- Friday 26 April 2019
- Dr Dong Li; Loughborough University
We consider the scheduling of limited resources to a large number of jobs (e.g. medical treatment) with uncertain lifetimes and service times, in the aftermath of a mass casualty incident. Jobs are subject to triage at time zero, and placed into a number of classes. Our goal is to maximise the expected number of job completions. We propose an effective yet simple index policy based on Whittle's restless bandits approach. The problem concerned features a finite and uncertain time horizon that is dependent upon the service policy. Moreover, the number of job classes still competing for service diminishes over time. Two versions of Lagrangian relaxation are proposed in order to decompose the problem. The first is a direct extension of the standard Whittle's restless bandits approach, while in the second the total number of job classes still competing for service is taken into account. We prove the indexability of all job classes in the Markovian case, and develop closed-form indices. Extensive numerical experiments show that the second proposal has much stronger and more consistent performance than both the first one and a number of existing heuristics in the literature, even in non-Markovian settings.