Job Splitting Research Articles

Heuristic algorithms for scheduling of a batch processor in automobile gear manufacturing

In this paper we address a scheduling problem for minimising total weighted tardiness. The motivation for the paper comes from the automobile gear manufacturing process. We consider the bottleneck operation of heat treatment stage of gear manufacturing. Real life scenarios like unequal release times, incompatible job families, non-identical job sizes and allowance for job splitting have been considered. A mathematical model taking into account dynamic starting conditions has been developed. Due to the NP-hard nature of the problem, a few heuristic algorithms have been proposed. The performance of the proposed heuristic algorithms is evaluated: (a) in comparison with optimal solution for small size problem instances, and (b) in comparison with ‘estimated optimal solution’ for large size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently obtaining near-optimal solutions (that is, statistically estimated one) in very reasonable computational time.

Two meta-heuristics for parallel machine scheduling with job splitting to minimize total tardiness

Parallel machine scheduling is a popular research area due to its wide range of potential application areas. This paper focuses on the problem of scheduling n independent jobs to be processed on m identical parallel machines with the aim of minimizing the total tardiness of the jobs considering a job splitting property. It is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We present a mathematical model for this problem. The problem of total tardiness on identical parallel machines is NP-hard. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using an optimization solver is extremely difficult. We propose two meta-heuristics: Tabu search and simulated annealing. Computational results are compared on random generated problems with different sizes.

A lower bound for weighted completion time variance

We consider a single machine scheduling problem to minimize the weighted completion time variance. This problem is known to be NP-hard. We propose a heuristic and a lower bound based on job splitting and the Viswanathkumar and Srinivasan procedure. The test on more than 2000 instances shows that this lower bound is very tight and the heuristic yields solutions very close to optimal ones since the gap between the solution given by the heuristic and the lower bound is very small.

Distributed analysis in ATLAS using GANGA

Distributed data analysis using Grid resources is one of the fundamental applications in high energy physics to be addressed and realized before the start of LHC data taking. The needs to manage the resources are very high. In every experiment up to a thousand physicists will be submitting analysis jobs to the Grid. Appropriate user interfaces and helper applications have to be made available to assure that all users can use the Grid without expertise in Grid technology. These tools enlarge the number of Grid users from a few production administrators to potentially all participating physicists.The GANGA job management system (http://cern.ch/ganga), developed as a common project between the ATLAS and LHCb experiments, provides and integrates these kind of tools. GANGA provides a simple and consistent way of preparing, organizing and executing analysis tasks within the experiment analysis framework, implemented through a plug-in system. It allows trivial switching between running test jobs on a local batch system and running large-scale analyzes on the Grid, hiding Grid technicalities.We will be reporting on the plug-ins and our experiences of distributed data analysis using GANGA within the ATLAS experiment. Support for all Grids presently used by ATLAS, namely the LCG/EGEE, NDGF/NorduGrid, and OSG/PanDA is provided. The integration and interaction with the ATLAS data management system DQ2 into GANGA is a key functionality. An intelligent job brokering is set up by using the job splitting mechanism together with data-set and file location knowledge. The brokering is aided by an automated system that regularly processes test analysis jobs at all ATLAS DQ2 supported sites. Large numbers of analysis jobs can be sent to the locations of data following the ATLAS computing model.GANGA supports amongst other things tasks of user analysis with reconstructed data and small scale production of Monte Carlo data.

Optimal job splitting on a multi‐slot machine with applications in the printing industry

AbstractIn this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m‐slot machine. A particular assignment of the types to the slots is called a “run” configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the “length” of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP‐hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst‐case bound for one of the heuristics. Extensive tests on real‐world and randomly generated instances show that the heuristics are both fast and effective, finding near‐optimal solutions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Distributed analysis using GANGA on the EGEE/LCG infrastructure

The distributed data analysis using Grid resources is one of the fundamental applications in high energy physics to be addressed and realized before the start of LHC data taking. The need to facilitate the access to the resources is very high. In every experiment up to a thousand physicist will be submitting analysis jobs into the Grid. Appropriate user interfaces and helper applications have to be made available to assure that all users can use the Grid without too much expertise in Grid technology. These tools enlarge the number of grid users from a few production administrators to potentially all participating physicists.The GANGA job management system (http://cern.ch/ganga), developed as a common project between the ATLAS and LHCb experiments provides and integrates these kind of tools. GANGA provides a simple and consistent way of preparing, organizing and executing analysis tasks within the experiment analysis framework, implemented through a plug-in system. It allows trivial switching between running test jobs on a local batch system and running large-scale analyzes on the Grid, hiding Grid technicalities.We will be reporting on the plug-ins and our experiences of distributed data analysis using GANGA within the ATLAS experiment and the EGEE/LCG infrastructure. The integration with the ATLAS data management system DQ2 into GANGA is a key functionality. In combination with the job splitting mechanism large amounts of jobs can be sent to the locations of data following the ATLAS computing model. GANGA supports tasks of user analysis with reconstructed data and small scale production of Monte Carlo data.

Robust and sustainable schedulability analysis of embedded software

For real-time systems, most of the analysis involves efficient or exact schedulability checking. While this is important, analysis is often based on the assumption that the task parameters such as execution requirements and inter-arrival times between jobs are known exactly. In most cases, however, only a worst-case estimate of these quantities is available at the time of analysis. It is therefore imperative that schedulability analysis hold for better parameter values ( Sustainable Analysis ). On the other hand, if the task or system parameters turn out to be worse off, then the analysis should tolerate some deterioration ( Robust Analysis ). Robust analysis is especially important, because the implication of task schedulability is often weakened in the presence of optimizations that are performed on its code, or dynamic system parameters. In this work, we define and address sustainability and robustness questions for analysis of embedded real-time software that is modeled by conditional real-time tasks. Specifically, we show that, while the analysis is sustainable for changes in the task such as lower job execution times and increased relative deadlines, it is not the case for code changes such as job splitting and reordering. We discuss the impact of these results in the context of common compiler optimizations, and then develop robust schedulability techniques for operations where the original analysis is not sustainable.

A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property

We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this ...

First experience and adaptation of existing tools to ATLAS distributed analysis

The ATLAS production system has been successfully used to run production of simulation data at an unprecedented scale in ATLAS. Up to 10000 jobs were processed on about 100 sites in one day. The experiences obtained operating the system on several grid flavours was essential to perform a user analysis using grid resources. First tests of the distributed analysis system were then performed. In the preparation phase data was registered in the LHC file catalog (LFC) and replicated in external sites. For the main test, few resources were used. All these tests are only a first step towards the validation of the computing model. The ATLAS management computing board decided to integrate the collaboration efforts in distributed analysis in only one project, GANGA. The goal is to test the reconstruction and analysis software in a large scale Data production using grid flavors in several sites. GANGA allows trivial switching between running test jobs on a local batch system and running large-scale analyses on the grid; it provides job splitting and merging, and includes automated job monitoring and output retrieval.

A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property

We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this problem, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of moderate sizes in a reasonable amount of computation time. Scope and purpose In this paper, we consider an operations scheduling problem in a real manufacturing system that produces printed circuit boards (PCBs). In the PCB manufacturing system, production orders are specified by the product types, production quantities and due dates. In a bottleneck workstation of the manufacturing system, in which there are multiple parallel machines, a job required for a production order can be split into basic processing units, each of which can be processed on a machine. We present an algorithm that can give an optimal schedule for a scheduling problem in the workstation for the objective of minimizing total tardiness of production orders. Since meeting due dates of customers’ orders become more and more important for the survival of a manufacturing company in highly competitive market environments of these days, the algorithm may provide the company with a competitive edge in the industry.

The Tool-Switching Problem With Magazine Capacity and Tool Size Constraints

Previous works often simplify the tool-switching problem by using uniform tool size and magazine capacity constraints. A tool has uniform size when it requires only one slot to be stored in the magazine. The magazine capacity constraints assume that the magazine can hold all tools for each job. This paper addresses the more general case of the tool-switching problem when both uniform tool size and magazine capacity constraints are relaxed. The problem is decomposed into two cases: partial and complete job splitting. In the first case, a job is said to be partially split into subjobs if each subjob requires at least two tools which occupy less than the capacity of the magazine. In the second case, a job is said to be completely split into subjobs if each subjob requires only one tool. The problems are proven to be NP complete. An attempt is made to solve these cases while the tools are changed either concurrently with job change or not. Some promising results are obtained.

A linear programming approach for identical parallel machine scheduling with job splitting and sequence-dependent setup times

In this study, we consider the problem of scheduling a set of independent jobs with sequence-dependent setup times and job splitting, on a set of identical parallel machines such that maximum completion time (makespan) is minimized. For this NP-hard problem, we suggest a heuristic algorithm improving an existing one, using a linear programming modeling with setup times and job splitting considerations. The performance of our new method is tested on over 6000 instances with different size by comparing it with a lower bound.

New exact method to solve the Pm/r j/∑C j schedule problem

This paper addresses a parallel machine scheduling problem (PMSP) with release dates to minimize sum of completion time. This problem presents numerous potential applications in real life. An efficient exact branch and bound method is developed using theoretical properties. By allowing job splitting or by relaxing release date constraints, a polynomial lower bounding scheme is proposed. The method was tested on more than 2000 randomly generated medium-sized instances. We have solved medium-sized instances in a reasonable amount of time. Our method is the first attempt to solve exactly the considered problem. It opens an interesting way in PMSP with sum of completion time criterion.

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.

An efficient heuristic approach for parallel machine scheduling with job splitting and sequence-dependent setup times

In this paper, we consider a simplified real-life identical parallel machine scheduling problem with sequence-dependent setup times and job splitting to minimize makespan. We propose a heuristic to solve this problem. Our method is composed of two parts. The problem is first reduced into a single machine scheduling problem with sequence-dependent setup times. This reduced problem can be transformed into a Traveling Salesman Problem (TSP), which can be efficiently solved using Little's method. In the second part, a feasible initial solution to the original problem is obtained by exploiting the results of the first part. This initial solution is then improved in a step by step manner, taking into account the setup times and job splitting. We develop a lower bound and evaluate the performances of our heuristic on a large number of randomly generated instances. The solution given by our heuristic is less than 4.88% from the lower bound.

OPTIMALITY CONDITIONS FOR JOB SPLITTING ON PARALLEL MACHINES

The control of manufacturing systems consisting of a certain number of parallel machines processing a given number of jobs is addressed in this work. A decentralized scheme is defined in which at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the optimal splitting of jobs on parallel machines is taken into account. At the local level, an optimization problem with quadratic cost function and nonlinear constraints is stated as a multistage control problem and solved by means of dynamic programming techniques.

Parallel Machine Scheduling to Minimize Total Completion Time with Release Dates Constraints

This paper addresses, using an exact method, the parallel machine scheduling problem (PMSP) with release dates contraints to minimize the total completion time. This criterion is equivalent to minimizing the total or mean flowtime, the total or mean waiting time. Theoritical properties are developed. A lower boudning scheme is proposed by allowing job splitting or relaxing the release dates constraints. These relaxed problems are shown to be polynomially solvable. These theoretical properties and the lower bound is incorporated in a branch and bound algorithm which has been tested on over 2000 randomly generated medium-sized problems.

Solutions to a modified tool loading problem for a single FMM

Due to the common experience of changing production requirements, many flexible manufacturing machines (FMM) must be used to produce parts requiring more tools than the tool magazine can hold. Tool changes must then be made during jobs as well as between jobs. Many previously developed solutions to the tool loading problem are not capable of obtaining optimal schedules in this modified problem. This is remedied through a unique solution involving job splitting that provides better solutions to a generalized tool loading problem than previously obtained. By additionally allowing concurrent job and tool changing, a new optimal tooling policy is obtained that is useful either with previously developed job scheduling heuristics, or the algorithm presented in this paper.

Loading strategies for a class of just-in-time manufacturing system

In this paper, based on the group technology and the just-in-time manufacturing concepts, two loading models for optimal utilisation of the processing capabilities of an integrated manufacturing system consisting of a set of heterogeneous workstations are developed. These loading models are developed to integrate and utilise the available information from both the bill of materials and the process plans. The objective functions for these models are: the maximum tardiness and the makespan. In these models, the production quantity of each customer order for any part or product always equals its corresponding demand quantity; each part requires a finite number of aggregated stages of operation; job splitting is allowed; and the processing priorities of all the jobs during the planning time horizon are specified based on a desirable dispatching rule. The proposed mathematical programming models are fixed charge problems which are solved by compatible mixed integer programming algorithms. Finally, to provide additional decision-making capabilities, based on these models and their corresponding solution algorithms, a compatible decision support system is suggested.

Scheduling with release dates on a single machine to minimize total weighted completion time

This paper considers the problem of scheduling jobs with release dates on a single machine to minimize the total weighted completion time. A branch and bound algorithm is proposed which incorporates three special features that contribute to its efficiency. Firstly, quickly computed lower bounds are obtained using a procedure which is based on job splitting. The job splitting methodology is shown to be applicable to a range of total weighted completion time scheduling problems. Secondly, the branching rule includes a release date adjustment mechanism which increases release dates at certain nodes of the tree with a view to tightening lower bounds. Thirdly, the branch and bound algorithm includes a new dominance rule for eliminating nodes of the search tree. Computational experience on problems with up to 50 jobs indicates that the proposed algorithm is superior to other known algorithms.