The Hospitals/Residents Problem with Couples: complexity and integer programming models

The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc

Thermal fatigue and oxidation data of oxide dispersion-strengthened alloys

Thermal fatigue and oxidation data were obtained 24 specimens representing 9 discrete oxide dispersion-strengthened alloy compositions or fabricating techniques. Double edge wedge specimens, both bare metal and coated for each systems, were cycled between fluidized beds maintained at 1130 C with a three minute immersion in each bed. The systems included alloys identified as 262 in hardness of HRC 38; 264 in hardness of HRC 38, 40 and 43; 265 HRC 39, 266 of HRC 37 and 40; 754; and 956. Specimens in the bare condition of 265 HRC 39 and 266 HRC 37 survived 6000 cycles without cracking on the small radius of the double edge wedge specimen. A coated specimen of 262 HRC 38, 266 HRC 37 and 266 HRC40 also survived 6000 cycles without cracking. A duplicate coated specimen of 262 HRC 38 alloy survived 5250 cycles before cracks appeared. All the alloys showed little weight change compared compared to alloys tested in prior programs

The development of a Human Factors Readiness Level tool for implementing industrial human-robot collaboration

The concept of industrial human-robot collaboration (HRC) is becoming increasingly attractive as a means for enhancing manufacturing productivity and product. However, due to traditional preventive health and safety standards, there have been few operational examples of true HRC, so it has not been possible to explore the organisational human factors that need to be considered by manufacturing organisations to realise the benefits of industrial HRC until recently. Charalambous, Fletcher and Webb (2015) made the first attempt to identify the key organisational human factors for the successful implementation of industrial HRC through an industrial exploratory case study. This work enabled (i) development of a theoretical framework of key organisational human factors relevant to industrial HRC and (ii) identification of these factors as enablers or barriers. Although identifying the key organisational human factors (HF) was an important step, it presented a crucial question: when should practitioners involved in HRC design and implementation consider these factors? New industrial processes are typically designed and implemented using a maturity or readiness evaluation system, but these do not incorporate of or link to any formal considerations of HF. The aim of this paper is to expand on the previous findings and link the key human factors in the theoretical framework directly to a recognised industrial maturity readiness level system to develop a new Human Factors Readiness Level (HFRL) tool for system design practitioners to optimise successful implementation of industrial HRC

An integer programming Model for the Hospitals/Residents Problem with Couples

The Hospitals/Residents problem with Couples (hrc) is a generalisation of the classical Hospitals/Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc. Further, we present an Integer Programming (IP) model for hrc and extend it the case where preference lists can include ties. Further, we describe an empirical study of an IP model for HRC and its extension to the case where preference lists can include ties. This model was applied to randomly generated instances and also real-world instances arising from previous matching runs of the Scottish Foundation Allocation Scheme, used to allocate junior doctors to hospitals in Scotland

Robustness of a high-resolution central scheme for hydrodynamic simulations in full general relativity

A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong shock waves. In this paper we apply this scheme in full general relativity (involving {\it dynamical} spacetimes), and assess its suitability by performing test simulations for oscillations of rapidly rotating neutron stars and merger of binary neutron stars. It is demonstrated that this HRC scheme can yield results as accurate as those by the so-called high-resolution shock-capturing (HRSC) schemes based upon Riemann solvers. Furthermore, the adopted HRC scheme has increased computational efficiency as it avoids the costly solution of Riemann problems and has practical advantages in the modeling of neutron star spacetimes. Namely, it allows simulations with stiff equations of state by successfully dealing with very low-density unphysical atmospheres. These facts not only suggest that such a HRC scheme may be a desirable tool for hydrodynamical simulations in general relativity, but also open the possibility to perform accurate magnetohydrodynamical simulations in curved dynamic spacetimes.Comment: 4 pages, to be published in Phys. Rev. D (brief report

"Almost-stable" matchings in the Hospitals / Residents problem with Couples

The Hospitals / Residents problem with Couples (hrc) models the allocation of intending junior doctors to hospitals where couples are allowed to submit joint preference lists over pairs of (typically geographically close) hospitals. It is known that a stable matching need not exist, so we consider min bp hrc, the problem of finding a matching that admits the minimum number of blocking pairs (i.e., is “as stable as possible”). We show that this problem is NP-hard and difficult to approximate even in the highly restricted case that each couple finds only one hospital pair acceptable. However if we further assume that the preference list of each single resident and hospital is of length at most 2, we give a polynomial-time algorithm for this case. We then present the first Integer Programming (IP) and Constraint Programming (CP) models for min bp hrc. Finally, we discuss an empirical evaluation of these models applied to randomly-generated instances of min bp hrc. We find that on average, the CP model is about 1.15 times faster than the IP model, and when presolving is applied to the CP model, it is on average 8.14 times faster. We further observe that the number of blocking pairs admitted by a solution is very small, i.e., usually at most 1, and never more than 2, for the (28,000) instances considered

Bilateral comparison in Rockwell C hardness scale between INRiM and GUM

This bilateral comparison in HRC is conducted in order to confirm the accuracy claimed by National Institute of Metrological Research in Italy (INRiM) and Central Office of Measures in Poland (GUM). Also, this study compares the difference of measurement results between two modernized deadweight-type Rockwell's hardness standard machines (HSMs) from GUM and primary hardness standard machine (PHSM) from INRiM. The hardness blocks of about 20 HRC, 35 HRC, 45 HRC, 50 HRC, 60 HRC and 65 HRC, which all have uniformity less then ±0.4 HRC according to EN ISO 6508-3, were used in this comparison

Keeping partners together: algorithmic results for the hospitals/residents problem with couples

The Hospitals/Residents problem with Couples (HRC) is a generalisation of the classical Hospitals/Residents problem (HR) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of hospitals (h i ,h j ). We consider a natural restriction of HRC in which the members of a couple have individual preference lists over hospitals, and the joint preference list of the couple is consistent with these individual lists in a precise sense. We give an appropriate stability definition and show that, in this context, the problem of deciding whether a stable matching exists is NP-complete, even if each resident’s preference list has length at most 3 and each hospital has capacity at most 2. However, with respect to classical (Gale-Shapley) stability, we give a linear-time algorithm to find a stable matching or report that none exists, regardless of the preference list lengths or the hospital capacities. Finally, for an alternative formulation of our restriction of HRC, which we call the Hospitals/Residents problem with Sizes (HRS), we give a linear-time algorithm that always finds a stable matching for the case that hospital preference lists are of length at most 2, and where hospital capacities can be arbitrary