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We present an analogy between cardinal characteristics from set theory and highness properties from computability theory, which specify a sense in which a Turing oracle is computationally strong. While this analogy was first studied explicitly by Rupprecht in his PhD thesis, many prior results can be viewed from this perspective. After a comprehensive survey of the analogy for characteristics from Cichon's diagram, we extend it to Kurtz randomness and the analogue of the Specker-Eda number., 28 pages; version 2 post refereeing, in particular with due credit to Rupprecht for results from his thesis of which we were previously unaware

The complexity of evaluating chance constraints makes chance-constrained programming problem difficult to solve. One way to handle this complexity is by devising satisficing measures for the relevant uncertainties. This paper focuses on solving the stochastic vehicle routing problem with time windows (VRPTW) by Satisficing Measure Approach (SMA) that mitigates the dissatisfaction experienced by the customers. Satisficing measures are first proposed for the VRPTW with stochastic demand on various distributions to demonstrate the dependency of customers' satisfaction towards lack of inventory based on the vehicle's capacity. Similar satisficing measures are extended to VRPTW with stochastic travel times. We integrate the proposed satisficing measures into an existing tabu-search heuristics to solve a set of generalized Solomon instances in a short amount of computation time. Compared with best-known results, the SMA saves the effort to design recourse actions, applicable to many popular probability distributions and produces very competitive results. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.