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A classical problem in appointment scheduling, with applications in healthcare, concerns the determination of the patients' arrival times that minimize acost function that is a weighted sum of mean waiting times and mean idle times.One aspect of this problem is the sequencing problem, which focuses on orderingthe patients. We assess the performance of the smallest-variance-first (SVF)rule, which sequences patients in order of increasing variance of their servicedurations. While it was known that SVF is not always optimal, it has beenwidely observed that it performs well in practice and simulation. We provide atheoretical justification for this observation by proving, in various settings,quantitative worst-case bounds on the ratio between the cost incurred by theSVF rule and the minimum attainable cost. We also show that, in greatgenerality, SVF is asymptotically optimal, i.e., the ratio approaches 1 as thenumber of patients grows large. While evaluating policies by considering anapproximation ratio is a standard approach in many algorithmic settings, ourresults appear to be the first of this type in the appointment schedulingliterature.

Performance of the smallest-variance-first rule in appointment sequencing