Timeliness, efficiency and public procurement in hip surgery in Italy

Considering different perspectives, the scope of this thesis is to investigate how to improve healthcare resources allocation and the provision efficiency for hip surgeries, a resource-intensive operation, among the most frequently performed on the elderly, with a trend in volume that is increasing in years due to population aging. Firstly, the effect of Time-To-Surgery (TTS) on mortality for hip fracture patients is investigated. The analysis attempts to account for TTS endogeneity due to the inability to fully control for variables affecting patient delay – e.g. patient severity. Exploiting an instrumental variable model, where being admitted on Friday or Saturday predicts longer TTS, findings show exogenous TTS does not have a significant effect on mortality. Thus suggesting surgeons prioritize patients effectively, neutralizing the adverse impact of longer TTS. Then, the volume-outcome relation for total hip replacement surgery is analyzed, seeking to account for selective referral, which may be present in elective surgery context, and induce reverse causality issue in the volume-outcome relation. The analysis employs a conditional choice model where patient travel distance from all regions' hospitals is used as a hospital choice predictor. Findings show the exogenous hospital volume significantly decreases adverse outcomes probability, especially in the short run. Finally, the change in public procurement design enforced in the Romagna LHA (Italy) is exploited to assess its impact on hip prostheses cost, surgeons' implant choice, and patient health outcomes. Hip prostheses are the major cost-driver of hip replacement surgeries, hence it is crucial to design the public tender such that implant prices are minimized, but cost-containment policies have to be weighted with patient well-being. Evidence shows that a cost reduction occurred without a significant surgeons’ choices impact. Positive or no effect of surgeons specialization is found on patients outcomes after the new procurement introduction.

Hybrid Methods for Resource Allocation and Scheduling Problems in Deterministic and Stochastic Environments

This work presents exact, hybrid algorithms for mixed resource Allocation and Scheduling problems; in general terms, those consist into assigning over time finite capacity resources to a set of precedence connected activities. The proposed methods have broad applicability, but are mainly motivated by applications in the field of Embedded System Design. In particular, high-performance embedded computing recently witnessed the shift from single CPU platforms with application-specific accelerators to programmable Multi Processor Systems-on-Chip (MPSoCs). Those allow higher flexibility, real time performance and low energy consumption, but the programmer must be able to effectively exploit the platform parallelism. This raises interest in the development of algorithmic techniques to be embedded in CAD tools; in particular, given a specific application and platform, the objective if to perform optimal allocation of hardware resources and to compute an execution schedule. On this regard, since embedded systems tend to run the same set of applications for their entire lifetime, off-line, exact optimization approaches are particularly appealing. Quite surprisingly, the use of exact algorithms has not been well investigated so far; this is in part motivated by the complexity of integrated allocation and scheduling, setting tough challenges for ``pure'' combinatorial methods. The use of hybrid CP/OR approaches presents the opportunity to exploit mutual advantages of different methods, while compensating for their weaknesses. In this work, we consider in first instance an Allocation and Scheduling problem over the Cell BE processor by Sony, IBM and Toshiba; we propose three different solution methods, leveraging decomposition, cut generation and heuristic guided search. Next, we face Allocation and Scheduling of so-called Conditional Task Graphs, explicitly accounting for branches with outcome not known at design time; we extend the CP scheduling framework to effectively deal with the introduced stochastic elements. Finally, we address Allocation and Scheduling with uncertain, bounded execution times, via conflict based tree search; we introduce a simple and flexible time model to take into account duration variability and provide an efficient conflict detection method. The proposed approaches achieve good results on practical size problem, thus demonstrating the use of exact approaches for system design is feasible. Furthermore, the developed techniques bring significant contributions to combinatorial optimization methods.

Constraint based methods for allocation and scheduling of periodic applications

This work presents exact algorithms for the Resource Allocation and Cyclic Scheduling Problems (RA&CSPs). Cyclic Scheduling Problems arise in a number of application areas, such as in hoist scheduling, mass production, compiler design (implementing scheduling loops on parallel architectures), software pipelining, and in embedded system design. The RA&CS problem concerns time and resource assignment to a set of activities, to be indefinitely repeated, subject to precedence and resource capacity constraints. In this work we present two constraint programming frameworks facing two different types of cyclic problems. In first instance, we consider the disjunctive RA&CSP, where the allocation problem considers unary resources. Instances are described through the Synchronous Data-flow (SDF) Model of Computation. The key problem of finding a maximum-throughput allocation and scheduling of Synchronous Data-Flow graphs onto a multi-core architecture is NP-hard and has been traditionally solved by means of heuristic (incomplete) algorithms. We propose an exact (complete) algorithm for the computation of a maximum-throughput mapping of applications specified as SDFG onto multi-core architectures. Results show that the approach can handle realistic instances in terms of size and complexity. Next, we tackle the Cyclic Resource-Constrained Scheduling Problem (i.e. CRCSP). We propose a Constraint Programming approach based on modular arithmetic: in particular, we introduce a modular precedence constraint and a global cumulative constraint along with their filtering algorithms. Many traditional approaches to cyclic scheduling operate by fixing the period value and then solving a linear problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model and tackles the problem as a whole: the period value is inferred from the scheduling decisions. The proposed approaches have been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances achieving good results on practical size problem.