The Application of Late Acceptance Heuristic Method for the Tanzanian High School Timetabling Problem

High School timetabling is the problem of scheduling lessons of different subjects and teachers to timeslots within a week, while satisfying a set of constraints which are classified into hard and soft constraints. This problem is different from university course timetabling problem because of the differences in structures including classroom allocations and grouping of subject combinations. Given the scarce education resources in developing countries, high school timetabling problem plays a very important role in optimizing the use of meager resources and therefore contribute to improvement of quality of education. The problem has attracted attention of many researchers around the world; however, very little has been done in Tanzania. This paper presents a solution algorithm known as Late Acceptance heuristic for the problem and compares results with previous work on Simulated Annealing and Great Deluge Algorithm for three schools in Dar es Salaam Tanzania. It is concluded that Late Acceptance heuristic gives results which are similar to the previous two algorithms but performs better in terms of time saving. Keywords: Late Acceptance; High School Timetabling; Combinatorial Optimization; Heuristics; NP-Har

Simulated Annealing Algorithm for the Linear Ordering Problem: The Case of Tanzania Input Output Tables

Linear Ordering is a problem of ordering the rows and columns of a matrix such that the sum of the upper triangle values is as large as possible. The problem has many applications including aggregation of individual preferences, weighted ancestry relationships and triangulation of input-output tables in economics. As a result, many researchers have been working on the problem which is known to be NP-hard. Consequently, heuristic algorithms have been developed and implemented on benchmark data or specific real-world applications. Simulated Annealing has seldom been used for this problem. Furthermore, only one attempt has been done on the Tanzanian input output table data. This article presents a Simulated Annealing approach to the problem and compares results with previous work on the same data using Great Deluge algorithm. Three cooling schedules are compared, namely linear, geometric and Lundy & Mees. The results show that Simulated Annealing and Great Deluge provide similar results including execution time and final solution quality. It is concluded that Simulated Annealing is a good algorithm for the Linear Ordering problem given a careful selection of required parameters. Keywords: Combinatorial Optimization; Linear Ordering Problem; Simulated Annealing; Triangulation; Input Output table

Mathematical Model for Tanzania Population Growth

In this paper, a mathematical model for Tanzania population growth is presented. The model is developed by using exponential and logistic population growth models. Real data from censuses conducted by Tanzania National Bureau of Statistics (NBS) are used. The Tanzania growth rate is obtained by using data of 1967 and 2012 censuses. The prediction of population for the period of 2013 to 2035 is done. Numerical results show that the population grows at the rate of 2.88%. In 2035 the population is expected to be 87,538,767 by exponential model and 85,102,504 by logistic model. The carrying capacity is 2,976,857,550, which implies that the population will still grow faster since it is far from its limiting value. Comparisons of the models with real data from the five censuses are done. Also NBS projections are compared with populations predicted by the two models. Both comparisons show that the exponential model is performing better than logistic model. Also, the projection up to 2050 gives the population of 135,244,161 by exponential model and 131,261,794 by logistic model.Keywords: Population growth, Exponential model, Logistic model, Carrying Capacity

Algorithms for the resource levelling problem

The Resource Levelling Problem (RLP) is a variation of resource-constrained scheduling problems with major applications in manufacturing. A critical path is determined for a set of jobs/items that needs to be manufactured or assembled to form a final product. In capacity planning, each of these jobs is associated with a predetermined load or 'hassle' factor (resource level). When these jobs are scheduled together in a planning horizon, different profiles with respect to the resource levels are developed. The objective of the RLP is to minimise the maximum resource peaks by moving jobs within their slack times. RLP is an NP-Hard combinatorial optimisation problem and therefore, no optimal algorithm is known. A few studies have been done on this problem during 1960's and early 1970's and various heuristics suggested (see [W64], [D66], [BFC62], [D73]). However, no recent studies have been done despite recent developments in algorithmic techniques. The objective of this project is to develop new algorithmic approaches to the RLP. In Chapter 1 we provide a definition of the problem using an example from the manufacturing industry. Chapter 2 presents a review of preprocessing techniques, which are useful in improving the performance of Integer Programming methods. In Chapter 3 we develop four Mixed Integer Programming (MIP) formulations. Our analysis shows that time-indexed formulations perform better for the RLP. In Chapters 4 and 5 we present three global heuristic methods; Simulated Annealing, Tabu Search and a Perturbation algorithm. We conclude that, these algorithms are feasible and good approaches to the RLP. The perturbation algorithm was found to perform better than the rest. Chapter 6 provides a discussion on how the theory of Human-Computer Interaction can be used to improve the solution of the RLP by providing a good Interface design. Lastly we summarise our project in Chapter 7 and suggest areas of further research

Solving the Examination Timetabling Problem Using a Two-Phase Heuristic: The case of Sokoine University of Agriculture

Examination timetabling is an important operational problem in any academic institution. The problem involves assigning examinations and candidates to time periods and examination rooms while satisfying a set of specific constraints. An increased number of student enrollments, a wider variety of courses, and the growing flexibility of students' curricula have contributed to the growing challenge in preparing examination timetables. Since examination timetabling problems differ from one institution to another, in this paper we develop and investigate the impact of a two-phase heuristic that combines Graph-Colouring and Simulated Annealing at Sokoine University of Agriculture (SUA) in Tanzania. Computational results are presented which shows great improvement over the previous work on the same problem

Eliciting harms data from trial participants: how perceptions of illness and treatment mediate recognition of relevant information to report

Background: There is no consensus on the ideal methodology for eliciting participant-reported harms, but question methods influence the extent and nature of data detected. This gives potential for measurement error and undermines meta-analyses of adverse effects. We undertook to identify barriers to accurate and complete reporting of harms data, by qualitatively exploring participants’ experiences of illness and treatment, and reporting behaviours; and compared the number and nature of data detected by three enquiry methods. Methods: Participants within antiretroviral/antimalarial interaction trials in South Africa and Tanzania were asked about medical history, treatments and/or adverse events by general enquiries followed by checklists. Those reporting differently between these two question methods were invited to an in-depth interview and focus group discussion. Health narratives were analysed to investigate accuracy and completeness of case record form data and to understand reasons for differential reporting between question methods. Outcomes were the number and nature of data by question method, themes from qualitative analyses and a theoretical interpretation of participants’ experiences. Results: We observed a cumulative increase in sensitivity of detection of all types of reports while progressing from general enquiry, through checklist, to in-depth interview. Questioning detail and terminology influenced participants’ recognition of health issues and treatments. Reporting patterns and vocabulary suggest influence from the relative importance that illnesses and treatments have for participants. Perceptions were often dichotomised (e.g. ‘street’ versus clinic treatments, symptoms experienced versus tests and examinations performed, chronic versus acute illness, persistent versus intermittent symptoms, activity- versus malaria-related symptoms) and this differentiation extended to ideas of relevance to report. South African participants displayed a ‘trial citizenship’, taking responsibility for the impact of their reporting on trial results, and even reaching reporting decisions by consensus. In contrast, Tanzanians perceived their role more as patients than participants; the locus of responsibility for knowing information relevant to the trial fell with trial staff as doctors rather than with themselves. Conclusions: Our observations of how reporting relates to participant perceptions inside and outside trials could help optimise how harms data are elicited. Questions reflecting the different ways that biomedically defined illness and treatment data are perceived by participants may help them understand relevance for reporting. We will theorise how these two disparate trial environments may have influenced how participants understood their role, as this could help researchers achieve empowered participation in similar trials

Role of Condom Negotiation on Condom use among Women of Reproductive Age in three Districts in Tanzania.

ABSTRACT: BACKGROUND: HIV/AIDS remains being a disease of great public health concern worldwide. In regions such as sub-Saharan Africa (SSA) where women are disproportionately infected with HIV, women are reportedly less likely capable of negotiating condom use. However, while knowledge of condom use for HIV prevention is extensive among men and women in many countries including Tanzania, evidence is limited about the role of condom negotiation on condom use among women in rural Tanzania. METHODS: Data originate from a cross-sectional survey of random households conducted in 2011 in Rufiji, Kilombero and Ulanga districts in Tanzania. The survey assessed health-seeking behaviour among women and children using a structured interviewer-administered questionnaire. A total of 2,614 women who were sexually experienced and aged 15--49 years were extracted from the main database for the current analysis. Linkage between condom negotiation and condom use at the last sexual intercourse was assessed using multivariate logistic regression. RESULTS: Prevalence of condom use at the last sexual intercourse was 22.2% overall, ranging from12.2% among married women to 54.9% among unmarried (single) women. Majority of the women (73.4%) reported being confident to negotiate condom use, and these women were significantly more likely than those who were not confident to have used a condom at the last sexual intercourse (OR = 3.13, 95% CI 2.22-4.41). This effect was controlled for marital status, age, education, religion, number of sexual partners, household wealth and knowledge of HIV prevention by condom use. CONCLUSION: Confidence to negotiate condom use is a significant predictor of actual condom use among women in rural Tanzania. Women especially unmarried ones or those in multiple partnerships should be empowered with condom negotiation skills to enhance their sexual and reproductive health outcomes

Timing of antenatal care for adolescent and adult pregnant women in south-eastern Tanzania

Early and frequent antenatal care attendance during pregnancy is important to identify and mitigate risk factors in pregnancy and to encourage women to have a skilled attendant at childbirth. However, many pregnant women in sub-Saharan Africa start antenatal care attendance late, particularly adolescent pregnant women. Therefore they do not fully benefit from its preventive and curative services. This study assesses the timing of adult and adolescent pregnant women's first antenatal care visit and identifies factors influencing early and late attendance.\ud The study was conducted in the Ulanga and Kilombero rural Demographic Surveillance area in south-eastern Tanzania in 2008. Qualitative exploratory studies informed the design of a structured questionnaire. A total of 440 women who attended antenatal care participated in exit interviews. Socio-demographic, social, perception- and service related factors were analysed for associations with timing of antenatal care initiation using regression analysis. The majority of pregnant women initiated antenatal care attendance with an average of 5 gestational months. Belonging to the Sukuma ethnic group compared to other ethnic groups such as the Pogoro, Mhehe, Mgindo and others, perceived poor quality of care, late recognition of pregnancy and not being supported by the husband or partner were identified as factors associated with a later antenatal care enrolment (p < 0.05). Primiparity and previous experience of a miscarriage or stillbirth were associated with an earlier antenatal care attendance (p < 0.05). Adolescent pregnant women started antenatal care no later than adult pregnant women despite being more likely to be single. Factors including poor quality of care, lack of awareness about the health benefit of antenatal care, late recognition of pregnancy, and social and economic factors may influence timing of antenatal care. Community-based interventions are needed that involve men, and need to be combined with interventions that target improving the quality, content and outreach of antenatal care services to enhance early antenatal care enrolment among pregnant women

How Experiences Become Data: The Process of Eliciting Adverse Event, Medical History and Concomitant Medication Reports in Antimalarial and Antiretroviral Interaction Trials.

Accurately characterizing a drug's safety profile is essential. Trial harm and tolerability assessments rely, in part, on participants' reports of medical histories, adverse events (AEs), and concomitant medications. Optimal methods for questioning participants are unclear, but different methods giving different results can undermine meta-analyses. This study compared methods for eliciting such data and explored reasons for dissimilar participant responses. Participants from open-label antimalarial and antiretroviral interaction trials in two distinct sites (South Africa, n = 18 [all HIV positive]; Tanzania, n = 80 [86% HIV positive]) were asked about ill health and treatment use by sequential use of (1) general enquiries without reference to particular conditions, body systems or treatments, (2) checklists of potential health issues and treatments, (3) in-depth interviews. Participants' experiences of illness and treatment and their reporting behaviour were explored qualitatively, as were trial clinicians' experiences with obtaining participant reports. Outcomes were the number and nature of data by questioning method, themes from qualitative analyses and a theoretical interpretation of participants' experiences. There was an overall cumulative increase in the number of reports from general enquiry through checklists to in-depth interview; in South Africa, an additional 12 medical histories, 21 AEs and 27 medications; in Tanzania an additional 260 medical histories, 1 AE and 11 medications. Checklists and interviews facilitated recognition of health issues and treatments, and consideration of what to report. Information was sometimes not reported because participants forgot, it was considered irrelevant or insignificant, or they feared reporting. Some medicine names were not known and answers to questions were considered inferior to blood tests for detecting ill health. South African inpatient volunteers exhibited a "trial citizenship", working to achieve researchers' goals, while Tanzanian outpatients sometimes deferred responsibility for identifying items to report to trial clinicians. Questioning methods and trial contexts influence the detection of adverse events, medical histories and concomitant medications. There should be further methodological work to investigate these influences and find appropriate questioning methods