Competitive Algorithms for the Online Minimum Peak Appointment Scheduling

Escribe, Célia; Hu, Michael S.; Levi, Retsef

doi:10.2139/ssrn.3787306

Cited by 4 publications

(9 citation statements)

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“…This allows for added scheduling flexibility which can be exploited. As Escribe [8] showed, this difference is sufficient to prove that the online MPAS problem is fundamentally different from bin packing. This is highlighted in Table 1, where the column denoted asymptotic ratio, referring to the asymptotic competitive ratio, gives a proven upper or lower bound on the ratio between objective function of the solution found to the optimal (taken in the limit over increasing input sizes).…”

Section: Introductionmentioning

confidence: 96%

“…This paper studies a variant of the well-known bin-packing problem called the minimum peak appointment scheduling (MPAS) problem [8]. Recently proposed, an input to this problem is a set of jobs, each of a given length, that needs to be scheduled within a period of time.…”

Section: Introductionmentioning

confidence: 99%

“…The objective is to minimize the peak utilization, that is, the maximum number of jobs being serviced simultaneously. In fact, Escribe et al [8] highlight this objective, since they considered an application in which each job is also assigned to a facility, and the aim is to minimize the number of facilities needed. One can view each facility as a bin, and the position within the bin as the time interval to which a job is assigned.…”

Section: Introductionmentioning

confidence: 99%

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

Devin¹,

Shmoys²

2021

Preprint

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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 deferred decision making. Specifically, it allows for the problem to be split into an online phase where a stream of appointment requests arrive requiring a scheduled time, followed by an offline phase where those appointments are scheduled into rooms. Similar to the bin-packing problem, the aim is to use the minimum number of rooms in the final configuration. This model more accurately captures scheduling appointments than bin packing. For example, a dialysis patient needs to know what time to arrive for an appointment, but does not need to know the assigned station ahead of time. Previous work developed a randomized algorithm for this problem which achieved an asymptotic competitive ratio of at most 1.5, proving that online MPAS was fundamentally different from the online bin-packing problem. Our main contribution is to develop a new randomized algorithm for the problem that achieves an asymptotic competitive ratio under 1.455, indicating the potential for further progress. This improvement is attained by modifying the process for scheduling appointments to increase the density of the packing in the worst case, along with utilizing the dual of the bin-packing linear programming relaxation to perform the analysis. We also present the first known lower bound of 1.2 on the asymptotic competitive ratio of both deterministic and randomized online MPAS algorithm. These results demonstrate how deferred decision-making can be leveraged to yield improved worst-case performance, a phenomenon which should be investigated in a broader class of settings.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Devin¹,

Shmoys²

2021

Preprint

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“…In the standard online bin packing problem [6,2,5] items are to be assigned to bins sequentially, and it is assumed that items just receive consecutive time slots in the bin, starting from time zero. An alternative online model was defined recently by Escribe, Hu, and Levi [11], where the online feature is the assignment to time slots rather than the bins. The problem is called minimum peak appointment scheduling (MPAS).…”

Section: Introductionmentioning

confidence: 99%

“…In the work by Escribe, Hu, and Levi [11], a randomized algorithm with asymptotic competitive ratio at most 1.5 was designed, which was recently improved to 16 11 ≈ 1.455 by Smedira and Shmoys [20]. A lower bound of 1.5 on the competitive ratio of deterministic algorithms was proved [11], while Smedira and Shmoys [20] proved a lower bound of 1.2 for the asymptotic competitive ratio of all randomized (and deterministic) algorithms. These results contrast with those known for the standard online bin packing.…”

Section: Introductionmentioning

confidence: 99%

Lower bounds on the performance of online algorithms for relaxed packing problems

Balogh¹,

Dósa²,

Epstein³

et al. 2022

Preprint

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We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level objective in both problems is to pack arriving items of sizes at most 1 into bins of capacity 1 as efficiently as possible, but the exact formalizations differ. In the appointment scheduling problem, every item has to be assigned to a position, which can be seen as a time interval during a workday of length 1. That is, items are not assigned to bins, but only once all the items are processed, the optimal number of bins subject to chosen positions is determined, and this is the cost of the online algorithm. On the other hand, in the removable knapsack problem there is a fixed number of bins, and the goal of packing items, which consists in choosing a particular bin for every packed item (and nothing else), is to pack as valuable a subset as possible. In this last problem it is possible to reject items, that is, deliberately not pack them, as well as to remove packed items at any later point in time, which adds flexibility to the problem.

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