Cyclic Scheduling Problems with Linear Precedences and Resource Constraints

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

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.

Some complexity results in cyclic scheduling

In this chapter, we deal with the cyclic scheduling problem usually observed in the FMS producing multi-type parts where the AGVS plays a role of a material handling system. Finding the conditions guaranteeing the AGVs deadlock-free and collision-free movement policy is the aim of this work. The AGVs co-sharing the common parts of the transportation route while executing repetitive processes, can be modeled in terms of Cyclic Concurrent Process Systems (CCPSs). The chapter suggests a novel approach for schedulability analysis employing the declarative modeling. In turn, the schedulability analysis for a given CCPS answers the question whether a cyclic schedule exists or not. A reference model of constraint satisfaction cyclic scheduling problem shows that unschedulability can be caused by a relation among an initial state and dispatching rules selected. The sufficient conditions guaranteeing CCPS schedulability are discussed and the recursive approach to their designing is proposed. Possible implementations are illustrated on example of the flexible manufacturing system operation.

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.

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.

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 genetic approach to solving the problem of cyclic job shop scheduling with linear constraints

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.

Multi-project Time-cost Optimization in Critical Chain with Resource Constraints

A project scheduling problem investigates a set of activities that have to be scheduled due to precedence priority and resource constraints in order to optimize project-related objective functions. This paper focuses on the multi-mode project scheduling problem concerning resource constraints (MRCPSP). Resource allocation and leveling, renewable and non-renewable resources, and time-cost trade-off are some essential characteristics which are considered in the proposed multi-objective scheduling problem. In this paper, a novel hybrid algorithm is proposed based on non-dominated sorting ant colony optimization and genetic algorithm (NSACO-GA). It uses the genetic algorithm as a local search strategy in order to improve the efficiency of the ant colony algorithm. The test problems are generated based on the project scheduling problem library (PSPLIB) to compare the efficiency of the proposed algorithm with the non-dominated sorting genetic algorithm (NSGA-II). The numerical result verifies the efficiency of the proposed hybrid algorithm in comparison to the NSGA-II algorithm.

In this paper, we propose a decentralized scheduling method for flowshop scheduling problems with resource constraints using the Lagrangian decomposition and coordination approach. When a flowshop scheduling problem with resource constraints is decomposed into machine-level sub-problems, the decomposed problem becomes very difficult to be solved to obtain the optimal solution even when the production sequence of operations is given. In this study, the decomposed sub-problems are solved by a simulated annealing algorithm combined with dynamic programming. By decomposing the problem into single machine sub-problems, the changeover cost can easily be incorporated in the objective function. In order to reduce the computation time, a heuristic algorithm for calculating the starting times of operations is also proposed. The performance of the proposed method is compared with that of the simulated annealing method in which a schedule of the entire machine is successively improved. Numerical results have shown that the proposed method can generate better solutions than those generated by the conventional method.

This paper uses timed Petri net to model and analyze the problem of instruction-level loop scheduling with resource constraints, which has been proven to be an NP complete problem. First, we present a new timed Petri net model to integrate functional unit allocation, register allocation and spilling into a unified theoretical framework. Then we develop a state subgraph, called Register Allocation Solution Graph, which can effectively describe the major behavior of our new model. The main property of this state subgraph is that the number of all its nodes is polynomial. finally we present and prove that the optimum loop schedules can be found with polynomial computation complexity, for almost all practical loop programs. Our work lightens a new idea of finding the optimum loop schedules.

A multiphase dynamic programming algorithm for the shortest path problem with resource constraints

In high-level synthesis, loop pipelining is a technique to improve the throughput and utilisation of hardware datapaths by starting new loop iterations after a fixed amount of time, called the initiation interval (II), allowing to overlap subsequent iterations. The problem is to find the smallest II and corresponding operation schedule that fulfils all data dependencies and resource constraints, both of which are usually found by modulo scheduling.We propose Moovac1, a novel integer linear program (ILP) formulation of the modulo scheduling problem based on overlap variables to model exact resource constraints. Given enough time, Moovac will find a mimimum-II solution. This is in contrast to Canis' state-of-the-art Modulo SDC approach, which requires heuristic simplifications of the resource constraints. Moovac can thus be used as a reference to evaluate heuristics, or in a time-limited mode as a heuristic itself to provide a best-so-far solution.We schedule kernels from the CHStone and MachSuite benchmarks for loop pipelining with Moovac, Modulo SDC and a prior exact formulation by Eichenberger.Moovac has competitive performance in its time-limited mode, and delivers better results faster than the Modulo SDC scheduler for some loops. Often its structure leads to quicker solution times than Eichenberger's formulation.Using the Moovac-computed optimal solutions as a reference, we can confirm that the Modulo SDC heuristic is indeed capable of finding optimal or near-optimal solutions for the majority of small- to medium-sized loops. However, for larger loops the two algorithms begin to diverge, with Moovac often being significantly faster to prove the infeasibility of a candidate II. This can be exploited by running both schedulers synergistically, leading to a quicker convergence to the final II.