T he design of efficient home care services is a quite recent and challenging field of study. We propose an integrated approach that jointly addresses: (i) the assignment of operators to patients so as to guarantee the compatibility between skills associated with operators and patient visits; (ii) the scheduling of the visits in a given planning horizon; and (iii) the determination of the operator tours in every day of the planning horizon. The main home care problem we investigate refers to providers dedicated to palliative care and terminal patients. In this context, balancing objective functions are particularly relevant. Therefore, two balancing functions are studied, i.e., maxmin, which maximizes the minimum operator utilization factor, and minmax, which minimizes the maximum operator utilization factor. In both cases, the concept of pattern is introduced as a key tool to jointly address assignment, scheduling, and routing decisions, where a pattern specifies a possible schedule for skilled visits. The approach we propose is, however, able to cope with peculiarities from other home care contexts. Model extensions to handle scenarios other than the palliative one are discussed in the paper.Extensive computational results are reported both on palliative home care instances based on real data, and on two real-world data sets from the literature, related to contexts very different from the palliative one. For both data sets the proposed approach is able to find solutions of good quality. In the palliative context, the results show that the selection of the pattern generation policy is crucial to solve large instances efficiently. Furthermore, the maxmin criterion is able to return more balanced solutions; i.e., the difference between the maximum and the minimum operator utilization factors is very small. On the other hand, the minmax criterion is more suitable for minimizing the operating costs, since it computes solutions with smaller total traveled time.

The adoption of the virtualization paradigm in both computing and networking domains portends a landscape of heterogeneous service capabilities and resources pervasively distributed and interconnected and deeply integrated through the 5G network infrastructure. In this service ecosystem, dynamic service demand can be flexibly and elastically accomplished by composing heterogeneous services provisioned over a distributed and virtualized resource infrastructure. Indeed, with the term Virtual Functions we refer to virtual computing as well as network service capabilities (e.g., routers and middlebox functions provided as Virtual Network Functions). In order to cope with the increasingly resource intensive demand, these virtual functions will be deployed in distributed clusters of small-scale datacenters typically located in current exchanges at the network edge and will supplement those deployed in traditional large cloud datacenters. In this work we formulate the problem of composing, computing and networking Virtual Functions to select those nodes along the path that minimizes the overall latency (i.e. network and processing latency) in the above mentioned scenario. The optimization problem is formulated as a Resource Constrained Shortest Path problem on an auxiliary layered graph accordingly defined. The layered structure of the graph ensures that the order of VFs specified in the request is preserved. Additional constraints can be also taken into account in the graph construction phase. Finally, we provide a use case preliminary evaluation of the proposed model.

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We study the Home Care Problem under uncertainty. Home Care refers to medical, paramedical and social services that may be delivered to patient homes. The term includes several aspects involved in the planning of home care services, such as caregiver-to-patient assignment, scheduling of patient requests, and caregiver routing. In Home Care, cancellation of requests and additional demand for known or new patients are very frequent. Thus, managing demand uncertainty is of paramount importance in limiting service disruptions that might occur when such events realize. We address uncertainty of patient demand over a multiple-day time horizon, when assignment, scheduling and routing decisions are taken jointly, both from a methodological and a computational perspective. In fact, we propose a non-standard cardinality-constrained robust approach, analyse its properties, and report the results of a wide experimentation on real-life instances. The obtained results show that, for instances of moderate size, the approach is able to efficiently determine robust solutions of good quality in terms of balancing among caregivers and number of uncertain requests that can be managed. Also, the robustness of the solutions with respect to possible realizations of uncertain requests, evaluated on a small subset of instances, appears to be significant. Furthermore, preliminary experiments on a decomposition method, obtained from the robust one by fixing the scheduling decisions, show a drastic gain in computational efficiency, with the determination of robust solutions of still good quality. Therefore, the approach appears to be very promising to cope with robustness even on Home Care instances of larger size

T his article introduces a game-theoretic approach for allocating protection resources among the components of a network so as to maximize its robustness to external disruptions. Specifically, we consider shortestpath networks where disruptions may result in traffic flow delays through the affected components or even in the complete loss of some elements. A multilevel program is proposed to identify the set of components to harden so as to minimize the length of the shortest path between a supply node and a demand node after a worst-case disruption of some unprotected components. An implicit enumeration algorithm is then developed to solve the multilevel problem to optimality. The approach is streamlined by solving the lower-level interdiction problem heuristically at each node of an enumeration tree and by using some variable fixing rules to reduce the dimension of the lower-level problems. A thorough computational investigation demonstrates that the proposed solution method is able to identify optimal protection strategies for networks of significant size. The paper is concluded with a study of the sensitivity of the solution approach to variations of the problem parameters such as the level of disruption and protective resources and the distribution of the arc lengths and delays.

Home health care services play a crucial role in reducing the hospitalization costs due to the increase of chronic diseases of elderly people. At the same time, they allow us to improve the quality of life for those patients that receive treatments at their home. Optimization tools are therefore necessary to plan service delivery at patients' homes. Recently, solution methods that jointly address the assignment of the patient to the caregiver (assignment), the definition of the days (pattern) in which caregivers visit the assigned patients (scheduling), and the sequence of visits for each caregiver (routing) have been proposed in the scientific literature. However, the joint consideration of these three levels of decisions may be not affordable for large providers, due to the required computational time. In order to combine the strength and the flexibility guaranteed by a joint assignment, scheduling and routing solution approach with the computational efficiency required for large providers, in this study we propose a new family of two-phase methods that decompose the joint approach by incrementally incorporating some decisions into the first phase. The concept of pattern is crucial to perform such a decomposition in a clever way. Several scenarios are analyzed by changing the way in which resource skills are managed and the optimization criteria adopted to guide the provider decisions. The proposed methods are tested on realistic instances. The numerical experiments help us to identify the combinations of decomposition techniques, skill management policies and optimization criteria that best fit with problem instances of different size

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