Robust Assignments via Ear Decompositions and Randomized Rounding

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling problems, where a set of tasks needs to be assigned to the available set of machines or personnel (resources), in a way that all tasks have assigned resources, and no two tasks share the same resource. In its nominal form, the resulting computational problem becomes the \emph{assignment problem} on general bipartite graphs. This paper deals with a robust variant of the assignment problem modeling situations where certain edges in the corresponding graph are \emph{vulnerable} and may become unavailable after a solution has been chosen. The goal is to choose a minimum-cost collection of edges such that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all tasks. We present approximation results and hardness proofs for this type of problems, and establish several connections to well-known concepts from matching theory, robust optimization and LP-based techniques.Comment: Full version of ICALP 2016 pape

Modelling and (re-)planning periodic home social care services with loyalty and non-loyalty features

This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacees).The aging population alongside little availability of informal care are two of the several factors leading to an increased need for assisted living support. In this work, we tackle a home social care service problem, motivated by two real case studies where a new loyalty scheme must be considered: within a week, patient-caregiver loyalty should be pursued but, between weeks, the caregivers must rotate among patients (non-loyalty). In addition, a common situation in this kind of service is also addressed: the need of a constant re-planning caused by the leaving of patients and the arrival of new ones. This new plan should be such that minimum disturbance is caused to the visiting hours of current patients, the caregivers’ travelling time between visits is minimized, and the workload is balanced among caregivers. A multi-objective optimization approach based on mixed-integer models is developed. Results on the two real case studies show that both institutions can efficiently re-plan their activities without much disturbance on the visits of their patients, and with a patient-caregiver loyalty scheme suiting their needs.authorsversionpublishe

Modelling the Home Health Care Nurse Scheduling Problem for Patients with Long-Term Conditions in the UK

In this work, using a Behavioural Operational Research (BOR) perspective, we develop a model for the Home Health Care Nurse Scheduling Problem (HHCNSP) with application to renal patients taking Peritoneal Dialysis (PD) at their own homes as treatment for their Chronic Kidney Disease (CKD) in the UK. The modelling framework presented in this paper can be extended to much wider spectra of scheduling problems concerning patients with different long-term conditions in future work

F-formation Detection: Individuating Free-standing Conversational Groups in Images

Detection of groups of interacting people is a very interesting and useful task in many modern technologies, with application fields spanning from video-surveillance to social robotics. In this paper we first furnish a rigorous definition of group considering the background of the social sciences: this allows us to specify many kinds of group, so far neglected in the Computer Vision literature. On top of this taxonomy, we present a detailed state of the art on the group detection algorithms. Then, as a main contribution, we present a brand new method for the automatic detection of groups in still images, which is based on a graph-cuts framework for clustering individuals; in particular we are able to codify in a computational sense the sociological definition of F-formation, that is very useful to encode a group having only proxemic information: position and orientation of people. We call the proposed method Graph-Cuts for F-formation (GCFF). We show how GCFF definitely outperforms all the state of the art methods in terms of different accuracy measures (some of them are brand new), demonstrating also a strong robustness to noise and versatility in recognizing groups of various cardinality.Comment: 32 pages, submitted to PLOS On

Matching for Balance, Pairing for Heterogeneity in an Observational Study of the Effectiveness of For-Profit and Not-For-Profit High Schools in Chile

Conventionally, the construction of a pair-matched sample selects treated and control units and pairs them in a single step with a view to balancing observed covariates x and reducing the heterogeneity or dispersion of treated-minus-control response differences, Y. In contrast, the method of cardinality matching developed here first selects the maximum number of units subject to covariate balance constraints and, with a balanced sample for x in hand, then separately pairs the units to minimize heterogeneity in Y. Reduced heterogeneity of pair differences in responses Y is known to reduce sensitivity to unmeasured biases, so one might hope that cardinality matching would succeed at both tasks, balancing x, stabilizing Y. We use cardinality matching in an observational study of the effectiveness of for-profit and not-for-profit private high schools in Chile—a controversial subject in Chile—focusing on students who were in government run primary schools in 2004 but then switched to private high schools. By pairing to minimize heterogeneity in a cardinality match that has balanced covariates, a meaningful reduction in sensitivity to unmeasured biases is obtained

Dynamically accepting and scheduling patients for home healthcare

The importance of home healthcare is growing rapidly since populations of developed and even developing countries are getting older and the number of hospitals, retirement homes, and medical staff do not increase at the same rate. We consider the Home Healthcare Nurse Scheduling Problem where patients arrive dynamically over time and acceptance and appointment time decisions have to be made as soon as patients arrive. The objective is to maximise the average number of daily visits for a single nurse. For the sake of service continuity, patients have to be visited at the same day and time each week during their episode of care. We propose a new heuristic based on generating several scenarios which include randomly generated and actual requests in the schedule, scheduling new customers with a simple but fast heuristic, and analysing results to decide whether to accept the new patient and at which appointment day/time. We compare our approach with two greedy heuristics from the literature, and empirically demonstrate that it achieves significantly better results compared to these other two methods

A Bayesian framework for describing and predicting the stochastic demand of home care patients

Home care providers are complex structures which include medical, paramedical and social services delivered to patients at their domicile. High randomness affects the service delivery, mainly in terms of unplanned changes in patients’ conditions, which make the amount of required visits highly uncertain. Hence, each reliable and robust resource planning should include the estimation of the future demand for visits from the assisted patients. In this paper, we propose a Bayesian framework to represent the patients’ demand evolution along with the time and to predict it in future periods. Patients’ demand evolution is described by means of a generalized linear mixed model, whose posterior densities of parameters are obtained through Markov chain Monte Carlo simulation. Moreover, prediction of patients’ demands is given in terms of their posterior predictive probabilities. In the literature, the stochastic description of home care patients’ demand is only marginally addressed and no Bayesian approaches exist to the best of our knowledge. Results from the application to a relevant real case show the applicability of the proposed model in the practice and validate the approach, since parameter densities in accordance to clinical evidences and low prediction errors are found