Effective Optimisation of the Patient Circuits of an Oncology Day Hospital: Mathematical Programming Models and Case Study

In this paper, we first use the information we have on the patients of an oncology day hospital to distribute the treatment schedules they have in each of the visits to this centre. To do this, we propose a deterministic mathematical programming model in such a way that we minimise the duration of the waiting room stays of the total set of patients and taking into account the restrictions of the circuit. Secondly, we will look for a solution to the same problem under a stochastic approach. This model will explicitly consider the existing uncertainty in terms of the different times involved in the circuit, and this model also allows the reorganisation of the schedules of medical appointments with oncologists. The models are complemented by a tool that solves the problem of assigning nurses to patients. The work is motivated by the particular characteristics of a real hospital and the models are used and compared with data from this case.

Mathematical Programming Application in Sublevel Caving Production Scheduling

Production scheduling determines the most beneficial mining sequence over the life of a mine. Developing a schedule that meets all mining aspects can substantially reduce mining costs and increase profitability. Among all underground mining methods, the sublevel caving method is a common method with moderate development requirements, a high production rate, and a high degree of mechanization and flexibility. None of the manual planning methods and heuristic algorithms used in commercial software will lead to a truly optimal schedule. Mathematical programming models, particularly mixed-integer programming (MIP), have been applied to provide an operationally feasible multi-time-period schedule in sublevel caving. However, confined blasting conditions, chaotic material flow, and frequent mixing of ore and waste while loading broken ore at the drawpoint make the sublevel caving method unique when producing a holistic plan. This paper reviews all mathematical programming models presented in sublevel caving production scheduling, highlights the inherent characteristics of the sublevel caving that affect production, and puts forward some promising ideas for future works.