Logistic Modelling Of Order Realization In The Complex Parallel Manufacturing System

The paper highlights the problem of mathematical modeling of the highly complex manufacturing system in which work stations are arranged serially within each production plant. Production plants are located in a parallel way. The specification details and the model resulting from them led to creating the simulator to be employed to solve the problem of realizing customers’ orders. Equations of state are given to illustrate the state of the system at each stage. The complex system is controlled by implementing heuristic algorithms. The criteria to be met are defined. The study case is based on randomly generated data and solved by means of the dedicated information tool. The search for the satisfactory solution is carried out either by an increased number of simulation runs or comparing the pairs or combinations of order and plant choosing algorithms. The main goal remains to meet the stated criterion. INTRODUCTION The growth of markets towards globalization results in materialization of automated industries with high performance of manufacturing systems. Traditional manufacturing systems are no longer able to satisfy these requirements. In the global market there is an increasing trend toward achieving a higher level of integration between designed and manufacturing functions in industries to make the operations more efficient and productive (Modrak and Pandian 2012). Effective organization and management of materials, processes and human resources of a company is a prerequisite in today’s highly competitive industrial landscape. Key goals are to improve planning and scheduling of processes, increase productivity, minimize inventory level, improve responsiveness to changes in demand, improve quality, and lower operation cost. These problems are solvable with the use of modelling and simulation of such production systems. One of the most useful tools in the arsenal of an operations research (industrial engineering) management science analyst consists in computer simulation. In this case it is necessary to put attention to the benefits resulting from combining both spheres, the one of formalized algorithms and the other one of the human instinct (Neumann 2011). The use of simulation, as a support tool to the operational decision making process, allows us to analyze, from a statistical point of view, the behavior of a production or logistic system that is subject generally to either controllable and or not controllable factors. Through computer simulation it is possible to select those operational decisions that maximize an objective function or a system performance parameter, and to evaluate effects of these decisions without controllable factors variability. An approach to implement efficiently and effectively simulation models in manufacturing systems is deployed in (Chramcov et al. 2011). Currently, a wide range of commercial products which use graphic interfaces (e.g. Arena, Witness, MapleSim 4, AutoMod, Quest, PlantSimulation, etc.) offer an extremely wide spectrum of possibilities for modelling and simulation of manufacturing, logistic and other queuing systems (Rizzoli 2009). Nevertheless, the general language C# has been adopted for creation of our production system simulator because the programming logic cannot be easily expressed in GUIbased systems (Babich and Bylev 1991). The initial specification and consequent modelling of the discussed manufacturing system is described in detail in (Bucki et al. 2012a). This paper is later expanded to the simulation form enabling us to carry out a simple simulation process (Bucki et al. 2012b). The simulation process shows that one of the suggested heuristics minimizes the total order realization time. However, the need to search for the solution to tasks carried out in the complex manufacturing system with buffer stores leads to extending specification details and the subsequent model which finally forms the basics for the simulation process (Bucki 2012). The simulation process is carried out by means of the simulation tool built on the basis of these specification details and the subsequent model (Marusza 2013). GENERAL SYSTEM FORMULATION Let us propose the information system imitating the continuous production process carried out in J work Proceedings 27th European Conference on Modelling and Simulation ©ECMS Webjorn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Editors) ISBN: 978-0-9564944-6-7 / ISBN: 978-0-9564944-7-4 (CD) stations arranged in a series. We assume that there is a machine in each work station which can perform I operations. However, we assume that only one tool can be determined to perform the operation on the order unit in each work station. We assume there are buffer stores between the work stations. The capacity of each buffer store is limited. Operations are performed in the work stations in sequence. Further, we assume there are more than one identical production systems available. Let us assume that A manufacturing plants are arranged in parallel. This system requires K stages to realize the order elements. The matrix of orders at the k-th stage is considered in the form (1), where k n m z , is the number of conventional units of the n-th order of the m-th customer at the k-th stage. The stage k, k=1,. ,K is the moment of making the production decision. [ ] k n m k z Z , = ,m=1,. ,M; n=1,. ,N; k=1,. ,K (1) The order matrix is modified after every decision about production in accordance with the specification (2). ⎪ ⎪ ⎩ ⎪⎪ ⎨ ⎧ − − = − − otherwise. stage, th at the realized is units of number the if 1 , , , 1 , , k n m k n m k n m k n m k n m z k x x z z (2) Some of the charge materials are used for manufacturing products of the specific order. The assignment matrix of ordered products to charges takes the form (3), where n m, ω is the number of charge material assigned to the order n m z , [ ] n m, ω = Ω , m=1,. ,M; n=1,. ,N (3) Elements of the assignment matrix take values according to (4). ⎪ ⎩ ⎪ ⎨ ⎧ − = otherwise. 0 charge, th the from realized is order the if