Batch Scheduling Research Articles

Minimizing the weighted number of tardy jobs on multiple machines: A review

We provide an overview of the history, the methods and the people who researched on minimizing the (weighted) number of tardy jobs as a performance measure. The review presents cases on multiple machines: parallel machines (including the identical, uniform and unrelated machines, flow shop, job shop and the open shop). The literature is divided into various sections for proper categorization. This includes setup time, preemption, batching, on-line and off-line scheduling, and other classifications. The complexity status of the various classifications is enumerated with its results and methods. Possible extension for future work is also highlighted.

Preference-Based Economic Scheduling in Grid Virtual Organizations

A preference-based approach is proposed for Grid computing with regard to preferences given by various groups of virtual organization (VO) stakeholders (such as users, resource owners and administrators) to improve overall quality of service and resource load efficiency. Computational resources being competed for by local jobs (initiated by owners) and global (users’) job flow complicate the problem of a required service quality level substantially. A specific cyclic job batch scheduling scheme is examined in the present work which enables to distribute and share resources considering all the VO stakeholders’ preferences and find a balance between VO global preferences and those of its users. Two different general utility functions are introduced to represent users’ preferences satisfaction.

An optimised genetic algorithm for energy aware grid computing with limited iterations

Grid computing is one of the emerging computing platforms that handles both parallel and distributed computing. This type of the grid environment appends the complicated nature to the scheduler. Genetic algorithm (GA) is a generally used approach by researchers to figure out this type of NP-complete problems. Yet, the conventional GA is also sluggish to figure out the scheduling issues in the realistic environment due to its time consuming iterations. In this composition, we adopt the independent batch scheduling by considering the objective as energy expenditure as the scheduling criteria. Here, we proposed an optimised energy aware genetic algorithm (OGA), which is suitable for grid scheduling, and it can improve the search performance by limited iterations and increase the computing capability of finding the reasonable solution.

A multi due date batch scheduling model on dynamic flow shop to minimize total production cost

A multi due date batch scheduling model on dynamic flow shop to minimize total production cost

A Batch Scheduling Problem with Two Agents

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.

Scheduling multicore workload on shared multipurpose clusters

With the advent of workloads containing explicit requests for multiple cores in a single grid job, grid sites faced a new set of challenges in workload scheduling. The most common batch schedulers deployed at HEP computing sites do a poor job at multicore scheduling when using only the native capabilities of those schedulers. This paper describes how efficient multicore scheduling was achieved at the sites the authors represent, by implementing dynamically-sized multicore partitions via a minimalistic addition to the Torque/Maui batch system already in use at those sites.The paper further includes example results from use of the system in production, as well as measurements on the dependence of performance (especially the ramp-up in throughput for multicore jobs) on node size and job size.

Capacitated Max-Batching with interval graph compatibilities

We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the weight of a clique is the maximum weight of any interval in the clique. The goal is then to find such a partition of minimum total weight. This graph problem can also be interpreted as a batch scheduling problem. Solving a long-standing open question, we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS for this case.

New results on the coordination of transportation and batching scheduling

We study a planning problem to coordinate production and transportation scheduling, where a set of jobs needs to be transported from a holding area to a single batch machine for further processing. A number of results for this combined transportation-and-scheduling environment have recently been published. They look into the complexity status of the minimization of the sum of total processing time and processing cost, and of the sum of makespan and processing cost, for a fixed number of transporters. In this paper, we add to these results in that (1) we show that the earlier complexity results are still valid when the processing cost is removed from the objective, thus reducing to more “classic” scheduling objectives; (2) we assess the complexity status of the relevant problem variants with free number of transporters; and (3) we prove that the weighted-completion-time objective leads to an intractable problem even with a single transporter, contrary to the unweighted case.

Efficient multi-product multi-BOM batch scheduling for a petrochemical blending plant with a shared pipeline network

We present an effective scheduling heuristic for realistic production planning in a petrochemical blending plant. The considered model takes into account orders spanning a multi-product portfolio with multiple bills of materials per product, that need to be scheduled on shared production facilities including a complex pipeline network. Capacity constraints, intermediate storage restrictions, due dates, and the dedication of resources to specific product families have to be respected. The primary objective of the heuristic is to minimize the total order tardiness. Secondary objectives include the minimization of pipeline cleaning operations, the minimization of lead times, and the balanced utilization of filling units.The developed algorithm is based on a dynamic prioritization-based greedy search that schedules the orders sequentially. The proposed method can schedule short to mid-term operations and evaluate different plant configurations or production policies on a tactical level. We demonstrate its performance on various real-world inspired scenarios for different scheduling strategies.Our heuristic was used during the construction phase of a new blending plant and was instrumental in the optimal design of the plant.

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016

Hot-rolling batch scheduling in round steel production with flexible maintenance planning

Hot-rolling batch scheduling in round steel production with flexible maintenance planning

The single machine serial batch scheduling problems with rejection

We consider several serial batch scheduling problems with rejection. Each job is either processed on a single serial batching machine or rejected by paying a penalty. We analyze two models with rejection. The first model is to minimize the sum of the scheduling cost of the accepted jobs and the total penalty of the rejected jobs, where the scheduling costs are the total completion time, the makespan, the maximum lateness and the weighted number of tardy jobs, respectively. For the former two problems, we propose two polynomial time algorithms to solve them. For the last two problems, we derive efficient dynamic programming algorithms. The second model is to minimize the makespan, given an upper bound on the total rejection cost, we present a fully polynomial time approximation scheme.

Static scheduling of multiple workflows with soft deadlines in non-dedicated heterogeneous environments

Typical patterns of using scientific workflows include their periodical executions using a fixed set of computational resources. Using the statistics from multiple runs, one can accurately estimate task execution and communication times to apply static scheduling algorithms. Several workflows with known estimates could be combined into a set to improve the resulting schedule. In this paper, we consider the mapping of multiple workflows to partially available heterogeneous resources. The problem is how to fill free time windows with tasks from different workflows, taking into account users’ requirements of the urgency of the results of calculations. To estimate quality of schedules for several workflows with various soft deadlines, we introduce the unified metric incorporating levels of meeting constraints and fairness of resource distribution.The main goal of the work was to develop a set of algorithms implementing different scheduling strategies for multiple workflows with soft deadlines in a non-dedicated environment, and to perform a comparative analysis of these strategies. We study how time restrictions (given by resource providers and users) influence the quality of schedules, and which scheme of grouping and ordering the tasks is the most effective for the batched scheduling of non-urgent workflows. Experiments with several types of synthetic and domain-specific sets of multiple workflows show that: (i) the use of information about time windows and deadlines leads to the significant increase of the quality of static schedules, (ii) the clustering-based scheduling scheme outperforms task-based and workflow-based schemes. This was confirmed by an evaluation of studied algorithms on a basis of the CLAVIRE workflow management platform.

Delay-differentiated scheduling in optical packet switches for cloud data centers

We consider differentiated timecritical task scheduling in a N×N input queued optical packet switch to ensure 100% throughput and meet different delay requirements among various modules of data center. Existing schemes either consider slot-by-slot scheduling with queue depth serving as the delay metric or assume that each input-output connection has the same delay bound in the batch scheduling mode. The former scheme neglects the effect of reconfiguration overhead, which may result in crippled system performance, while the latter cannot satisfy users’ differentiated Quality of Service (QoS) requirements. To make up these deficiencies, we propose a new batch scheduling scheme to meet the various portto- port delay requirements in a best-effort manner. Moreover, a speedup is considered to compensate for both the reconfiguration overhead and the unavoidable slots wastage in the switch fabric. With traffic matrix and delay constraint matrix given, this paper proposes two heuristic algorithms Stringent Delay First (SDF) and m-order SDF(m-SDF) to realize the 100% packet switching, while maximizing the delay constraints satisfaction ratio. The performance of our scheme is verified by extensive numerical simulations.

Bi-criteria sequencing of courses and formation of classes for a bottleneck classroom

In this paper, the problem of class formation and sequencing for multiple courses subject to a bottleneck classroom with an ordered bi-criteria objective is studied. The problem can be modelled as a single-machine batch scheduling problem with incompatible job families and parallel job processing in batches, where the batch size is family-dependent. For the minimisation of the number of tardy jobs, the strong NP-hardness is proven. For the performance measure of the maximum cost, we consider single criterion and bi-criteria cases. We present an O(n2logn) algorithm, n is the number of jobs, for both cases. An Integer Programming model as well as Simulated Annealing and Genetic Algorithm matheuristics to solve a fairly general case of the bi-criteria problem is presented and computationally tested.

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This paper considers the scheduling problem of minimizing earliness–tardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.

A batch scheduling model for m heterogeneous batch processor

This research addresses a batch scheduling problem for single item parts with multi due date on m heterogeneous batch processors. The objective is to minimise total actual flowtime of parts through the shop. The total actual flowtime of parts in a batch is the multiplication of the interval between batch arrival time and the due date by the number of parts in the batch. Using the actual flowtime as the objective means it is oriented to satisfy the due date as a commitment to customers, and simultaneously to minimise the length of time of the parts spending in the shop. An algorithm to solve this problem is proposed.

Level based batch scheduling strategy with idle slot reduction under DAG constraints for computational grid

Scheduling in a grid environment optimizing the given objective parameters has been proven to be NP-complete. This work proposes a Level based Batch scheduling Strategy with Idle slot Reduction (LBSIR) while considering the inter module communication within the modules of the jobs represented using Direct Acyclic Graph (DAG) with the objective of optimizing the turnaround time and response time for a computational grid. The model works in two phases, allocation phase and idle slot reduction phase. Allocation phase begins by dividing the batch into a number of partitions as per the precedence level/depth level followed by the assignment of sub-jobs/modules from the partition to the best fit node in terms of the execution time offered for all the partitions. The idle slots generated during the allocation phase in each depth level are then reduced by inserting the best fit modules into these slots in the idle slot reduction phase after allocation of modules from higher depth level. Levelized allocation ensures minimizing the average response time being very useful for user interactive applications. An experimental study of the proposed strategy has been performed by comparing it with other similar methods having common objectives for evaluating its place in the middleware.

Switch cost and packet delay tradeoff in data center networks with switch reconfiguration overhead

Cost minimization is a major concern in data center networks (DCNs). Existing DCNs generally adopt Clos network with crossbar middle switches to achieve non-blocking data switching among the servers, and the number of middle switches is proportional to the number of ports of the aggregation switches in a fixed manner. Besides, reconfiguration overhead of the switches is generally ignored, which may contradict the engineering practice. In this paper, we consider batch scheduling based packet switching in DCNs with reconfiguration overhead at each middle switch, which inevitably leads to packet delay. With existing state-of-the-art traffic matrix decomposition algorithms, we can generate a set of permutations, each of which stands for the configuration of a middle switch. By reconfiguring each middle switch to fulfill multiple configurations in parallel with others, we reveal that a tradeoff exists between packet delay and switch cost (denoted by the number of middle switches), while performance guaranteed switching with bounded packet delay can be achieved without any packet loss. Based on the tradeoff, we can minimize the number of middle switches (under a given packet delay bound) and an overall cost metric (by translating delay into a comparable cost factor), as well as formulating criteria for choosing a proper matrix decomposition algorithm. This provides a flexible way to reduce the number of middle switches by slightly enlarging the packet delay bound.

Single-machine batch scheduling with job processing time compatibility

We consider scheduling problems with job processing time compatibility on a single unbounded batch machine. Each job's processing time is characterized by an interval. Any number of jobs can be processed in a batch under the condition that the processing time intervals of the jobs in the same batch have a nonempty intersection. The processing time of a batch is given by the left endpoint of the intersection of the processing time intervals of the jobs in the batch. For the makespan minimization problem with individual job release dates, we design a pseudo-polynomial dynamic programming algorithm for the case where the number of distinct release dates is fixed. We also present a class of online algorithms that are 2-competitive and a polynomial-time approximation scheme for the case where the number of release dates is arbitrary. For the problem to minimize the weighted number of tardy jobs under a common due date, we show that it is binary NP-hard and provide a polynomial-time algorithm when the jobs have a common weight.