A Cardinality-constrained Approach for Robust Machine Loading Problems

The Machine Loading Problem (MLP) refers to the allocation of operative tasks and tools to machines for the production of parts. Since the uncertainty of processing times might affect the quality of the solution, this paper proposes a robust formulation of an MLP, based on the cardinality-constrained approach, to evaluate the optimal solution in the presence of a given number of fluctuations of the actual processing time with respect to the nominal one. The applicability of the model in the practice has been tested on a case study

A Bayesian approach for the identification of patient-specific parameters in a dialysis kinetic model

Hemodialysis is the most common therapy to treat renal insufficiency. However, notwithstanding the recent improvements, hemodialysis is still associated with a non-negligible rate of comorbidities, which could be reduced by customizing the treatment. Many differential compartment models have been developed to describe the mass balance of blood electrolytes and catabolites during hemodialysis, with the goal of improving and controlling hemodialysis sessions. However, these models often refer to an average uremic patient, while on the contrary the clinical need for customization requires patient-specific models. In this work, we assume that the customization can be obtained by means of patient-specific model parameters. We propose and validate a Bayesian approach to estimate the patient-specific parameters of a multi-compartment model, and to predict the single patient’s response to the treatment, in order to prevent intra-dialysis complications. The likelihood function is obtained by means of a discretized version of the multi-compartment model, where the discretization is in terms of a Runge–Kutta method to guarantee convergence, and the posterior densities of model parameters are obtained through Markov Chain Monte Carlo simulation. Results show fair estimations and the applicability in the clinical practice

Applying the Cardinality–Constrained Approach in Health Care Systems: The Home Care Example

Many approaches are applied to deal with uncertainty in health care optimization problems. However, a recently proposed technique, namely, the cardinality–constrained approach, is only marginally applied in health care. This approach accounts for a given degree of uncertainty with a reasonable computational effort, providing a trade-off between computational time and robustness. In this paper, we apply such approach to the nurse-to-patient assignment problem under continuity of care arising in home care services. A linear programming model is developed for solving the problem, and the robustness is included in the formulation according to the cardinality–constrained approach. The overall robust model is applied to a Home Care provider operating in Italy, in order to evaluate its capability of reducing the costs related to nurses’ overtimes, and to compare the results both with the real practice of the analyzed provider and with previously developed approaches. Relevant benefits are achieved by applying the proposed model in the practice, and results suggest that such benefits could be also achieved in other optimization problems within the health care domain

Robust nurse-to-patient assignment in home care services tominimize overtimes under continuity of care

Home Care (HC) providers are complex organizations that manage a large number of patients, different categories of operators, support staff and material resources in a context affected by high variability. Hence, robust resource planning is crucial for operations in HC organizations, in order to avoid process inefficiencies, treatment delays, and low quality of service. Under continuity of care, one of the main issues in HC planning is the assignment of a reference nurse to each assisted patient, because this decision has an impact on the workload assigned to the nurse for the entire patient’s length of stay. In this paper, we derive an analytical structural policy for solving the nurse-to-patient assignment problem in the HC context under continuity of care. This policy accounts for randomness related to both the demands from patients already assigned to nurses and the demands from new patients who need assignments. The policy is compared to other previously developed approaches, and applied to a relevant real case

A cardinality-constrained robust model for the assignment problem in Home Care services

Home Care includes medical, paramedical and social services which are delivered to patients at their domicile rather than in hospital. Managing human and material resources in Home Care services is a difficult task, as the provider has to deal with peculiar constraints (e.g., the continuity of care, which imposes that a patient is always cared for by the same nurse) and to manage the high variability of patients’ demands. One of the main issues encountered in planning Home Care services under continuity of care requirement is the nurse-to-patient assignment. Despite the importance of this topic, the problem is only marginally addressed in the literature, where conti- nuity of care is usually treated as a soft-constraint rather than as a hard one. Uncertainty is another relevant feature of nurse-to-patient assignment problem, and it is usually managed adopt- ing stochastic programming or analytical policies. However, both these approaches proved to be limited, even if they improve the quality of the assignments upon those actually provided in prac- tice. In this paper, we develop a cardinality-constrained robust assignment model, which allows exploiting the potentialities of a mathematical programming model without the necessity of gener- ating scenarios. The developed model is tested on real-life instances related to a relevant Home Care provider operating in Italy, in order to evaluate its capability of reducing the costs related to nurses’ overtimes

COMPARING TWO DIFFERENT OBJECTIVE FUNCTIONS IN A CARDINALITY-CONSTRAINED MODEL FOR THE ASSIGNMENTS IN HOME CARE

Human resource planning in Home Care (HC) services is a difficult task, as the provider has to deal with peculiar constraints (e.g., the continuity of care) and to manage the high variability of patients' demands. Indeed, under continuity of care, one of the main issues encountered in planning HC ser- vices is the nurse-to-patient assignment. In the literature, several techniques are adopted to manage the uncertainty of the demand in such assignment problem and, recently, the problem has been solved adopting a cardinality-constrained robust model. The objective function of that robust model was the minimization of the nurses' overtime costs, which arise in case nurses work for a time larger than the contractual value. In this paper, we model a new objective function for the above mentioned problem, i.e., the fairness of the nurses' utilizations, and we compare the two objective functions