Teaching Linear Programing in Mathematics Education to Improve Human Health

The 1984 World Health Organization (WHO) defines health as "the extent to which an individual or group is able to realize aspirations and satisfy needs, and to change or cope with the environment.” Health is a resource for everyday life. It is a positive concept emphasizing social and personal resources, as well as physical capacities. To maintain human health is a complex matter, thus the need to apply mathematics education, and in particular, linear programming knowledge and skills, in order to bring up a healthy community. Linear Programming is about making maximum benefit or minimum loss out of limited resources in daily life. Applications of linear programming date back to 1930 and were first attempted by the Soviet mathematician Leonid Kantorovich and by the American economist, Wasilly Leontief. Linear programming is applied in many health programs. These include; application of linear programming in health care, in the most affordable heath diet, in surgery, menu planning, food production and in feeding. Linear programming is used by farmers to determine how much space to be used for each crop especially when practicing mixed farming and for optimal health care resource allocation. Linear programming is also used in home health care and medical services. It is used in radiation therapy treatment, for menu planning in restaurants and in nurses scheduling. It is therefore recommended that the topic linear programming be taught to all Kenyan students irrespective of what career they hope to pursue. This will go a long way in enabling the Kenyan society to maintain good health at minimum cost

Operational and strategic decision making in the perioperative setting: Meeting budgetary challenges and quality of care goals.

Efficient operating room (OR) management is a constant balancing act between optimal OR capacity, allocation of ORs to surgeons, assignment of staff, ordering of materials, and reliable scheduling, while according the highest priority to patient safety. We provide an overview of common concepts in OR management, specifically addressing the areas of strategic, tactical, and operational decision making (DM), and parameters to measure OR efficiency. For optimal OR productivity, a surgical suite needs to define its main stakeholders, identify and create strategies to meet their needs, and ensure staff and patient satisfaction. OR planning should be based on real-life data at every stage and should apply newly developed algorithms

Flexible hospital-wide elective patient scheduling

In this paper, we build on and extend Gartner and Kolisch (2014)’s hospital-wide patient scheduling problem. Their contribution margin maximizing model decides on the patients' discharge date and therefore the length of stay. Decisions such as the allocation of scarce hospital resources along the clinical pathways are taken. Our extensions which are modeled as a mathematical program include admission decisions and flexible patient-to-specialty assignments to account for multi-morbid patients. Another flexibility extension is that one out of multiple surgical teams can be assigned to each patient. Furthermore, we consider overtime availability of human resources such as residents and nurses. Finally, we include these extensions in the rolling-horizon approach and account for lognormal distributed recovery times and remaining resource capacity for elective patients. Our computational study on real-world instances reveals that, if overtime flexibility is allowed, up to 5% increase in contribution margin can be achieved by reducing length of stay by up to 30%. At the same time, allowing for overtime can reduce waiting times by up to 33%. Our model can be applied in and generalized towards other patient scheduling problems, for example in cancer care where patients may follow defined cancer pathways

Optimal Design of a Solar Assisted Cooling System

Rapid development around the globe is fairly associated with huge consumption of energy; regardless of the continuous attempts of exploiting renewable energy resources, further investigations in renewable energy involvement in comfort cooling appears to be interesting. District Cooling Systems (DCS) are chilled water based systems operate to provide comfort cooling. DCS consists of chilled water plant, chilled water distribution network and energy transfer station(s), where Thermal Energy Storage system (TES) might be included alongside with DCS as auxiliary components(s). Although typical DCS are fully dependent on fossil fuel as source of energy in their operation, providing comfort cooling is considered as a necessity in some regions of the globe. Such circumstances highlight the imperative of examining other sources of energy, such as renewable energy. One think there is no better alternative of energy resource problem than solar energy, specifically the science of converting heat into cool. Researches in the field of Solar Assisted Cooling systems (SAC) designated typical components of solar assisted cooling system to be solar collector(s) and absorption chiller(s); where TES and water boiler utilized as auxiliary components. In comparison to conventional cooling systems, SAC systems have the advantages of renewable energy utilization beside the correlation of high availability of solar energy with the high demand of comfort cooling. Yet, their relatively high investment costs introduces barriers toward their implementation; thus, the contribution of this research is realized in mathematically modeling SAC system and obtaining the optimal design of such system with the aim of minimizing the investment and operational costs. The problem is modeled as Mixed Integer Linear Problem (MILP) and the optimization of the model is implemented using CPLEX optimizer. The optimized solution specify the optimal area of the solar collector, size of absorption chiller, size and existence of chilled and hot water storage tanks, and the auxiliary boiler

Developing a multi-methodological approach to hospital operating theatre scheduling

Operating theatres and surgeons are among the most expensive resources in any hospital, so it is vital that they are used efficiently. Due to the complexity of the challenges involved in theatre scheduling we split the problem into levels and address the tactical and day-to-day scheduling problems.Cognitive mapping is used to identify the important factors to consider in theatre scheduling and their interactions. This allows development and testing of our understanding with hospital staff, ensuring that the aspects of theatre scheduling they consider important are included in the quantitative modelling.At the tactical level, our model assists hospitals in creating new theatre timetables, which take account of reducing the maximum number of beds required, surgeons’ preferences, surgeons’ availability, variations in types of theatre and their suitability for different types of surgery, limited equipment availability and varying the length of the cycle over which the timetable is repeated. The weightings given to each of these factors can be varied allowing exploration of possible timetables.At the day-to-day scheduling level we focus on the advanced booking of individual patients for surgery. Using simulation a range of algorithms for booking patients are explored, with the algorithms derived from a mixture of scheduling literature and ideas from hospital staff. The most significant result is that more efficient schedules can be achieved by delaying scheduling as close to the time of surgery as possible, however, this must be balanced with the need to give patients adequate warning to make arrangements to attend hospital for their surgery.The different stages of this project present different challenges and constraints, therefore requiring different methodologies. As a whole this thesis demonstrates that a range of methodologies can be applied to different stages of a problem to develop better solutions

Livro de atas do XVI Congresso da Associação Portuguesa de Investigação Operacional

Fundação para a Ciência e Tecnologia - FC

Modelling the Demand for Long-term Care to Optimise Local Level Planning

Long-term care (LTC) includes the range of health, social and voluntary support services provided to those with chronic illness, physical or mental disability. LTC has been widely studied in the literature, in particular due to concerns surrounding how future demographic shifts may impact the LTC system’s ability to cater to increasing amounts of patients not withstanding what the future cost impact might be. With that said, few studies have attempted to model demand at the local level for the purposes of informing local service delivery and organisation. Many developing countries with mature and developed systems of LTC in place are under pressure to reduce health care spend, whilst delivering greater value for money. We suggest that the lack of local studies in LTC stems from the lack of a strong case for the benefits of demand modelling at the local level in combination with low quantity and incomplete social care data. We propose a mathematical model to show how savings may be generated under different models of commitment with third party providers. Secondly, we propose a hybrid-fuzzy demand model to generate estimates of demand in the short to medium term that can be used to inform contract design based on local area needs – such an approach we argue is more suited to problems in which historic activity is incomplete or limited. Our results show that commitment models can be of great use to local health care planners with respect to lowering their care costs, at the same time our formulation had wider generic applicability to procurement type problems where commitment size in addition to the timing of commitments needs to be determined