Single Processing Machine Research Articles

COMMIT TIME DECISION FOR MEASURING DEMAND SIDE QUALITY COSTS WITH LIMITED DISTRIBUTION INFORMATION

Consider a single machine processing multiproducts situation when only the mean and standard deviation of processing time for each product are available. The bounds of optimal commit delivery time range are obtained. A decision of the robust commit delivery time is suggested. An extension to the situation with information of orders in queue is also discussed. Numerical examples show that the suggested decision performs well. The expected value of additional information, which measures the maximum amount a decision maker is willing to pay for knowledge of true distribution information, is small, and that further demonstrates the worthiness of the suggested robust decision.

Robust commit time decisions and bounds for measuring demand-side quality costs

In this paper, we discuss a single machine processing multi-product situation. The upper and lower bounds of demand-side costs and optimal commit delivery time range with only the mean and standard deviation of the processing time distribution are obtained. We propose two robust commit delivery times, one using the mid-point of the optimal solution range and the other using the min-max regret criterion. The expected value of distribution information, which measures the maximum amount a decision-maker is willing to pay for the true knowledge of the distribution, is used to evaluate the performance of the delivery times. An extension to the situation where information of orders in a queue is available is also discussed. Numerical examples show that both decision rules are promising, and they have potential for practical applications.

Suitable switching policies for FMS scheduling

Switching server, otherwise known as hybrid dynamical approaches can be used highly effectively to solve flexible manufacturing systems scheduling problems. Papers published in this field have accepted that the demand rates determining the production tasks have some given values. In the present paper it is shown that the demand rates should be selected from some given domains. The “control variables” to realize suitable processes are the switching policies, and the demand rates. These uniquely determine the processes through the switching time sequences. In the present paper, two variants: the single machine processing, and the multiple machine processing cases are analyzed. It is very problematic to use continuously coupled parts flows for stable and effective production. To eliminate this difficulty, in the present paper, the method called controlled buffer technique is proposed, which uses the opportunity that the computer controlled “virtual buffers” can be filled up before the regular working time, and used for part flow compensation.

Discrete Model for Hybrid Dynamical Approach to FMS Scheduling

Introduction to the use of hybrid dynamical approach to FMS scheduling is given. New results in formatting the demand rate requirements in the field of discrete models of switching laws are outlined. It is relatively simple task to determine the suitable processes at single machine processing. It is rather complicated to handle the multiple machine job shop type manufacturing case. In the paper a new way: the use of controlled buffer technique is proposed to solve this problem.

Optimal control laws for lot-sizing and timing of jobs on a single production facility

The optimal control of a single machine processing a certain number of jobs and modeled as a discrete-event dynamic system is considered. The number of jobs and their sequence are fixed, whereas their timing and sizes represent the control variables of the system. The objective function to be optimized is a weighted sum of the quadratic earliness and tardiness of each job, and of the quadratic deviations of job lot sizes and actual machine service speeds from those specified by the production demand and by the regular machine speeds. An optimization problem with quadratic cost function and nonlinear constraints is stated and formalized as a multistage optimal control problem. Necessary conditions to be satisfied by an optimal control sequence are derived. A simpler model is also considered in which the machine speeds are fixed; in this case, the control problem is solved by a procedure making use of dynamic programming techniques. The optimal control laws at each stage are thus obtained.

Nonlinear dynamics in distributed arrival time control of heterarchical manufacturing systems

Heterarchical control architectures with fully distributed control have been developed in order to improve responsiveness and effectiveness of manufacturing shop-floor control systems. The dynamics of these highly distributed systems have been difficult to predict particularly when control is based on heuristics. In this paper a dynamical model is developed for a single machine processing an arbitrary number of parts. The structure of the system, which requires queuing of parts when they arrive at a machine, leads to nonlinearities such as dead-zone and discontinuities. A continuous arrival time controller of the integrating type is used that results in a system that can be modeled using nonlinear differential equations that can be solved using a method due to Filippov (1960, 1988). This enables prediction of trajectories of part arrival times and derivation of closed form expressions for steady-state values. The analytical model for the dynamics is validated and the dynamic response of the system is illustrated using numerical simulation.

Analysis of a class of real-time multiproduct lot scheduling policies

A single machine processing different types of parts is considered. Switching from one type to another involves a setup time. The part types may have different processing times. The resulting scheduling problem is treated as a dynamical system for which several feedback policies that are implementable in real time and that stabilize the system are discussed. The main results are a characterization of the dynamics induced by clear-the-largest-work policies and the derivation of bounds on the total work-in-process which are better than those available in the literature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>