Declarative Approach to Cyclic Scheduling of Multimodal Processes

Some complexity results in cyclic scheduling

The cyclic scheduling problem modeled in terms of Cyclic Concurrent Process Systems is considered. The problem can be seen as a kind of Diophantine problem, hence its solvability, i.e. schedulability, plays a pivotal role in many supply-chain problems. In contradiction to the traditionally offered solutions the approach proposed allows one to take into account such behavioral features as transient periods and deadlocks occurrence. So, the contribution’s aim is the modeling framework enabling an evaluation of cyclic scheduling problems solvability, i.e., the declarative approach to reachability problems regarding cyclic steady states determination as well as conditions guaranteeing assumed performance of multimodal processes executed within a concurrent cyclic processes environment.

A multi-job cyclic scheduling problem for an automated job-shop-type manufacturing system was analyzed. In the cyclic scheduling problem, an optimum schedule is a non-idle schedule, where a bottleneck machine produces jobs without idle time in the steady state. A dividing method of the jobs was introduced and the job output interval in the steady state was clarified. A lower bound on the buffer capacity was obtained to construct a non-idle schedule.

Converging to periodic schedules for cyclic scheduling problems with resources and deadlines

In this paper, we address some issues on the interface of buffer design and cyclic scheduling decisions in a multi-product deterministic flow line. We demonstrate the importance of the above interface for the throughput performance of the flow line. In particular, we point out that the use of sequence-independent information, such as workload distribution and variability in processing times among stations, is not adequate to decide the optimal buffer configuration of the flow line. We formulate the buffer design problem for a fixed sequence of jobs as a general resource allocation problem, and suggest two effective heuristics for its solution. For the simultaneous buffer design and cyclic scheduling problem, we suggest an iterative scheme that builds on the effectiveness of the above heuristics. One of the side results of our extensive computational studies on this problem is that the general guidelines of buffer design in single-product flow lines with stochastic processing times are not directly transferable to the multiproduct deterministic flow line environment.

In this paper, we study the scheduling problem with resource constraints using the Petri nets based on the transitive matrix P-invariant. This work focuses on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of work-in-process. Especially, this paper deals with product FMS cyclic scheduling problem with each other products using the transitive matrix. The time Petri net slice is applied to analyze this FMS model. We can divide the original system into subsystems using the transitive matrix and permutate these sub-nets for analyzing the optimal scheduling.

A natural starting strategy for Aronson's heuristic 1 for solving the deterministic, single operator, multiple machine, multiple run cyclic scheduling

Optimal sizing of user-side energy storage considering demand management and scheduling cycle

This paper concerns the problem of cyclic job shop scheduling problem with linear constraints. The main characteristic of this problem is that the tasks of each job are generic, that is, they have an infinite number of occurrences; moreover, these tasks are constrained by linear precedence constraints. The general approach to solving this scheduling problem, is based on the coupling of a genetic algorithm and a scheduler. The scheduler uses a Petri net to construct a feasible solution step by step, respecting the linear constraints between the tasks. The genetic algorithm aims at proposing heuristics for solving the resource conflicts that occur during the simulation process achieved by the scheduler. Finally, a benchmark and some preliminary results of this approach are presented.

The problem of lot sizing and scheduling of production runs for multiple products to be processed on a machine was studied. The problem is formulated as a dynamic system, for which we show that cyclical schedules with the clearing lot sizing rule leads the system to a steady state. In the steady state we obtained a closed-form formula for the cycle time, the lot size and the maximum inventory level for each product. Finally, we showed that the clearing lot sizing rule is the optimal linear lot sizing rule that minimizes the system's inventory levels in the steady state.

Cyclic Scheduling Problems with Linear Precedences and Resource Constraints

How to Fit Response to Intervention Into a Heavy Workload

Deadline constrained cyclic scheduling on pipelined dedicated processors considering multiprocessor tasks and changeover times

This paper studies flowshop cyclic scheduling and schedule execution in the presence of random machine failures that may delay execution of tasks and thus may cause the actual production to deviate from a specified schedule. Practitioners are now interested in robust schedules that would remain efficient if unexpected disturbances occur. The slack-based technique for robustness increasing is presented. These slacks introduce some insensibility to online perturbations in the schedule designed offline so that schedule robustness is maximized. An analytical model for robustness evaluation of the single machine flowshop cyclic scheduling problem is proposed. This problem is formulated into a convex program for which the objective is to maximize the probability of scheduling solutions' robustness.

The complexity of scheduling jobs in repetitive manufacturing systems