Modelling and control of discrete event manufacturing flow lines
van Jawm Joost Eekelen · TU/e Research Portal · 2008
Over the last decades complexity of products and production processes has increased tremendously, moving towards high-tech production systems: manufacturing expensive products with even more expensive resources. Failures or mistakes have therefore become expensive too and need to be avoided to ful??ll the manufacturers' targets: generating products while maximizing the pro??t. In general, this is to be achieved by keeping vast control over the manufacturing processes, resources, stocks and labour. Easier said than done, since controlling all phenomena that occur in a manufacturing system is very expensive, if possible at all. Therefore, speci??c parts of a manufacturing facility are modelled to reduce its complexity. With the models, predictions of future behavior of the system can be made. Moreover, different control strategies can be tested of??ine at low risks, before implementing them on the real production system. In this dissertation, manufacturing ??ow lines are modelled using several modelling paradigms. These are divided into three groups: discrete event models, continuous models and hybrid models. The presented modelling methods are used throughout the remainder of the thesis and therefore the survey is by no means an attempt to give a complete overview of the whole area of modelling manufacturing systems. A state space representation of a manufacturing workstation is introduced, which is ??nite dimensional, can be measured instantaneously and does not contain any information about production or control policy. This state space representation is used in the coupling of different model paradigms, facilitating the use of analysis techniques in both time domain and event domain. In addition, the introduced state space representation is used in the development of a continuous time receding horizon state feedback controller. For a ??ow line of multiple workstations, each with its own buffer capacity and process time, and for an event based control horizon, an optimal production schedule controller is developed. This state feedback controller provides optimal schedules, even when unexpected disturbances occur. Switching servers are found in a wide variety, like in manufacturing industries, traf??c networks and call-centers. Switching servers process multiple types of jobs, with a switchover time involved. A hybrid ??uid model is used to describe the dynamics of switching servers. Continuous dynamics is used to describe the evolution of buffer levels. The discrete event part of the model describes the switches between the product types. For a workstation processing two product types that arrive at constant rates, optimal switching policies with respect to minimal time averaged weighted work in process levels are de??ned for situations with and without maximum buffer level capacities. An important insight is the possible appearance of a slow-mode in optimal process cycles. During a slow-mode, a buffer is empty and products are served at their arrival rate, instead of switching to the other product type. The slow-mode represents a tradeoff between losing capacity due to serving products at a lower rate than the maximum rate and losing capacity due to relatively often switching in time. Conditions on the appearance of a slow-mode in optimal process cycles are derived explicitly. In a manufacturing network, arrivals of products at a workstation are in general not at a constant rate. For a switching server processing two product types and with piecewise constant periodic arrival rates (on/off), optimal system behavior with respect to work in process levels is de??ned. The total optimization problem then splits into several subproblems, which need to be solved separately. The optimal mean work in process level for a single switching server is also a lower bound on the mean work in process level that can be realized for a switching server ??ow line in which that server resides. For a ??ow line consisting of two switching servers, each processing two product types, it is investigated under which conditions this lower bound can actually be achieved. An important conclusion is that, in certain cases, workstations in a ??ow line need a synchronization mechanism to get to the desired process cycles. For the single switching server and the switching server ??ow lines with constant arrival rates of products, state feedback controllers are proposed to steer the trajectory of the switching server (??ow line) to the determined optimal process cycle from arbitrary feasible starting point. Contrary to many methods proposed in literature, in this research ??rst the desired (optimal) system behavior is de??ned, regardless of any control policy. Then a control policy is formulated to achieve this desired behavior. It is questionable whether optimal system behavior should be looked for. The studies in this thesis show that optimal process cycles can be determined for a rather small class of workstations. Taking more than two product types into account or more than two workstations leads to very complex optimization problems. Apart from the complexity, it is not even known whether optimal cyclic behavior for these larger systems exists. Manufacturers might not be interested in the theoretically optimal solution. Often, a better solution than the current solution will do. Moreover, a manufacturer might prefer suboptimal solutions over optimal solutions when the suboptimal solution handles disturbances or uncertainties better. This dissertation can serve as a starting point for further research on modelling and control of manufacturing networks. The introduced state space representation topic can be extended for larger networks and other manufacturing resources. In addition, other research areas can be linked to this research, including stochastic behavior and effective process times.