Major: Combinatorial Optimization; Minor: Probability Distribution
At the Mathematics department office
Appointment on Visitation important
Topic: Multiobjective Optimization In A Flow Shop Scheduling
Description: IntroductionMultiobjective optimization MOO is an area in combinatorial optimization encompassing multiple-criteria decision-making. It is a concept of mathematical optimization problems having more than one objective function to be optimized simultaneously. Multiobjective optimization is being applied to numerous fields of science, engineering, economics and psychology where the best among many decisions must be taken in the presence of trade-offs between two or more conflicting objectives. Undeniably, in many practical applications, inventors are making decisions between conflicting objectives - for instance, maximizing performance while minimizing fuel consumption and emission of pollutants of a vehicle. Scheduling in a Flow shop environment like assembly plants encompasses making decisions with several contradicting objectives to be optimized simultaneously. Schedule may involve minimizing earliness, make-span, flow-time and as well maximizing on-time jobs at the same time. The solution of MOO models is mostly expressed as a set of Pareto optima PO , representing optimal trade-offs between given criteria. Identifying the best Pareto solution from this set for practical implementation is a complex and challenging task.AimThe aim of this research is to develop, analyze and implement a bi-level optimization algorithm in a Flow Shop to support MOO decision-making in the post-optimal analysis of Pareto fronts.MethodologyThe method to be employed will be theoretical and experimental based. An algorithm characterized by a trust region technique for the post-optimal Pareto front is considered. In the algorithm, a reference point among set of non-dominated points is selected using its density function and area around this point explored. It will ensure uniformity of solutions distribution for problems with more than two objective functions.Contribution to knowledgeAn algorithm that is capable of selecting non-dominated solutions which can be appealing for decision-makers, aiding computation of the distance between any suboptimal points of a MOO model and its Pareto front is proposed. Also, it will improve targets for suboptimal solutions, that if attained, would make them optimal.
|Mathematics, University of Lagos, Akoka
Algorithms for Just-In-Time Scheduling In A Flow Shop with Distinct Due Windows
IntroductionThe study of Just In Time JIT scheduling in a Flow Shop FS has wide applications in the industry, science and engineering. Such applications include, inventory cost reduction, input control and meeting customers order. However, most of the existing studies relating to JIT in a FS has been carried out without considering due windows effect on the complexity analysis of large problems in-spite of their importance in real life situations where jobs are expected to finish in a certain interval rather than a single due date.Aim The focus of this research is to develop mathematical models, prove the complexity of solving JIT scheduling problems, develop and implement tractable algorithms that minimize both number of early/tardy jobs and earliness/tardiness criteria. MethodologyMixed Binary Integer Programming MBILP models will be developed as template for obtaining optima solution. Karps reduction technique will be explored to establish that JIT is NP-Complete in the strong sense. In view of this, a two stage iterative local search heuristic based on Foward Shift Search FSS technique will be formulated and employed to obtain near optima schedules for minimizing number of early/tardy jobs while a hybrid of meta-heuristic algorithm is considered to minimize earliness/tardiness. For the assessment of these algorithms, a benchmark of 12500 problem instances will be solved and compare with existing algorithms from the literature. The results are expected to be better in terms of quality of solution and computational time. In addition, the MBILP codes will be implemented on XPRESS-MP software package for small instance problems and compared with FSS. Contribution to KnowledgeIt is expected that the mean relative deviation index is not up to 1% in all cases where optima solutions are obtained within 600 seconds of computational time.
IDOWU GBOLAHAN is a Senior Lecturer at the Department of Mathematics
IDOWU has a Ph.D in Statistics from Mathematics, University of Lagos, Akoka