Multistage Open-Shop-Problem: Schedules for N Tasks on K Machines with Different Technical Characteristics for an Arbitrary order of Tasks

The statements and mathematical models of the open — shop-problem are considered: performing N tasks on K machines with an arbitrary order of processing each task on all machines. Unlike most publications on solving this problem, the task posed is solved in a multi-stage formulation under the conditions of a sequential chain of sections and workshops of the enterprise, as well as in the presence of restrictions on the start and end times of tasks and the permissible operating times of machines. In addition, for scheduling systems of enterprises, it is extremely important to consider this task in a multi-stage setting, i.e. in a sequential chain of plots and workshops. The properties of admissible and optimal schedules, as well as algorithms of exact and approximate methods for solving these problems by successive optimization algorithms are investigated. At the early stages of solving the problem, the fact of incompatibility of the system of constraints of the task and the definition of a subset of tasks or resources, the time range of which should be expanded, is established. The described algorithms for solving the problem are illustrated by numerical examples.

Comparative Solutions of Exact and Approximate Methods for Traveling Salesman Problem

There are two major optimization methods: Exact and Approximate methods. A well known exact method, Branch and Bound algorithm (B&B) and approximate methods, Elimination-based Fruit Fly Optimization Algorithm (EFOA) and Artificial Atom Algorithm (A3) are used for solving the Traveling Salesman Problem (TSP). For 56 destinations, the results of total distance, processing time, and the deviation between exact and approximate method will be compared where the distance between two destinations is a Euclidean distance and this study shows that the distance of B&B is 270 , EFOA is 270 and A3 is 288.38 which deviates 6.81%. For time processing aspect, B&B needs 12.5 days to process, EFOA needs 36.59 seconds, A3 needs 35.34 seconds. But for 29 destinations, exact method is more powerful than approximate method.

Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.

Bio-Inspired Metaheuristics

In real life, problems becoming more complicated, among them NP-Hard problems. To resolve them, two families of methods exist, exact and approximate methods. When exact methods provide the optimal solution in an unacceptable amount of time, the approximate ones provide good solutions in a reasonable amount of time. Approximate methods are two kinds, heuristics and metaheuristics. The first ones are problem specific, while metaheuristics are independent from problems. A broad number of metaheuristics are inspired from nature, specially from biology. These bio-inspired metaheuristics are easy to implement and provide interesting results. This paper aims to provide a comprehensive survey of bio-inspired metaheuristics, their classification, principals, algorithms, their application domains, and a comparison between them.

Improvement of Operational Performance through Value Stream Mapping and Yamazumi Chart: A case of Bangladeshi RMG Industry

To secure a competitive position in the global market, the Ready Made Garment (RMG) sector in Bangladesh has been facing various challenges including the improvement of industrial operational performance. Among the various operational issues, balancing the cycle time along the production line is felt to be a common and effective way for enhanced performance. There are numerous exact and approximate methods which have already been proposed and are available in literature for repetitive batch production. Unfortunately such approaches are rarely applied in the real RMG shop floor presumably due to the enormous efforts needed to align with the frequent changes of product lines. Compared to the exact and approximate methods, adoption of lean tools like VSM and Yamazumi chart is highly acclaimed for their simpler and wider applicability with superior capability in addressing and solving the balancing problems. So for balancing purposes of the RMG shop floor an attempt is made to frame and apply an integrated model combining the VSM and Yamazumi chart as presented in this article. Depending on the theoretical framework, operational performance of an RMG shop floor is evaluated upon balancing the cycle time. In doing so, firstly a current state map (CSM) and the corresponding Yamazumi chart are plotted to comprehend the existing operational procedure and analyse the workstation cycle time with respect to the takt time. Using the Yamazumi chart, the workstations are reorganized to reduce or eliminate the non-value added activities, to introduce parallel workstations, and to merge workstations so that a balanced production line is attained. Performance is then assessed by means of Overall Effectiveness of Equipment (OEE), Capacity Utilization and Efficiency. The results as obtained through testing a real life case study of RMG industry, ensure the effectiveness of the integrated system of VSM and Yamazumi chart to identify the wastes, restore the line balance and improve operational performance.