decision variables. We state conditions on the distribution of the parameters representing the uncertainty such that the minima of the optimisation problem are unique. We formulate a model of competition and collaboration of two different types of telecom service providers, the owner of a bottleneck facility and a virtual network operator. This represents an application of a bilevel stochastic programming formulation to a liberalised telecommunications environment. Furthermore, the utilisation of the bilevel stochastic programming framework and the developed solution concepts for the analysis of principal agent models is demonstrated. Also here the background of a regulated telecom environment, more specific the relations between a regulator and a regulated telecommunications company, was chosen.</p>

We analyse several facets of bilevel decision problems under uncertainty. These problems can be interpreted as an extension of stochastic programming problems where part of the uncertainty is attributed to the behaviour of another actor. The field of decision making under uncertainty with bilevel features is quite new and most approaches focus on the interactions and relations between the decision makers. In contrast to these studies, the approach of bilevel stochastic programming pursued here stresses the stochastic programming aspect of the problem formulation. The framework enables a direct application of stochastic programming concepts and solution methods to the bilevel relationship between the actors. Thus more complex problem structures can be studied and the aspect of uncertainty can be treated adequately. Our analysis covers both theoretical and more practically oriented issues. We study different formulations of one and two stage bilevel stochastic programming problems and state necessary optimality conditions for each of the problem instances. Additionally we present a solution algorithm utilising a stochastic quasi-gradient method. A further study is concerned with the uniqueness of the minima of a convex stochastic programming problem with uncertainty about the decision variables. We state conditions on the distribution of the parameters representing the uncertainty such that the minima of the optimisation problem are unique. We formulate a model of competition and collaboration of two different types of telecom service providers, the owner of a bottleneck facility and a virtual network operator. This represents an application of a bilevel stochastic programming formulation to a liberalised telecommunications environment. Furthermore, the utilisation of the bilevel stochastic programming framework and the developed solution concepts for the analysis of principal agent models is demonstrated. Also here the background of a regulated telecom environment, more specific the relations between a regulator and a regulated telecommunications company, was chosen.

Sweden experiences heavy snowfall during the winter season and cost effective road maintenance is significantly affected by the routing of snowplows. The routing problem becomes more complex as the SwedishNational Road Administration (Vägverket) sets operational requirements such as satisfying a time window for each road segment. This thesis focuses on route optimization for snowplows after snowfall; to develop and implement an algorithm for finding combinations of generated routes which minimize the total cost. The results are compared to those stated in the licentiate thesis by Doctoral student Nima Golbaharan (2001). The algorithm calculates a lower bound to the problem using a Lagrangian master problem. A common subgradient approach is used to find near-optimal dual variables to be sent to a column-generation program which returns routes for the snowplows. A greedy heuristic chooses a feasible solution, which gives an upper bound to the problem. This entire process is repeated as needed. This method for routing snowplows produces favorable results with a relatively small number of routes and are comparable to Golbaharan's results. An interesting observation involves the allocation of vehicles in which certain depots were regularly over- or under-utilized. This suggests that the quantity and/or distribution of available vehicles may not be optimal.