Papers by Mohamed Bashir Omar
A two-level hierarchy software architecture framework for the manufacturing industry
Tenth Asia-Pacific Software Engineering Conference, 2003.
The main objective is to propose an integrated framework architecture that facilitates coordinati... more The main objective is to propose an integrated framework architecture that facilitates coordination and collaboration among different managerial levels in a manufacturing facility. We are deploying an object-oriented approach as the conceptual modeling methodology. Our thesis is that local decisions (at the operation level) can benefit from the timely accessibility of appropriately aggregate decisions that are imposed by top management. In turn, the manufacturing system as a whole can benefit from timely dissemination of appropriate aggregate decisions pertaining to improvements of the overall productivity, and profitability of the manufacturing system. We report on the development and implementation of framework for integrating tactical and operational decisions. The developed framework is user-friendly, generic in nature and will be of interest to practitioners and managers for the manufacturing industry to assist their decision-making.
Integers, 2018
It is classically known that the proportion of lattice points visible from the origin via functio... more It is classically known that the proportion of lattice points visible from the origin via functions of the form $f(x)=nx$ with $n\in \mathbb{Q}$ is $\frac{1}{\zeta(2)}$ where $\zeta(s)$ is the classical Reimann zeta function. Goins, Harris, Kubik and Mbirika, generalized this and determined the proportion of lattice points visible from the origin via functions of the form $f(x)=nx^b$ with $n\in \mathbb{Q}$ and $b\in\mathbb{N}$ is $\frac{1}{\zeta(b+1)}$. In this article, we complete the analysis of determining the proportion of lattice points that are visible via power functions with rational exponents, and simultaneously generalize these previous results.
Australas. J Comb., 2018
For a given weight of a complex simple Lie algebra, the q-analog of Kostant’s partition function ... more For a given weight of a complex simple Lie algebra, the q-analog of Kostant’s partition function is a polynomial valued function in the variable q, where the coefficient of q is the number of ways the weight can be written as a nonnegative integral sum of exactly k positive roots. In this paper we determine generating functions for the q-analog of Kostant’s partition function when the weight in question is the highest root of the classical Lie algebras of types B, C, and D, and the exceptional Lie algebras of type G2, F4, E6, E7, and E8. ∗ This research was supported by research funds from Harvey Mudd College. P.E. HARRIS ET AL. /AUSTRALAS. J. COMBIN. 71 (1) (2018), 68–91 69
Aquila: The FGCU Student Research Journal, 2019
Given a graph G with n vertices and a bijective labeling of the vertices using the integers 1, 2,... more Given a graph G with n vertices and a bijective labeling of the vertices using the integers 1, 2,. .. , n, we say G has a peak at vertex v if the degree of v is greater than or equal to 2 and if the label on v is larger than the label of all its neighbors. For each subset S ⊂ V(G), we want to determine the number of distinct labelings of the vertices of G such that the vertices in S are precisely the peaks of G. The set S is called the peak set of the graph G, and the set of all labelings with peaks at every vertex in S is denoted by P(S ; G). In this paper, we present an algorithm for constructing all of the labelings in P(S ; G) and explore special cases of peak sets in certain families of graphs, specifically those related to the joins of graphs. We note that this work is a direct generalization of the research of peak sets of permutations, which is the special case when G is the path graph on n vertices.
Discrete Mathematics, 2019
Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon prov... more Let n be a nonnegative integer and I be a finite set of positive integers. In 1915, MacMahon proved that the number of permutations in the symmetric group S n with descent set I is a polynomial in n. We call this the descent polynomial. However, basic properties of these polynomials such as a description of their coefficients and roots do not seem to have been studied in the literature. Much more recently, in 2013, Billey, Burdzy, and Sagan showed that the number of elements of S n with peak set I is a polynomial in n times a certain power of two. Since then, there have been a flurry of papers investigating properties of this peak polynomial. The purpose of the present paper is to study the descent polynomial. We will see that it displays some interesting parallels with its peak relative. Conjectures and questions for future research are scattered throughout.
Journal of Combinatorial Theory, Series A, 2017
We say that a permutation π = π 1 π 2 • • • π n ∈ S n has a peak at index i if π i−1 < π i > π i+... more We say that a permutation π = π 1 π 2 • • • π n ∈ S n has a peak at index i if π i−1 < π i > π i+1. Let P(π) denote the set of indices where π has a peak. Given a set S of positive integers, we define P S (n) = {π ∈ S n : P(π) = S}. In 2013 Billey, Burdzy, and Sagan showed that for subsets of positive integers S and sufficiently large n, |P S (n)| = p S (n)2 n−|S|−1 where p S (x) is a polynomial depending on S. They gave a recursive formula for p S (x) involving an alternating sum, and they conjectured that the coefficients of p S (x) expanded in a binomial coefficient basis centered at max(S) are all nonnegative. In this paper we introduce a new recursive formula for |P S (n)| without alternating sums, and we use this recursion to prove that their conjecture is true.
Framework for Integrating Optimization and Heuristic Models for Solving Planning and Scheduling Problem in a Resin Manufacturing Plant
Studies in Computational Intelligence, 2011
This chapter introduces a three-level hierarchical production planning and scheduling approach fo... more This chapter introduces a three-level hierarchical production planning and scheduling approach for a multi-product batch processing resin plant in South East Asia. The approach integrates optimization and heuristic models to determine aggregate plans, master production schedule, number of batches that need to be scheduled and finally sequencing of jobs with the objective to minimize the total weighted tardiness. At the top level of the hierarchy, our approach deploys a mixed-integer linear programming model to solve the aggregate plans where setups occur. At the second level a weighted integer goal programming model is developed to disaggregate the aggregate plans and provides an optimal number of monthly batches to be sequenced in the presence of setups activities. At the third level of the hierarchy, a job-sequencing model is developed that combines two heuristics approaches that aims to minimize the total weighted tardiness. Real industrial data is used to test and validate the proposed approach. The results indicate that the approach is capable of dealing with a full range of the products produced by the resin plant.
Mixed integer programming formulation for hybrid flow shop scheduling problem
2010 IEEE International Conference on Industrial Engineering and Engineering Management, 2010
... The second issue is the increased complexity of the HFS environment in the presence of sequen... more ... The second issue is the increased complexity of the HFS environment in the presence of sequence dependent setup times which is scarcely studied in HFS settings (see Allahverdi et al [13]). ... Problem Mohamed K. Omar 1 , Teo. SC 2 . and Yasothei Suppiah 3 ...
2011 IEEE International Conference on Industrial Engineering and Engineering Management, 2011
Méndez et al., [1] proposed an elegant MILP that provides a solution to a complicated short-term ... more Méndez et al., [1] proposed an elegant MILP that provides a solution to a complicated short-term scheduling of resource-constraint multistage flowshop batch facilities. Moreover, the work presents a three-variation of the problem and provides a solution for each variation. In recent years, many metaheuristics are developed to work as add-in to spreadsheet popular software to provide solutions for optimization problems. This paper reports on an application of spreadsheet based Genetic Algorithm (GA) to solve the problem reported by Méndez. Moreover, our results indicate that it is possible to solve complex scheduling problems using the proposed approach, however, spreadsheet formulation knowledge and modelling skills are required. .
EPSO for solving non-oriented two-dimensional bin packing problem
2011 IEEE International Conference on Industrial Engineering and Engineering Management, 2011
The non-oriented two-dimensional bin packing problem is dealing with a set of rectangular pieces ... more The non-oriented two-dimensional bin packing problem is dealing with a set of rectangular pieces that need to be packed into identical rectangular bins. Moreover and in order to minimize the number of bins, the pieces are allowed to rotate by 90° without overlapping. There are many real life applications for this operations research problem. Among these applications: loading of boxes to pallets, trucks and containers, packing of box bases on shelves and other applications in the wood and metal industry. In this paper, we propose evolutionary particle swarm optimization algorithm (EPSO) for solving the non-oriented two-dimensional bin packing problem. Extensive numerical investigations are performed to determine the solution quality of the proposed algorithm. Moreover, the performance of our proposed algorithm is compared with a best known greedy algorithm published in the literature.
Investigating the impact of quality control decisions on cost of quality
2011 Fourth International Conference on Modeling, Simulation and Applied Optimization, 2011
In this paper, the cost of quality model developed by Chiadamrong [4] was considered and modified... more In this paper, the cost of quality model developed by Chiadamrong [4] was considered and modified and extended. The new model is then used to develop a simulation model for two processing stations in a manufacturing system. Using real life data from the industry and through simulation works, the model was tested with a set of managerial quality control decision
Process and labour utilisation in the electronic industry: A simulation approach
2012 IEEE International Conference on Management of Innovation & Technology (ICMIT), 2012
Process utilisation that ensures all workstations are balanced is essential factor for factory pr... more Process utilisation that ensures all workstations are balanced is essential factor for factory productivity. Another important factor that has to be considered is the Man-to-Machine (M-to-M) ratio which provides an answer to how much manpower should be assigned to a machine. This paper reports on a simulation approach that aims to simultaneously provide a solution to the problems of process and M-to-M ratio utilisation. The results of the simulation provide an accurate picture for the system understudy in terms of the bottleneck process, optimal utilisation and M-to-M ratio.
An integrated architecture for lean waste analysis
2012 IEEE International Conference on Industrial Engineering and Engineering Management, 2012
Lean has become very popular for companies striving towards reducing wastes and improving their e... more Lean has become very popular for companies striving towards reducing wastes and improving their efficiency. The fundamental work in Lean implementation includes establishing the standard times for the process under study before the information can be used to determine the resource capacity. The traditional work study methods such as Process Mapping and Man-Machine Charts are no longer suitable to be used in the complicated manufacturing environment such as in the electronics. This paper reports on an integrated architecture for conducting work study and performing lean waste analysis. The developed architecture was implemented at an electronic manufacturing company. The benefits observed from the implementation phase indicate that the proposed architecture has reduced the lengthy time that work-study usually takes, eliminated human error during analysis and improved the accuracy of data.
Genetic algorithm for solving total weighted tardiness and sum of earliness and tardiness penalties of job-shop scheduling problem
2011 Fourth International Conference on Modeling, Simulation and Applied Optimization, 2011
This paper addresses a scheduling problem known in the job-shop industrial environment and recomm... more This paper addresses a scheduling problem known in the job-shop industrial environment and recommends solving the problem using the Microsoft Excel spreadsheet and an add-in that provides Genetic Algorithm which is capable of solving complex scheduling problems. The authors selected total weighted tardiness and sum of earliness and tardiness penalties as performance measures to determine the quality of the solution.
2011 IEEE International Conference on Industrial Engineering and Engineering Management, 2011
In this paper, the recommended extensions by Chiadamrong [1] was successfully adopted and signifi... more In this paper, the recommended extensions by Chiadamrong [1] was successfully adopted and significant modifications was proposed when computing costs of quality model in a manufacturing system In the literature shows that there is strong connection exist between the tolerance designs with the quality characteristic of a product and the cost associate in achieving the specific quality of the product. With the intention of utilizing the reciprocal power model in determine the relation between the tolerance and the cost, the tolerance has to be converted and set to a standard value at different confidence level. The proposed costs of quality model was tested using real life data obtain from the industry and through simulation works, the results was generated. .
Cost of quality model development, verification and validation
2011 IEEE International Conference on Quality and Reliability, 2011
Undoubtedly simulation can help managers to enhance their decisions since it provide an opportuni... more Undoubtedly simulation can help managers to enhance their decisions since it provide an opportunity to understand complex systems. In the case of quality control activities, simulation can be used to assist quality control managers to determine the cost involved to implement a specific quality control policy. Having said all that, one of the most challenging problems faced by the simulation
The solutions of DT and AHP for supplier selection problem
2011 IEEE International Conference on Quality and Reliability, 2011
In real-life situations, supplier selection problems involve multiple selection criteria and the ... more In real-life situations, supplier selection problems involve multiple selection criteria and the risk associated with supplier failure. It is a fact that the best solution is to develop a solution methodology that combines these two decision factors simultaneously. The literature proposes the analytic hierarchical process (AHP) as a solution to multiple selection criteria problem. On the other hand, the decision
Cost of quality modeling: Extension and improvement
2010 IEEE International Conference on Industrial Engineering and Engineering Management, 2010
This paper proposes a new cost of quality model that taken into consideration inspections errors,... more This paper proposes a new cost of quality model that taken into consideration inspections errors, tolerance design and important process quality control techniques in a manufacturing environment. Through simulation works and using a real life data, the model was validated. Results indicate that the model accurately confirms the improvements suggested in the literature.
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Papers by Mohamed Bashir Omar