Browsing by Author "Mushi, Allen"
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Item An Examination Scheduling Algorithm Using Graph Colouring(International Journal of Computer Engineering & Applications, 2013-04) Mohamed, Selemani; Mujuni, Egbert; Mushi, AllenThis paper presents a graph coloring based algorithm for Examinations Timetabling Problem at Sokoine University of Agriculture (SUA) in Tanzania. A Recursive Largest First algorithm for graph coloring is applied to find timeslots. We present a summary of results which indicates good performanceItem Great Deluge Algorithm for the Linear Ordering Problem(International Journal of Information Technology and Computer Science, 2015) Mathias, Amos; Mushi, AllenGiven a weighted complete digraph, the Linear Ordering Problem (LOP) consists of finding and acyclic tournament with maximum weight. It is sometimes referred to as triangulation problem or permutation problem depending on the context of its application. This study introduces an algorithm for LOP and applied for triangulation of Tanzanian Input-Output tables. The algorithm development process uses Great Deluge heuristic method. It is implemented using C++ programming language and tested on a personal computer with 2.40GHZ speed processor. The algorithm has been able to triangulate the Tanzanian input-output tables of size 79×79 within a reasonable time (1.17 seconds). It has been able to order the corresponding economic sectors in the linear order, with upper triangle weight increased from 585,481 to 839,842 giving the degree of linearity of 94.3%.Item Implementation of a goal programming model for solid waste management: a case study of Dar es Salaam – Tanzania(International Journal for Simulation and Multidisciplinary Design Optimization (IJSMDO), 2017) Lyeme, Halid; Mushi, Allen; Yaw, GyekyeIn 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 final 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.Item Implementation of a Tabu Search Heuristic for the Examinations Timetabling Problem(Tanzania Journal of Science, 2011) Mushi, AllenThis paper reports on the design and implementation of an algorithm for the construction of an examinations timetable. The Examinations Timetabling Problem is the problem of assigning examinations and candidates to time periods and examination rooms while satisfying a set of specific constraints. Every University has a different set of constraints and structure of examinations. Generally, timetabling problems are NP-Hard and therefore very difficult to solve. However, they are of great interest due to their important practical application in educational institutions. This paper discusses a heuristic algorithm basing on the examinations timetabling at the University of Dar es salaam. The algorithm uses a Tabu Search technique, which has been successfully applied to other variations of the problem. Real life instance of the problem has been solved within reasonable time and compares with results of the previous work which used a Simulated Annealing Algorithm. It is concluded that the algorithm gives a better performance than manual system and compares well with Simulated Annealing results; Tabu Search is therefore applicable and a good approach to the problem of Examinations timetabling at UDSM.Item Irrigation water allocation optimization using multi-objective evolutionary algorithm (MOEA) a review(International Journal for Simulation and Multidisciplinary Design Optimization (IJSMDO), 2018-01-10) Mwita Fanuel, Ibrahim; Mushi, Allen; Kajunguri, DamianThis 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.Item Late Acceptance Heuristic for University Course Timetabling Problem(International Journal of Advanced Research in Computer Science, 2013-02) Marwa, Yohana; Mushi, AllenThis paper describes a Late Acceptance Heuristic for University Course Timetabling Problem, using a case study of a University College in Tanzania. Late Acceptance is one of relatively new heuristic procedures that try to improve searching by delaying acceptance of latest solutions. The results are compared with an implementation on Simulated Annealing heuristic, which is a well documented and successful heuristic procedure for similar problems. It is shown that Late Acceptance Procedure is a good procedure for Course timetabling problem and compares well with Simulated Annealing.Item The Linear Ordering Problem: An Algorithm for the Optimal Solution(African Journal of Science and Technology (AJST), 2005-06) Mushi, AllenIn this paper we describe and implement an algorithm for the exact solution of the Linear Ordering problem. Linear Ordering is the problem of finding a linear order of the nodes of a graph such that the sum of the weights which are consistent with this order is as large as possible. It is an NP - Hard combinatorial optimisation problem with a large number of applications, including triangulation of input - output matrices in Economics, aggregation of individual preferences and ordering of teams in sports. We implement an algorithm for the exact solution using cutting plane and branch and bound procedures. The program developed is then applied to the triangulation problem for the input - output tables. We have been able to triangulate input - output matrices of size up to 41 x 41.Item Mathematical Programming Formulations for the Examinations Timetable Problem(African Journal of Science and Technology (AJST), 2004-12) Mushi, AllenExaminations Timetabling Problem (ETP) is the problem of assigning courses to be examined and candidates to time periods and examination rooms while satisfying a set of constraints. Every University has a different set of constraints and structure of examinations. Thus there is no general ETP model for all Universities around the world [1]. ETP is NP-Hard [2] and therefore no optimal algorithm is known for this problem which can solve a general problem within reasonable time. However, exact methods can be used to provide a benchmark for the heuristic methods. There is no general model for University Timetabling Problems because the problem feature differs from one University to another. In this paper we focus in the formulation of the ETP for the University of Dar as salaam. We formulate, test and compare three Integer Programming models. It is concluded that, although exact methods cannot give a solution to a real-size problem, these models give a good benchmark for testing the performance of other approaches. This paper also gives a direction for better exact models for the University of Dar es salaam’s ETP. INTRODUCTION The Examination-Timetabling Problem (ETP) essentially involves the assignment of courses to be examined and their candidates to time periods and examination rooms while satisfying a given set of constraints. These constraints are divided into hard and soft [i], [ii]. Hard constraints must be satisfied such as avoiding studentexamination collision and room over-sizing. Soft constraints mayItem Multi-Objective Optimization Model for Irrigation Water Allocation(ASIAN JOURNAL OF MATHEMATICS AND APPLICATIONS, 2018) Fanuel, Ibrahim; Mushi, AllenIn Tanzania, management of land and water resources is considered an ab- solutely strategic priority for agricultural development. In this study, a Multi-Objective optimization (MOO) model was formulated to utilize the available water by identifying the best crop patterns which maximize the farm total net bene t and minimize the total vari- able costs. The data for 6 crops collected from Nkoanrua region and FAO were used for the model analysis. The Subdivision Algorithm which is a set oriented numerical method was used to analyse the model. After 54 subdivision steps, the model proposed that, the amount of land allocated to crops which are less pro table depends on the minimum requirement constraints, while, for more pro table crops, the allocation is based on costs of production, minimum and maximum requirement constraints, Bene t, and water requirements. Lastly, the sensitivity analysis shows that, the price and production costs for carrots and maize has no impact on the model solutions.Item Multi-Objective Optimization Model Formulation for Solid Waste Management in Dar es Salaam, Tanzania(ASIAN JOURNAL OF MATHEMATICS AND APPLICATIONS, 2017) Lyeme, Halid; Mushi, Allen; Yaw, GyekyeSolid 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 systemItem Non-Linear Great Deluge algorithm for Tanzanian High Schools Timetabling(International Journal of Advanced Research in Computer Science, 2011-07) Mushi, AllenHigh school timetabling problem involves allocation of students, lessons, and teachers into timeslots while respecting constraints, both on students, teachers and other available resources. It is one of the Combinatorial Optimization Problems which are known to be NP-Hard and therefore no optimal algorithm is known for its solution. The problems differ from one institution to another depending on the educational system and administrative structures. In this paper, a Great Deluge Algorithm is developed based on an adaptation which employs a non-linear decay rate in the reduction of ‘water level’. This is a case study in the application of the algorithm to Tanzanian high schools. The algorithm is tested on three high school systems in Tanzania. Since no such work has been previously done in Tanzania, the algorithm is compared with the manually generated timetables for the same schools. It has been shown that, the algorithm performs very well and can be used to greatly improve timetabling at Tanzanian high schools.Item Optimal Solution Strategy for University Course Timetabling Problem(International Journal of Advanced Research in Computer Science, 2013-01) Chacha, Stephen; Mushi, AllenThis paper describes formulations of the University Course Timetabling Problem as used at Mkwawa University College of Education. University Course Timetabling is the Problem of scheduling resources such as lectures, courses and rooms to a number of timeslots over a planning horizon, normally a week, while satisfying a number of problem-specific constraints. In this study, we have developed three models and tested using real data from the stated University. It has been possible to get optimal solution for real problem instances through reformulations of models which involve a mixture of binary and time-indexed variables.Item Optimizing Schedules for School Bus Routing Problem: the case of Dar Es Salaam Schools(International Journal of Advanced Research in Computer Science, 2015-02) Ngonyani, Beatha; Mujuni, Egbert; Mushi, AllenThe School Bus Routing Problem (SBRP) deals with transportation of students to and from their schools. Given a set of fleet of buses of a school, a set of bus stops, the time matrix and the number of students at each stop, the task is to determine the schedule of buses that minimizes amount of time students spend in the buses on the way to and from school. The school bus routing problem is a special case of the Vehicle Routing Problem (VRP) and is known to be NP-hard. This NP-hardness implies that it is very unlikely that the problem can be solved in polynomial time. The common methods used to solve NP-hard problems are heuristic algorithms which gives quick and good solutions without guarantee that the solution obtained is optimal. In this paper a Tabu search based heuristic for SBRP is developed. The algorithm has been implemented using Borland C++ 4.5 programming language and tested using data from Tusiime Nursery and Primary School in Dar es salaam, Tanzania. The proposed implementation results in reduction of students’ travelling time by 19.24%.Item Projecting Tanzania pension fund system(African Journal of Applied Statistics, 2017) Andongwisye, John; Larsson, Tobjorn; Singull, Martin; Mushi, AllenA mandatory Tanzania pension fund with a nal salary de ned bene t is analyzed. This fund is a contributory pay-as-you-go de ned bene t pension system which is much a ected by the change in demography. Two kinds of pension bene t, 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, bene ts, 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 bene t 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 insu cient to cover bene t payouts.Item Review of Multi-Objective Optimization Models for Solid Waste Management Systems with Environmental Considerations(Journal of Mathematics and Computer Science (JMCS), 2017) Lyeme, Halid; Mushi, Allen; Yaw, GyekyeThis paper analyzes more than 50 papers with a limited area in the field of solid waste management systems and supply chain management, extending over mathematical models that include economic factors, as well as environmental and/or waste flow allocation. The review finds that there are a number of limitations to the current research in sustainable solid waste management systems. The narrow scope of environmental factors as constraints in the current models means that there is a need to go further and include new environmental metrics. The effective inclusion of environmental objectives in models with improved multi-objective approaches is a gap that needs to be filled. Furthermore, there are significant gaps in sensitivity analysis of models limiting the general applicability of the models. The paper concludes with promising new avenues of research that demand effective inclusion of sustainability into solid waste management system models.Item Sensitivity analysis of multi-objective optimization for solid waste management(New Trends in Mathematical Sciences, 2017-11-08) Lyeme, Halid; Mushi, Allen; Yaw, GyekyeIn this study, a sensitivity analysis of a multi-objective optimization model for solid waste management (SWM) for Dar es Salaam city in Tanzania is considered. Our objectives were to identify the most sensitive parameters and effect of other input data to the model output. Five scenarios were considered by varying their associated parameter values. The results showed that the decrease of total cost for the SWMsystem in all scenarios was observed compared to the baseline solution when the single landfill was considered. Furthermore, the analysis shows that the variable cost parameter for the processing facilities is very sensitivity in such a way that if you increase the variable cost then, there is a rapid increase of total cost for the SWM system and the vice versa is true. The relevant suggestions to the decision makers were also discussed.Item Simulated Annealing Algorithm for the Examinations Timetabling Problem(African Journal of Science and Technology (AJST), 2007-12) Mushi, AllenExamination scheduling is a very important process in Educational Institutions. The main challenge is to assign examinations to timeslots and rooms over a fixed period of time while satisfying a set of constraints on both candidates and invigilators. The problem becomes even more difficult when student number rises and student choice widens which makes automated system a necessary tool. The problem varies in detail from Institution to Institution. Thus any generic approach may not be able to capture sufficiently the characteristics of specific problems. This paper reports the design of an algorithm for the Examinations Timetabling Problem at University of Dar es salaam, based on a Simulated Annealing heuristic. We have been able to solve an existing problem and show that the automated system performs better and faster than the manually generated solution.Item A Simulated Annealing Heuristic for Tanzania High Schools Timetabling Problem(Global Journal of Computer Applications and Technology, 2011) Mushi, Allen; Batho, PeterHigh School Course Timetabling Problem involves scheduling of lessons and teachers to timeslots within a week while satisfying a set of constraints. Like many other variants of timetabling problems, it is known to be NP- Hard, and therefore no optimal solution procedure is known to solve the problem in a reasonable time scale. Currently, very little work has been done in automating the high schools timetabling in Tanzania. Given the growing needs for educational resources in the country, optimization techniques for these resources cannot be avoided. In this paper, we present a heuristic algorithm based on Simulated Annealing. The algorithm has been tested with success on real data obtained from three high schools. A thorough experimentation has been done on six of cooling schedules. The results compare well with the previous work on the same data set and perform much better than manual system.Item Solving the Examination Timetabling Problem Using a Two-Phase Heuristic(World Academic Press, World Academic Union, 2015-06-07) Mujun, Egbert; Mushi, AllenExamination 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 enrolments, 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.Item Solving the Examination Timetabling Problem Using a Two-Phase Heuristic(2015) Mujuni, Egbert; Mushi, AllenExamination 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 enrolments, 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.