A multi-objective optimization problem has two or more objectives to be minimized or maximized simultaneously. It is usually difficult to arrive at a solution that optimizes every objective. Therefore, the best way of dealing with the problem is to obtain a set of good solutions for the decision maker to select the one that best serves his/her interest. In this paper, a ratio min-max strategy is incorporated (after Pareto optimal solutions are obtained) under a weighted sum scalarization of the objectives to aid the process of identifying a best compromise solution. The bi-objective discrete optimization problem which has distance and social cost (in rail construction, say) as the criteria was solved by an improved Ant Colony System algorithm developed by the authors. The model and methodology were applied to hypothetical networks of fourteen nodes and twenty edges, and another with twenty nodes and ninety-seven edges as test cases. Pareto optimal solutions and their maximum margins of error were obtained for the problems to assist in decision making. The proposed model and method is user-friendly and provides the decision maker with information on the quality of each of the Pareto optimal solutions obtained, thus facilitating decision making.

In this paper, the concept of assignment problem was applied to solve a problem for a Legal Firm A in Kumasi which had a difficulty in assigning nine different cases to its nine junior lawyers. Based on the data collected, Management Scientist Version 5 Software which uses Hungarian Method was used to solve the problem. Optimal assignments of the cases to the junior lawyers were obtained for the Legal Firm A. It was obtained that,

This paper presents a state of the art review of water quality optimisation models and techniques from early 1970s to date in terms of the model/technique category, model/technique type, purpose and application. The models are categorised into Mathematical Programming Models and Meta-heuristic Programming Models. Similarly, the techniques are categorised into Mathematical Programming Techniques and Meta-heuristic Programming Techniques. The review is concluded by drawing attention to the rare nature of application of interior-point methods to water quality optimisation.

The objective of the study was to use the concept of game theory to analyze the patronage of two Radio Stations in Kumasi and suggest how the stations could plan some of their programmes to enable them receive higher patronage. Data of all the programmes aired by the two radio stations were collected. The two stations had ten (10) common programmes. After interviewing one hundred (100) purposively selected 18 D. K. Boah, S. B. Twum and S. K. Amponsah listeners in Ashanti Region of Ghana to find their patronage preferences for the two radio stations named Station A and Station B based on the common programmes, a matrix was constructed. A critical analysis of the matrix revealed that Station A did better in sporting programmes than station B and Station B did better in news broadcasting and musical programmes than Station A. It is recommended that the two Stations should not air two similar programmes simultaneously to enable them receive higher patronage.

We used a system of linear equations to determine the number of vehicles that should be allowed to route a four one-way streets in Kumasi, in order to keep traffic flowing. The systems of equations used in the model were solved analytically using the method of Gauss-Jordan elimination. Our work shows that if 155vph, 276vph, and 240vph are allowed to route intersection A and B, A and D and D and C of the 654 Isaac Kwasi Adu et al. model respectively, traffic congestion in the area of Kumasi discussed in the model would be minimized. We recommend to the stakeholders of Kumasi to provide exclusive lanes for public transport, ensure the use of traffic regulations and traffic engineers to control the traffic, use innovative ideas to reduce traffic impacts on public transport, provide traffic lights at the four intersections under discussion in this research and adjust them in the direction of the results of this research.