Dynamic setup scheduling and flow control in manufacturing systems

We propose a method for flow control of parts in a manufacturing system with machines that require setups. The setup scheduling problem is investigated in the context of a multilevel hierarchy of discrete events with distinct frequencies. The higher level of the hierarchy calculates a target trajectory in the surplus/backlog space of the part types which must be tracked at the level of setups. We consider a feedback setup scheduling policy which usescorridors in the surplus/backlog space of the part types to determine the timing of the set-up changes in order to guide the trajectory in the desired direction. An interesting case in which the trajectory leads to a target point (e.g., a hedging point) is investigated in detail. It is shown that in this case the surplus/backlog trajectory at the setup level can lead to a limit cycle. Conditions for linear corridors which result in a stable limit cycle are determined.     

Hierarchical production and setup scheduling in stochasticmanufacturing systems

This paper is concerned with an asymptotic analysis of hierarchical production and setup scheduling in a stochastic manufacturing system consisting of a single failure-prone machine and facing constant demands for a number of products. At any given time the system can only produce one type of product, and the system requires a setup if production is to be switched from one type of product to another. A setup may involve setup time or setup cost or both. The objective of the problem is to minimize the total costs of setup, production, and surplus. The control variables are a sequence of setups and a production plan. An asymptotic analysis with respect to increasing rates of change in machine states gives rise to a deterministic limiting optimal control problem in which there is a control variable associated with each of the machine states and the production rate is obtained by weighting these controls with the stationary probabilities of the corresponding states. Asymptotic optimal controls for the original problem from optimal or near-optimal controls for the limiting problem are constructed     

A new scheduling method for manufacturing systems

In this paper, we present a new method for scheduling jobs with due dates on sequential and parallel machines. The jobs have different levels of importance (weights) and various processing times, and some of the jobs must follow certain sequences on the machines. The objective is to minimize the total weighted tardiness of the schedule. The new approach is based on Lagrange relaxation and it is a near-optimal approach. For the problem tested, the result is within 1% of the optima with reasonable CPU time. Furthermore, the method provides job interaction information which can be used to reconfigure the schedule to accommodate dynamic changes, and also to schedule new jobs. These capabilities have enormous value for researchers and practitioners alike, and would result in considerable direct and indirect savings.     

A constraint programming approach to tool allocation and production scheduling in flexible manufacturing systems

This paper presents a constraint programming (CP) methodology to deal with the scheduling of flexible manufacturing systems (FMSs). The proposed approach, which consists of both a model and a search strategy, handles several features found in industrial environments, such as limitations on number of tools in the system, lifetime of tools, as well as tool magazine capacity of machines. In addition, it tackles the problem in a integrated way by considering tool planning and allocation, machine assignment, part routing, and task timing decisions altogether in the approach. The formulation, which is able to take into account a variety of objective functions, has been successfully applied to the solution of test problems of various sizes and degrees of difficulty.     

The robustness of scheduling policies in multi-product manufacturing systems with sequence-dependent setup times and finite buffers

In this paper, a continuous time Markov chain model is introduced to study multi-product manufacturing systems with sequence-dependent setup times and finite buffers under seven scheduling policies, i.e., cyclic, shortest queue, shortest processing time, shortest overall time (including setup time and processing times), longest queue, longest processing time, and longest overall time. In manufacturing environments, optimal solution may not be applicable due to uncertainty and variation in system parameters. Therefore, in this paper, in addition to comparing the system throughput under different policies, we introduce the notion of robustness of scheduling policies. Specifically, a policy that can deliver good and stable performance resilient to variations in system parameters (such as buffer sizes, processing rates, and setup times) is viewed as a “robust” policy. Numerical studies indicate that the cyclic and longest queue policies exhibit robustness in subject to parameter changes. This could provide production engineers a guideline in operation management.     

A survey of dynamic scheduling in manufacturing systems

In most real-world environments, scheduling is an ongoing reactive process where the presence of a variety of unexpected disruptions is usually inevitable, and continually forces reconsideration and revision of pre-established schedules. Many of the approaches developed to solve the problem of static scheduling are often impractical in real-world environments, and the near-optimal schedules with respect to the estimated data may become obsolete when they are released to the shop floor. This paper outlines the limitations of the static approaches to scheduling in the presence of real-time information and presents a number of issues that have come up in recent years on dynamic scheduling. The paper defines the problem of dynamic scheduling and provides a review of the state-of-the-art of currently developing research on dynamic scheduling. The principles of several dynamic scheduling techniques, namely, heuristics, meta-heuristics, multi-agent systems, and other artificial intelligence techniques are described in detail, followed by a discussion and comparison of their potential.     

An optimal control method for aggregate production planning in large-scale manufacturing systems with capacity expansion and deterioration

An optimal control approach to continuous-time aggregate production planning problems is presented. The proposed approach describes the production and capacity evolution (expansion, sell and deterioration) processes in the form of differential equations with regular production, subcontracting and capacity change rates controllable on one hierarchical level. In this way, the traditional disadvantages of the two-level problem consideration (one level for strategic capacity planning and the other for production smoothing) are avoided. Analytical properties for optimal production and capacity control regimes and conditions for their changeover are derived by the maximum principle. Based on these results, an insight into the optimal behaviour of the production system is gained and a fast numerical method is developed to identify and sequence the optimal regimes for arbitrary demand profiles. A computational example illustrates the effectiveness of the approach.     

Using scheduling in flexible manufacturing systems

In this paper the concept of recursive Allen temporal algebra is fully described, along with its relationship to the smart scheduler program and the concept of smart scheduling in general. Flexible manufacturing systems (FMS) are described, and their relationship with smart scheduling is explored. A case study that shows the utility of SSP in an FMS environment is presented in detail. Conclusions about the concept of smart scheduling are presented in closing.     

One-machine n-part-type optimal setup scheduling: analyticalcharacterization of switching surfaces

The authors consider optimal setup scheduling of a single reliable machine. Production flow of n different part types and the setup process are described by differential equations. Setup change rates are control variables. Necessary conditions on optimal setup changes are characterized analytically, and optimal setup change times are derived for a given setup change sequence. The linearization of optimal setup switching surfaces is derived, indicating the existence of attractors observed in numerical optimal solutions. The approach developed in this paper establishes a strong basis for studying multimachine production systems and for constructing tractable near-optimal numerical solution techniques     

A numerical method to find optimal submeasures

Algorithms are developed that find the optimum of a functional dependent on probability measures subject to special constraints.Translated from Kibernetika, No. 2, pp. 70–77, March–April, 1990.     

A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

Stable scheduling policies for flexible manufacturing systems

In this brief note we provide a new analysis of the transient behavior of the clear-a-fraction policy of Perkins and Kumar (1989). In addition, we show that a new “clear-average-oldest-buffer” policy and a “random part selection” policy (of which “first-come-first-served” is a special case) are stable. Finally, we introduce a stable and efficient “stream modifier” that can be used to obtain network level stability results     

Real-time feedback scheduling of flexible manufacturing systems

A genetic manufacturing environment is considered. The emphasis is on small-lot, discrete, and asynchronous type of manufacturing systems rather than high volume and continuous type. Two classes of scheduling policies are proposed to render the machine stable. The policies are of feedback type. The decision is made in real-time and on-line.     

On optimal lateness and tardiness scheduling in real-time systems

We address lateness and tardiness scheduling policies for real-time systems. It is well-known that preemptive Earliest Deadline First (EDF) minimizes the worst lateness and tardiness of a finite set of tasks with known arrival times, service times and deadlines to the finishing time, on a uniprocessor. We extend this result significantly, to include an arbitrary (possibly infinite) number of tasks with arbitrary arrival and service times, and deadlines, and to show thatEDF

1. minimizes the lateness and tardiness of the tasks that are in the system at an arbitrary time.
2. minimizes lateness within a busy interval, for an arbitrary, possibly infinite number of tasks.
3. maximizes the time to the first missed deadline, and
4. minimizes the length of time during which there is at least one missed deadline in the system.

We also show that a combination ofEDF and Shortest Remaining Processing Time First (SRPTF) policy minimizes maximum latenesses in a vector sense (as defined tin the paper) and minimizes the number of tasks that miss their deadline at the time the first missed deadline occurs. For non-preemptive non-idling polices, we establish new, similar results in a stochastic sense. We attempt extending our findings to multiprocessor systems. We demonstrate that under the assumptions of arbitrary distributions of arrival times, service times and deadlines, our results no longer hold true. When a further assumption of unit-length service times and integer-valued arrival times is introduced, we are able to re-establish the results in the multiprocessor case.     

A note on optimal policies for two group scheduling problems with deteriorating setup and processing times

Conventionally, job processing times are known and fixed. However, there are many situations where the job processing time deteriorates as time passes. In this note, we consider the makespan problems under the group technology with deteriorating setup and processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. For both linear functions, we show that the makespan problems remain polynomially solvable. In addition, the constructive algorithms are also provided.     

The equivalence between infinite-horizon optimal control ofstochastic systems with exponential-of-integral performance index andstochastic differential games

A new method, based on the theory of large deviations from the invariant measure, is introduced for the analysis of stochastic systems with an infinite-horizon exponential-of-integral performance index. It is shown that the infinite-horizon optimal exponential-of-integral stochastic control problem is equivalent to a stationary stochastic differential game for an auxiliary system. As an application of the developed technique, the infinite-horizon risk-sensitive LQG problem is analyzed for both the completely observed and partially observed case