Chance Constrained Programming Methods in Probabilistic Programming

摘要

This is a response to the article 'Decision Problems Under Risk and Chance Constrained Programming: Dilemmas in the Transition' (25) in which Professors Hogan, Morris and Thompson (HMT hereafter) recommend abandonment of Chance Constrained Programming (=CCP) in favor of Stochastic Programming with Recourse (=SPR)--which we shall also refer to as 2-stage Linear Programming Under Uncertainty (=LPUU) since this is the main variant of SPR which is relied upon for these conclusions in (25). In the interest of clarity and brevity, we do not pursue all of the topics covered in (25) since, as will become evident, a rather lengthy response is required to chase down even major issues. We also believe that (25) is directed to conceptual rather than practical issues of application and so, also for brevity, we brush aside qualifiers that appear in statements like the following: 'We wish to emphasize that recourse problems characterize almost all (sic) real decision problems involving risk.' Except for possibly affording some degree of protection to HMT, we do not see that such qualifiers serve any useful purpose.