Abstract
This paper investigates an appointment system with deterministic arrival times and non-identical exponential service times with the objective of minimizing the expected costs of customer-waiting and server-idle times (WIT). For two customers, this paper shows analytically that the smallest-variance-first-rule (SV) and, equivalently, the smallest-mean-first-rule (SM) minimize WIT when the second customer arrives at either optimal or arbitrary arrival time. For three customers, this paper shows analytically that either SV or SM minimize WIT, assuming that each customer arrives at the cumulative sum of expected service times of prior customers. Based on numerical evaluation, this paper recommends that the exponential distribution parameter, which determines either SV or SM sequences, be used for a general number of customers.
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