Non-Parametric Stochastic Sequential Assignment With Random Arrival Times

Abstract

We consider a problem wherein jobs arrive at random times and assume random values. Upon each job arrival, the decision-maker must decide immediately whether or not to accept the job and gain the value on offer as a reward, with the constraint that they may only accept at most n jobs over some reference time period. The decision-maker only has access to M independent realisations of the job arrival process. We propose an algorithm, Non-Parametric Sequential Allocation (NPSA), for solving this problem. Moreover, we prove that the expected reward returned by the NPSA algorithm converges in probability to optimality as M grows large. We demonstrate the effectiveness of the algorithm empirically on synthetic data and on public fraud-detection datasets, from where the motivation for this work is derived.

Optimal Admission Control for Multiclass Queues with Time-Varying Arrival Rates via State Abstraction

“…We assume that there are 20 staff (servers), and that transactions of different values require different processes to review, and therefore have the following service rates: {low val= 1 900 , med val= 1 3600 , high val= 1 10,800 }. We learn the adjusted price distributions and arrival rate functions from M train with the method from Dervovic et al (2021). We then simulate the total adjusted price of transactions reviewed using the remainder of the data, M test .…”

“…This problem is also referred to as the dynamic and stochastic knapsack problem (Kleywegt and Papastavrou 1998). The SSAP was recently revisited by Dervovic et al (2021) to address the problem when the arrival and reward distributions must be learnt from historical data. In contrast to our work, the SSAP problem assumes that the number of tasks to be accepted is known a priori, whereas we assume that tasks have stochastic processing times.…”

“…The mean shortage function can be computed in closed form for many common distributions (e.g. exponential, Pareto), and can be computed efficiently for the nonparametric representation of the task price distribution used in Dervovic et al (2021).…”