{"id":{"repo_id":"lancaster","oai_identifier":"oai:eprints.lancs.ac.uk:82869"},"canonical_url":"https://search.dev.ndltd.org/etd/lancaster/oai:eprints.lancs.ac.uk:82869","repository":{"repo_id":"lancaster","name":"Lancaster University","base_url":"https://eprints.lancs.ac.uk/cgi/oai2"},"display":{"title":"Problem-driven scenario generation for stochastic programs","abstract":"Stochastic programming concerns mathematical programming in the presence of uncertainty. In a stochastic program uncertain parameters are modeled as random vectors and one aims to minimize the expectation, or some risk measure, of a loss function. However, stochastic programs are computationally intractable when the underlying uncertain parameters are modeled by continuous random vectors. Scenario generation is the construction of a finite discrete random vector to use within a stochastic program. Scenario generation can consist of the discretization of a parametric probabilistic model, or the direct construction of a discrete distribution. There is typically a trade-off here in the number of scenarios that are used: one must use enough to represent the uncertainty faithfully but not so many that the resultant problem is computationally intractable. Standard scenario generation methods are distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution. In this thesis we promote the idea of problem-based scenario generation. By taking into account the structure of the underlying problem one may be able to represent uncertainty in a more parsimonious way. The first two papers of this thesis focus on scenario generation for problems which use a tail-risk measure, such as the conditional value-at-risk, focusing in particular on portfolio selection problems. In the final paper we present a constraint driven approach to scenario generation for simple recourse problems, a class of stochastic programs for minimizing the expected shortfall and surplus of some resources with respect to uncertain demands.","abstract_html":"Stochastic programming concerns mathematical programming in the presence of uncertainty. In a stochastic program uncertain parameters are modeled as random vectors and one aims to minimize the expectation, or some risk measure, of a loss function. However, stochastic programs are computationally intractable when the underlying uncertain parameters are modeled by continuous random vectors. Scenario generation is the construction of a finite discrete random vector to use within a stochastic program. Scenario generation can consist of the discretization of a parametric probabilistic model, or the direct construction of a discrete distribution. There is typically a trade-off here in the number of scenarios that are used: one must use enough to represent the uncertainty faithfully but not so many that the resultant problem is computationally intractable. Standard scenario generation methods are distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution. In this thesis we promote the idea of problem-based scenario generation. By taking into account the structure of the underlying problem one may be able to represent uncertainty in a more parsimonious way. The first two papers of this thesis focus on scenario generation for problems which use a tail-risk measure, such as the conditional value-at-risk, focusing in particular on portfolio selection problems. In the final paper we present a constraint driven approach to scenario generation for simple recourse problems, a class of stochastic programs for minimizing the expected shortfall and surplus of some resources with respect to uncertain demands.","abstract_has_math":false,"creators":["Fairbrother, Jamie","Turner, Amanda","Wallace, Stein W."],"institution":"Lancaster University","degree_name":"Ph.D.","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016","date_published":"2016","updated_at":"2026-07-24T02:48:32Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Fairbrother, Jamie","Turner, Amanda","Wallace, Stein W."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016"]},{"key":"dc:date.issued","label":"Date","values":["2016"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["Lancaster University"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Mathematics and Statistics","Management Science"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["Lancaster University"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://eprints.lancs.ac.uk/id/eprint/82869/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://eprints.lancs.ac.uk/id/eprint/82869/1/master.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Stochastic programming concerns mathematical programming in the presence of uncertainty. In a stochastic program uncertain parameters are modeled as random vectors and one aims to minimize the expectation, or some risk measure, of a loss function. However, stochastic programs are computationally intractable when the underlying uncertain parameters are modeled by continuous random vectors. Scenario generation is the construction of a finite discrete random vector to use within a stochastic program. Scenario generation can consist of the discretization of a parametric probabilistic model, or the direct construction of a discrete distribution. There is typically a trade-off here in the number of scenarios that are used: one must use enough to represent the uncertainty faithfully but not so many that the resultant problem is computationally intractable. Standard scenario generation methods are distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution. In this thesis we promote the idea of problem-based scenario generation. By taking into account the structure of the underlying problem one may be able to represent uncertainty in a more parsimonious way. The first two papers of this thesis focus on scenario generation for problems which use a tail-risk measure, such as the conditional value-at-risk, focusing in particular on portfolio selection problems. In the final paper we present a constraint driven approach to scenario generation for simple recourse problems, a class of stochastic programs for minimizing the expected shortfall and surplus of some resources with respect to uncertain demands."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Problem-driven scenario generation for stochastic programs"]}]}],"canonical_facts":{"dc:creator":["Fairbrother, Jamie","Turner, Amanda","Wallace, Stein W."],"dc:date":["2016"],"dc:date.issued":["2016"],"dc:description.abstract":["Stochastic programming concerns mathematical programming in the presence of uncertainty. In a stochastic program uncertain parameters are modeled as random vectors and one aims to minimize the expectation, or some risk measure, of a loss function. However, stochastic programs are computationally intractable when the underlying uncertain parameters are modeled by continuous random vectors. Scenario generation is the construction of a finite discrete random vector to use within a stochastic program. Scenario generation can consist of the discretization of a parametric probabilistic model, or the direct construction of a discrete distribution. There is typically a trade-off here in the number of scenarios that are used: one must use enough to represent the uncertainty faithfully but not so many that the resultant problem is computationally intractable. Standard scenario generation methods are distribution-based, that is they do not take into account the underlying problem when constructing the discrete distribution. In this thesis we promote the idea of problem-based scenario generation. By taking into account the structure of the underlying problem one may be able to represent uncertainty in a more parsimonious way. The first two papers of this thesis focus on scenario generation for problems which use a tail-risk measure, such as the conditional value-at-risk, focusing in particular on portfolio selection problems. In the final paper we present a constraint driven approach to scenario generation for simple recourse problems, a class of stochastic programs for minimizing the expected shortfall and surplus of some resources with respect to uncertain demands."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://eprints.lancs.ac.uk/id/eprint/82869/1/master.pdf"],"dc:publisher.commercial":["Lancaster University"],"dc:publisher.department":["Mathematics and Statistics","Management Science"],"dc:publisher.institution":["Lancaster University"],"dc:relation.isreferencedby":["https://eprints.lancs.ac.uk/id/eprint/82869/"],"dc:title":["Problem-driven scenario generation for stochastic programs"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D."]},"updated_at":"2026-07-24T02:48:32Z"}