scholarly journals Eigen Problem Over Max-Plus Algebra on Determination of the T3 Brand Shuttlecock Production Schedule

Author(s):  
Andra Permana ◽  
Siswanto Siswanto ◽  
Pangadi Pangadi

The production process is included in the Discrete Event System (DES). The DES independent variable generally depends on the event, so an event is influenced by the previous event. Max-plus algebra can be applied in the DES problem to change the system of nonlinear equations obtained into linear equations. Max-plus algebra is a set of real numbers  combined with  equipped with operations max  and plus ⊗ or can be denoted  with . An effective and efficient production process needs to pay attention scheduling steps well. The purpose of this research is to determine the Shuttlecock T3 production schedule using eigenvalue and eigenvector in max-plus algebra. The research method in this research is study of literature and observation. Literature study is carried out by studying references about max-plus algebra, especially material related to scheduling problems, while observation are carried out in the process of taking data of the Shuttlecock T3 production process in Surakarta. The linear equation system that is formed based on the results of the observation is then presented in the form  and . The periodic time and initial system production time are determined from the eigenvalue and eigenvector matrix  where . The results of the research showed that the production system run periodically every 249 minutes, then the best time for each processing unit to start working can be determined, as well as the Shuttlecock T3 production schedule according to the working hours more effective and efficient can be determined too.

2010 ◽  
Vol 25 (3) ◽  
pp. 319-336 ◽  
Author(s):  
Gérard Verfaillie ◽  
Cédric Pralet ◽  
Michel Lemaître

AbstractThe CNT framework (Constraint Network on Timelines) has been designed to model discrete event dynamic systems and the properties one knows, one wants to verify, or one wants to enforce on them. In this article, after a reminder about the CNT framework, we show its modeling power and its ability to support various modeling styles, coming from the planning, scheduling, and constraint programming communities. We do that by producing and comparing various models of two mission management problems in the aerospace domain: management of a team of unmanned air vehicles and of an Earth observing satellite.


2018 ◽  
Vol 20 (1) ◽  
pp. 40-47
Author(s):  
Abdul Rahim Matondang ◽  
Widodo Widodo

Production system take an important role in industries, especially in manufacturing industries. This role determine the keys of successful company. Production process is an activity which produce finished product from raw material that involve machine, energy, and technique knowledge. Production process is real activity and can be seen by human being. The problems those always be faced in indutries management’s are the arrangement of production schedule, such lack of inventory or overstock once the settlement of production process isn’t on time. Production planning and control is activity to determine what product that will be produced, how many product that will be produced and how many labors needed in production processes. By using production planning and control’s method, those problems can be minimalized. Aggregate planning is one of production planning a.nd control’s method. By using this method, production planning could be done by using unit of replacement product so that the output of this planning isn’t declared in individual product. So, the output of aggregate planning isn’t planning in form of individual product but aggregate’s product. There are some strategies on aggregate planning such as pure strategy on aggregate planning and mixed strategy on aggregate planning. In this research, method of aggregate planning that used is optimization approach by linier rule. This method used to make long term planning and middle term planning. Long term planning consists of product forecasting and aggregate planning. The middle term planning consist of master production schedule and rough cut capacity planning. The result of this research is capacity needed and capacity available to determine which work center is drum and which isn’t. Conclusion of this research that capacity of each work center in perioad january to december 2018 is non drum. This indicate the good scheduling in capacity planning.


Author(s):  
Dimitri Lefebvre

Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.


2009 ◽  
Vol 3 (4) ◽  
pp. 191-201 ◽  
Author(s):  
P Solding ◽  
P Thollander ◽  
P R Moore

Author(s):  
John G. Michopoulos ◽  
Samuel G. Lambrakos ◽  
Athanasios Iliopoulos

The initial progress towards the design and development of a framework for automating the process of integrating experimental data with stakeholder specifications describing usability requirements, along with multiscale models for tailoring material and structural behavior characteristics is reported in the present paper. The proposed framework consists of a layered architecture that is comprised of three main layers. The first layer involves the computational infrastructure that implements the low level computational container that encompasses the computational codes that enable the modeling of the forward problem for various physical problems at specific time and length scales. The second layer of the framework implements the cascaded and hierarchical implementation of the inverse problem in terms of a composition of discrete event system and differential equation system specifications. The third element of the proposed architecture utilizes Category theory abstractions and their computational implementations to provide the necessary infrastructure for automating the process of developing synthetic specifications driven from experimental data and performance requirements related to the design and use of material and structural systems.


2013 ◽  
Vol 572 ◽  
pp. 235-238
Author(s):  
Soumia Ichoua ◽  
Agnes Pechmann

In this paper we investigate the elaboration of an efficient production schedule for sustainable manufacturing systems. Because renewable energies are irregular by nature as they often depend on meteorological conditions (e.g. wind and solar energy), their use in the competitive field of manufacturing production must be addressed with caution. The challenge is to elaborate a reliable production schedule that accommodates energy stochastic fluctuations while satisfying customer and operational constraints. We propose to solve the problem using a meta-heuristic based on Tabu search and discuss major elements that are critical to the success of this approach.


2014 ◽  
Vol 57 ◽  
pp. 487-496 ◽  
Author(s):  
M. Joly ◽  
Y. Antonetti ◽  
M. Python ◽  
M.A. Gonzalez Lazo ◽  
T. Gascou ◽  
...  

2008 ◽  
Vol 07 (02) ◽  
pp. 249-252 ◽  
Author(s):  
HELAN LIANG ◽  
SUJIAN LI

Focusing on the limitations of the traditional Continuous Casting-Direct Hot Charge Rolling (CC-DHCR) planning and scheduling methods that rarely consider dynamic scheduling problems, a new method is put forward. The key idea is to make out clusters and integrated plans in the planning layer, and then to adjust the rolling sequences according to the slab cluster-based strategy in the dynamic scheduling layer. Results of the test with data from practical production process show that the method can effectively solve the CC-DHCR planning and scheduling problem and increase the DHCR ratio.


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