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The recently introduced online Minimum Peak Appointment Scheduling (MPAS)problem is a variant of the online bin-packing problem that allows for deferreddecision making. Specifically, it allows for the problem to be split into anonline phase where a stream of appointment requests arrive requiring ascheduled time, followed by an offline phase where those appointments arescheduled into rooms. Similar to the bin-packing problem, the aim is to use theminimum number of rooms in the final configuration. This model more accuratelycaptures scheduling appointments than bin packing. For example, a dialysispatient needs to know what time to arrive for an appointment, but does not needto know the assigned station ahead of time.  Previous work developed a randomized algorithm for this problem whichachieved an asymptotic competitive ratio of at most 1.5, proving that onlineMPAS was fundamentally different from the online bin-packing problem. Our maincontribution is to develop a new randomized algorithm for the problem thatachieves an asymptotic competitive ratio under 1.455, indicating the potentialfor further progress. This improvement is attained by modifying the process forscheduling appointments to increase the density of the packing in the worstcase, along with utilizing the dual of the bin-packing linear programmingrelaxation to perform the analysis. We also present the first known lower boundof 1.2 on the asymptotic competitive ratio of both deterministic and randomizedonline MPAS algorithm. These results demonstrate how deferred decision-makingcan be leveraged to yield improved worst-case performance, a phenomenon whichshould be investigated in a broader class of settings.

Scheduling Appointments Online:\\ The Power of Deferred Decision-Making