Robust scenario formulations for strategic supply chain optimization under uncertainty

Strategic supply chain optimization (SCO) problems are often modelled as a two-stage optimization problem, in which the first-stage variables represent decisions on the development of the supply chain and the second-stage variables represent decisions on the operations of the supply chain. When uncertainty is explicitly considered, the problem becomes an intractable infinite-dimensional optimization problem, which is usually solved approximately via a scenario or a robust approach. This paper proposes a novel synergy of the scenario and robust approaches for strategic SCO under uncertainty. Two formulations are developed, namely, naïve robust scenario formulation and affinely adjustable robust scenario formulation. It is shown that both formulations can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded with the infinity-norm, and the uncertain equality constraints can be reformulated into deterministic constraints without assumption of the uncertainty region. Case studies of a classical farm planning problem and an energy and bioproduct SCO problem demonstrate the advantages of the proposed formulations over the classical scenario formulation. The proposed formulations not only can generate solutions with guaranteed feasibility or indicate infeasibility of a problem, but also can achieve optimal expected economic performance with smaller numbers of scenarios.

The Olivia Framework:Concepts for Use in Finely-Grained, Integrated Social Policy Analysis (Working Paper 45)

The Olivia framework is a set of concepts and measures that, when mature, will allow users to describe, in a consistent and integrated manner, everything about individuals and institutions that is of potential interest to social policy. The present paper summarizes the current stage of development in achieving this highly ambitious goal. The current version of the framework supports analysis of social trends and policy responses from many perspectives: • The point-in-time, resource-flow perspectives that underlie most traditional, economics-based policy analysis. • Life-course perspectives, including both transitions/trajectories analysis and asset-based analysis. • Spatial perspectives that anchor people in space and history and that provide a link to macro-analysis. • The perspective of the purposes/goals of individuals and institutions, including the objectives of different types of government programming. The concepts of the framework, which are all potentially measurable, provide a language that can support integrated analysis in all these areas at a much finer level of description than is customary. It provides a language that is especially well suited for analysis of the incremental policy changes that are typical of a mature welfare state. It supports both qualitative and quantitative analysis, enabling some integration between the two. It supports citizen-centric as well as a government-centric view of social policy. In its current version, the concepts are most highly developed as they related to social policies as they related to labour markets, equality and social integration, care-giving, immigration, income security, sustainability, and social and economic well-being more generally. However the paper points to likely extensions in the areas of health, justice and safety.

CT Image Electron Density Quantification in Regions with Metal Implants: Implications for Radiotherapy Treatment Planning

In radiotherapy planning, computed tomography (CT) images are used to quantify the electron density of tissues and provide spatial anatomical information. Treatment planning systems use these data to calculate the expected spatial distribution of absorbed dose in a patient. CT imaging is complicated by the presence of metal implants which cause increased image noise, produce artifacts throughout the image and can exceed the available range of CT number values within the implant, perturbing electron density estimates in the image. Furthermore, current dose calculation algorithms do not accurately model radiation transport at metal-tissue interfaces. Combined, these issues adversely affect the accuracy of dose calculations in the vicinity of metal implants. As the number of patients with orthopedic and dental implants grows, so does the need to deliver safe and effective radiotherapy treatments in the presence of implants. The Medical Physics group at the Cancer Centre of Southeastern Ontario and Queen's University has developed a Cobalt-60 CT system that is relatively insensitive to metal artifacts due to the high energy, nearly monoenergetic Cobalt-60 photon beam. Kilovoltage CT (kVCT) images, including images corrected using a commercial metal artifact reduction tool, were compared to Cobalt-60 CT images throughout the treatment planning process, from initial imaging through to dose calculation. An effective metal artifact reduction algorithm was also implemented for the Cobalt-60 CT system. Electron density maps derived from the same kVCT and Cobalt-60 CT images indicated the impact of image artifacts on estimates of photon attenuation for treatment planning applications. Measurements showed that truncation of CT number data in kVCT images produced significant mischaracterization of the electron density of metals. Dose measurements downstream of metal inserts in a water phantom were compared to dose data calculated using CT images from kVCT and Cobalt-60 systems with and without artifact correction. The superior accuracy of electron density data derived from Cobalt-60 images compared to kVCT images produced calculated dose with far better agreement with measured results. These results indicated that dose calculation errors from metal image artifacts are primarily due to misrepresentation of electron density within metals rather than artifacts surrounding the implants.