Erlang loss bounds for OT-ICU systems

In hospitals, patients can be rejected at both the operating theater (OT) and the intensive care unit (ICU) due to limited ICU capacity. The corresponding ICU rejection probability is an important service factor for hospitals. Rejection of an ICU request may lead to health deterioration for patients, and for hospitals to costly actions and a loss of precious capacity when an operation is canceled.\ud There is no simple expression available for this ICU rejection probability that takes the interaction with the OT into account. With c the ICU capacity (number of ICU beds), this paper proves and numerically illustrates a lower bound by an $M|G|c|c$ system and an upper bound by an $M|G|c-1|c-1$ system, hence by simple Erlang loss expressions.\ud The result is based on a product form modification for a special OT–ICU tandem formulation and proved by a technically complicated Markov reward comparison approach. The upper bound result is of particular practical interest for dimensioning an ICU to secure a prespecified service quality. The numerical results include a case study.\u

Position-dependent shear-induced austenite-martensite transformation in double-notched TRIP and dual-phase steel samples

While earlier studies on transformation-induced-plasticity (TRIP) steels focused on the determination of the austenite-to-martensite decomposition in uniform deformation or thermal fields, the current research focuses on the determination of the local retained austenite-to-martensite transformation behaviour in an inhomogeneous yet carefully controlled shear-loaded region of double-notched TRIP and dual-phase (DP) steel samples. A detailed powder analysis has been performed to simultaneously monitor the evolution of the phase fraction and the changes in average carbon concentration of metastable austenite together with the local strain components in the constituent phases as a function of the macroscopic stress and location with respect to the shear band. The metastable retained austenite shows a mechanically induced martensitic transformation in the localized shear zone, which is accompanied by an increase in average carbon concentration of the remaining austenite due to a preferred transformation of the austenite grains with the lowest carbon concentration. At the later deformation stages the geometry of the shear test samples results in the development of an additional tensile component. The experimental strain field within the probed sample area is in good agreement with finite element calculations. The strain development observed in the low-alloyed TRIP steel with metastable austenite is compared with that of steels with the same chemical composition containing either no austenite (a DP grade) or stable retained austenite (a TRIP grade produced at a long bainitic holding time). The transformation of metastable austenite under shear is a complex interplay between the local microstructure and the evolving strain fields

A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search

The parallel machine scheduling problem with unrelated machines is studied where the objective is to minimize the maximum makespan. In this paper, new local search algorithms are proposed where the neighborhood search of a solution uses the 'efficiency' of the machines for each job. It is shown that this method yields better solutions and shorter running times than the more general local search heuristics