Performance of the Smallest-Variance-First Rule in Appointment Sequencing

Abstract

Performance of the Smallest-Variance-First Rule in Appointment Sequencing

Dynamic Appointment Scheduling

“…The results are given in Table 5. The main conclusion is that the numerics align with findings of [13], in the sense that the cost of serving clients with decreasing µ i is substantially lower than for increasing µ i or randomly ordered µ i . ♦…”

“…With the above dynamic programming algorithm at our disposal, we can assess which order of the clients minimizes the objective function C 1 (1). As backed by the results in [13], the so-called smallest-variance-first rule (ordering the clients such that their mean service times, and hence also the corresponding variances, are increasing) is a logical candidate.…”

“…We do so for equally spaced µ i in the interval [0.5, 1.5] and n = 10. We first compute the cost when the µ i are increasing, corresponding to the smallest-variance-first strategy studied in [13]. Secondly, we pick a randomly selected permutation of the µ i .…”

“…The analysis borrows elements from e.g. [13,21,22]. We start by separately analyzing the cases N t+ = k + 1 and N t+ = 1.…”

“…Another related domain concerns the sequencing of the clients: whereas in our framework the order of the clients is fixed, one could also study the question of identifying the best sequence [4,17]. In this respect, there is empirical evidence and formal backing to opt for the rule that sequences clients in order of increasing variance of their service durations [13,14].…”