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

O problema de roteamento e escalonamento de profissionais de saúde: The home healthcare routing and scheduling problem

Problema de Roteamento e Escalonamento de Profissionais de Saúde consiste em determinar a melhor rota para profissionais de saúde para atendimento domiciliar. Existem diversas variantes deste problema que diferem nas restrições e funções objetivo. Este artigo apresenta uma revisão da literatura, com o objetivo de identificar os problemas de roteamento utilizados pelos autores, os diferentes tipos de função objetivo, e as técnicas de solução utilizadas

DEVELOPING AN OPTIMAL MODEL FOR INFANT HOME VISITATION

The United States, Great Britain, Denmark, Canada and many other countries have accepted home visitation (HV) as a promising strategy for interventions for infants after births and for their mothers. Prior HV studies have focused on theoretical foundations, evaluations of programs, cost/benefit analysis and cost estimation by using hospital/payer/insurance data to prove its effectiveness and high cost. As governments and private organizations continue to fund HVs, it is an opportune time to develop and formulate operations research (OR) models of HV coverage, quality and cost so they might be used in program implementation as done for adult home healthcare (HHC) and home care (HC). This dissertation introduces a new modeling approach and proposes a solution methodology which helps to determine the schedules of follow-up nursing care providers (NCP) to visit discharged patients in order to minimize total follow-up cost at the planning and operational level, and to improve the quality of care. The model improves the quality of treatment of infants and mothers during pregnancy, after birth and discharge from the hospital by maximizing the quality of assignment of the right NCP with the right skill, nurse type and years of experience to the right patient with the specific health need. The modeling approach is based on a mixed-interger programming (MIP) formulation that represents the dynamics of the system comprising aspects such as visit schedules and total program’s cost while satisfying a variety of requirements modeled as constraints. The model is tested and validated with real life data. Computational results for the formulation for real life instances of the problem with the Nurse Family Partnership Program (NFP) obtained using IBM CPLEX optimization Studio version 12.6.1 are presented. The intent is to enhance the administrative and deployment process of HV programs, minimize risks, allow planners to explore the best scenarios under different conditions related to cost, treatment and coverage requirements, and highlight the best course of action when assigning NCPs to clients. Results show significant cost savings and enhanced quality treatment in several cases studied and tested. Finally, the study identifies and presents fertile avenues for future research for this field