{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/16750"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/16750","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Essays on robust optimization, integrated inventory and pricing, and reference price effect","abstract":"This dissertation consists of two distinct lines of research e orts. Chapter 2 proposes a general methodology to seek robust solution to multi-stage stochastic optimization problems. Chapters 3, 4 and 5 all deal with models that arise from inventory management and dynamic pricing. Chapter 2 introduces the Extended Affinely Adjustable Robust Counterpart(EAARC). We first propose the general steps of extending affine decision rules via re-parameterizing the uncertainty set, then propose the example of splitting-based EAARC. We show that this approach extends the versatility of affine decision rules beyond what has been proposed by Ben-Tal et al. while retaining tractability. Chapter 3 looks at the classical joint inventory-and-pricing model (single product periodic-review) with concave ordering cost. Concave cost structures may often occur in settings with multiple sources of supply. For this model, assuming additive demand uncertainty, we show that a generalized (s; S; p) policy is optimal under certain conditions imposed on the distribution of the random perturbation. Chapter 4 and 5 focus on the reference price effect in which the price impact on demand is no longer instantaneous, but history-dependent. Chapter 4 analyzes a joint inventory-and-pricing model with reference price e ffect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected pro t may not be concave. In the in finite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Chapter 5 represents some initial e orts in modeling heterogeneity in the consumer group, in which we study a continuous-time dynamic pricing problem under stochastic reference price e ffect. Stochastic optimal control theory is applied to the problem to derive an explicit solution. Various comparative statics are then conducted to benchmark our model against a few simpli ed models.","abstract_html":"This dissertation consists of two distinct lines of research e orts. Chapter 2 proposes a general methodology to seek robust solution to multi-stage stochastic optimization problems. Chapters 3, 4 and 5 all deal with models that arise from inventory management and dynamic pricing. Chapter 2 introduces the Extended Affinely Adjustable Robust Counterpart(EAARC). We first propose the general steps of extending affine decision rules via re-parameterizing the uncertainty set, then propose the example of splitting-based EAARC. We show that this approach extends the versatility of affine decision rules beyond what has been proposed by Ben-Tal et al. while retaining tractability. Chapter 3 looks at the classical joint inventory-and-pricing model (single product periodic-review) with concave ordering cost. Concave cost structures may often occur in settings with multiple sources of supply. For this model, assuming additive demand uncertainty, we show that a generalized (s; S; p) policy is optimal under certain conditions imposed on the distribution of the random perturbation. Chapter 4 and 5 focus on the reference price effect in which the price impact on demand is no longer instantaneous, but history-dependent. Chapter 4 analyzes a joint inventory-and-pricing model with reference price e ffect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected pro t may not be concave. In the in finite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Chapter 5 represents some initial e orts in modeling heterogeneity in the consumer group, in which we study a continuous-time dynamic pricing problem under stochastic reference price e ffect. Stochastic optimal control theory is applied to the problem to derive an explicit solution. Various comparative statics are then conducted to benchmark our model against a few simpli ed models.","abstract_has_math":false,"creators":["Zhang, Yuhan"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Industrial Engineering","degree_department":null,"school":null,"contributors":["Chen, Xin","Klabjan, Diego","Feng, Liming","Petruzzi, Nicholas C."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-08-20T17:56:42Z","date_published":"2010-08-20T17:56:42Z","updated_at":"2026-07-22T22:25:09Z","subjects":["Robust Optimization","Inventory Management","Dynamic Pricing","Reference Price Effect"],"languages":["en"],"rights":["Copyright 2010 Yuhan Zhang"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/16750","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Chen, Xin","Klabjan, Diego","Feng, Liming","Petruzzi, Nicholas C."]},{"key":"dc:creator","label":"Author","values":["Zhang, Yuhan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2010-08-20T17:56:42Z","2010-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Industrial Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Robust Optimization","Inventory Management","Dynamic Pricing","Reference Price Effect"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2010 Yuhan Zhang"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/16750"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation consists of two distinct lines of research e orts. Chapter 2 proposes a general methodology to seek robust solution to multi-stage stochastic optimization problems. Chapters 3, 4 and 5 all deal with models that arise from inventory management and dynamic pricing. Chapter 2 introduces the Extended Affinely Adjustable Robust Counterpart(EAARC). We first propose the general steps of extending affine decision rules via re-parameterizing the uncertainty set, then propose the example of splitting-based EAARC. We show that this approach extends the versatility of affine decision rules beyond what has been proposed by Ben-Tal et al. while retaining tractability. Chapter 3 looks at the classical joint inventory-and-pricing model (single product periodic-review) with concave ordering cost. Concave cost structures may often occur in settings with multiple sources of supply. For this model, assuming additive demand uncertainty, we show that a generalized (s; S; p) policy is optimal under certain conditions imposed on the distribution of the random perturbation. Chapter 4 and 5 focus on the reference price effect in which the price impact on demand is no longer instantaneous, but history-dependent. Chapter 4 analyzes a joint inventory-and-pricing model with reference price e ffect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected pro t may not be concave. In the in finite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Chapter 5 represents some initial e orts in modeling heterogeneity in the consumer group, in which we study a continuous-time dynamic pricing problem under stochastic reference price e ffect. Stochastic optimal control theory is applied to the problem to derive an explicit solution. Various comparative statics are then conducted to benchmark our model against a few simpli ed models.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-25T18:43:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Zhang_Yuhan.pdf: 571521 bytes, checksum: d9654e564adcac1e782498a4ceedb20e (MD5)","Made available in DSpace on 2010-08-20T17:56:42Z (GMT). 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We first propose the general steps of extending affine decision rules via re-parameterizing the uncertainty set, then propose the example of splitting-based EAARC. We show that this approach extends the versatility of affine decision rules beyond what has been proposed by Ben-Tal et al. while retaining tractability. Chapter 3 looks at the classical joint inventory-and-pricing model (single product periodic-review) with concave ordering cost. Concave cost structures may often occur in settings with multiple sources of supply. For this model, assuming additive demand uncertainty, we show that a generalized (s; S; p) policy is optimal under certain conditions imposed on the distribution of the random perturbation. Chapter 4 and 5 focus on the reference price effect in which the price impact on demand is no longer instantaneous, but history-dependent. Chapter 4 analyzes a joint inventory-and-pricing model with reference price e ffect. We prove that a reference price dependent base-stock policy is optimal even though the single period expected pro t may not be concave. In the in finite horizon case, we further show that in the optimal trajectory, reference price converges to a steady state and provide a characterization. Chapter 5 represents some initial e orts in modeling heterogeneity in the consumer group, in which we study a continuous-time dynamic pricing problem under stochastic reference price e ffect. Stochastic optimal control theory is applied to the problem to derive an explicit solution. Various comparative statics are then conducted to benchmark our model against a few simpli ed models.","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-25T18:43:20Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Zhang_Yuhan.pdf: 571521 bytes, checksum: d9654e564adcac1e782498a4ceedb20e (MD5)","Made available in DSpace on 2010-08-20T17:56:42Z (GMT). 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