Mathematics and Statistics

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Start date: 2010End date: 2019

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    Two phase heuristic algorithm for the university course timetabling problem: The case of University of Dar es Salaam
    (Tanzania Journal of Science, 2011) Mushi, Allen R.
    University course timetabling is the problem of scheduling resources such as lecturers, courses, and rooms to a number of timeslots over a planning horizon, normally a week, while satisfying a number of problem-specific constraints. Since timetabling problems differ from one institution to another, this paper investigated the case of the University of Dar Es salaam, based on the combination of Simulated Annealing (SA), and steepest descent in a two-phase approach. Solutions have been generated which greatly outperform the manually generated ones. Furthermore, the method compares well with previous work on Tabu Search but with faster execution time and higher quality on rooms allocation. It is concluded that the approach gives good results given a careful selection of parameters.
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    Asset liability management for Tanzania: Pension funds by stochastic programming
    (Afrika Statistika, 2018) John, Andongwisye; Larsson, Torbjörn; Singull, Martin; Mushi, Allen R.
    We present a long-termmodel of asset liability management for Tanzania pension funds. The pension system is pay-as-you-go where contributions are used to pay current benefits. The pension plan is a final salary defined benefit. Two kinds of pension benefits, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor for a long-term asset liability management is that, Tanzania pension funds face an increase of their members’ life expectancy, which will cause the retirees to contributors dependence ratio to increase. We present a stochastic programming approach which allocates assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001, with features from Tanzania pension system. In contrast to most asset liability management models for pension funds by stochastic programming, liabilities are modeled by using number of years of life expectancy for monthly benefit. Scenario trees are generated by using Monte Carlo simulation. Numerical results suggest that, in order to improve the long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target funding ratios to characterize the pension funds’ solvency situation.
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    Projecting Tanzania pension fund system
    (Statistics and Probability African Society, 2017) John, Andongwisye; Torbjörn, Larsson; Singull, Martin; Mushi, Allen R.
    A mandatory Tanzania pension fund with a final salary defined benefit is analyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the analysis is the increased life expectancy of members of the fund. The projection of the fund's future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possible reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts. Un fonds de pension obligataire en Tanzanie avec un salaire final défini est défini. Ce fonds est un système de retraite à prestations déterminées contributif et payant qui est très affecté par les changements démographiques. Deux types de prestations de retraite, une retraite de rachat (à la retraite) et une pension mensuelle (vieillesse) sont considérés. Un facteur décisif dans l'analyse est l'augmentation de l'espérance de vie des participants au fonds. La projection des futurs membres et des retraités du fonds se fait à l'aide des taux de mortalité attendus de la population active et de la longévité espérée. Les contributions futures, les avantages, la valeur de l'actif et du passif sont analysés. Nos projections montrent que le fonds ne sera pas pleinement durable à long terme, en raison de l'augmentation de l'espérance de vie de membres. Les contributions ne couvriront pas les paiements de prestations et la valeur de l'actif ne couvrira pas entièrement le passif. Une évaluation de certaines réformes possibles du fonds montre qu'ils ne peuvent garantir une viabilité à long terme. Un rendement plus élevé de la valeur de l'actif améliorera le ratio de financement, mais les contributions restent insuffisantes pour couvrir les paiements des prestations.
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    Optimization model for solid waste management at Ilala Municipal, Tanzania
    (Journal of Informatics and Virtual Education, 2011) Lyeme, Halidi A; Mujuni, Egbert; Mushi, Allen R.
    The existing solid waste management system at Ilala Municipal suffers from the lack of a real plan for collection centre locations and vehicle routes. In this study, a proposed mathematical model for municipal solid waste management process for Ilala municipality is presented. It includes the use of the concept of collection centres. Operational research methodology particularly Mixed Integer Programming is used to model the problem. The problem is solved to optimality which provides the best distribution of collection centres and their capacities. The solution shows a leastcost transportation plan with a cost saving of 38.3% per day compared to the current system.
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    Implementation of a goal programming model for solid waste management: A case study of Dar es Salaam – Tanzania
    (EDP Sciences, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
    In this research article, the multi-objective optimization model for solid waste management problem is solved by the goal programming method. The model has three objectives: total cost minimization, minimization of f inal waste disposal to the landfill, and environmental impact minimization. First, the model is solved for the higher priority goal, and then its value is never allowed to deteriorate. The model is solved for the next priority goal and so on until the problem is solved. The model was tested with real data for solid waste management system from Dar es Salaam city. The results determine the best locations for recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. Furthermore, the solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 78% and 57.5% respectively if fully implemented compared to the current system.
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    Multi-objective optimization model formulation for solid waste management in Dar es Salaam, Tanzania
    (Asian Journal of Mathematics and Applications, 2017) Lyeme, Halidi Ally; Mushi, Allen R.; Nkansah-Gyekye, Yaw
    Solid waste management is a challenging problem in developing nations. The health and environmental negative implications associated with solid waste management are very serious particularly in the developing nations where a large percent of waste is dumped into open areas. These implications are essentially on climate change and global warming due to environmental problems. In this paper, a multiobjective optimization model is developed to address the conflicting objectives of cost minimization, minimization of final waste disposal to the landfill, and environmental impact minimization. The model follows a mixed-integer programming formulation and tested by data from selected wards in Dar es Salaam city. The output is the best location of recycling plants, separating plants, composting plants, incinerating plants, landfill and waste flow allocation between them. The solution shows a high reduction of the amount of waste to the landfill and greenhouse gas emissions by 76% and 55.2% respectively compared to the current system.
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    Irrigation water allocation optimization using Multi-Objective Evolutionary Algorithm (MOEA): A review
    (EDP Sciences, 2018) Fanuel, Ibrahim Mwita; Mushi, Allen R.; Kajunguri, Damian
    This paper analyzes more than 40 papers with a restricted area of application of Multi-Objective Genetic Algorithm, Non-Dominated Sorting Genetic Algorithm-II and Multi-Objective Differential Evolution (MODE) to solve the multi-objective problem in agricultural water management. The paper focused on different application aspects which include water allocation, irrigation planning, crop pattern and allocation of available land. The performance and results of these techniques are discussed. The review finds that there is a potential to use MODE to analyzed the multi-objective problem, the application is more significance due to its advantage of being simple and powerful technique than any Evolutionary Algorithm. The paper concludes with the hopeful new trend of research that demand effective use of MODE; inclusion of benefits derived from farm byproducts and production costs into the model.
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    Mathematical model for Tanzania population growth
    (Tanzania Journal of Science, 2019) Mwakisisile, Andongwisye; Mushi, Allen R.
    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.
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    Application of K-Means and Partitioning Around Mediods (PAM) clustering techniques on Maize and Beans yield in Tanzania
    (KY Publications, 2016) Mbukwa, Justine Nkundwe; Anjaneyulu, G.V.S.R.
    This paper contributes to the application of k-means and k-mediods multivariate statistical methods for the purpose of revealing optimal clusters and assessing the consistency of individual districts within the group. Data used were extracted from united republic of Tanzania (Ministry of Agriculture, Livestock and Fisheries(MALF) (2003/12) consisted a total of (n=36 districts) with both maize and beans yield. The R-statistical computing version (3.1.1) was used. The study findings revealed that 36 districts were grouped into six clusters using k-means algorithm. Using the k-mediods, it was revealed that only 11 districts were found to very well structured since their silhouette width (Si) is above 0.5. Nevertheless, the clusters validation was done in such a way that individual district whose silhouette width (Si) close to 1 was regarded as highly consistency clustered whereas districts with (Si) greater or equal to 0.25 were said to be somehow well clustered and otherwise. The paper concludes that few districts that are very consistent given the threshold margin should to be monitored and evaluated effectively to ascertain productivity. The study recommends that the government should pay attention on allocating the scarce resources to the consistency clusters along with policy review in favour of smallholder farmers through access and timely for all important farm inputs in future.
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    Statistical Analytic Tool for Dimensionalities in Big Data: The role of Hierarchical Cluster Analysis
    (Research India Publications, 2016) Mbukwa, Justine N.; Tabita, G Neeha; Anjaneyulu, GVSR; Rajasekharam, OV
    An interest for presenting this paper rose because of massive increase information with a very high dimensional from different sources in this era of globalization. Data are produced continuously and are unstructured (1). This paper is confined to literature review search for big data issue and challenges of several scopes in data. It brings a detailed discussion on the problem on these data and analysis done using the effective multivariate statistical tool namely clustering analysis technique as a data reduction technique. It is used as a base for discussion for existing challenge of multi-dimensionalities of data. The findings indicated that, the world is noisy due to massive flow of information continuously. Findings revealed that data emanating from face book, you tube and twitter can be used to predict the epidemic of influenza and even market trend (2 and 3). With face book data is used to predict the people`s interest. However, data from different sources have been proved to be useful in decision making efficiently and effectively for public as well as private sector. Cluster analysis technique sorts data/alike things into groups, to see if there a high natural degree association among members of the same group and low between members of different groups. Finally, this technique has proved failure to handle such heap of data with varied sources. With regards to data stored, it remains to be a challenge in terms of analysis among researchers and scientists. Therefore, it calls for advanced statistical software to cater for such an existing challenges.