Minimum Finish Time Research Articles

Comparison of Heuristic Priority Rules in the Solution of the Resource-Constrained Project Scheduling Problem

Resource-constrained project scheduling (RCPS) aims to minimize project duration under limited resource availabilities. The heuristic methods that are often used to solve the RCPS problem make use of different priority rules. The comparative merits of different priority rules have not been discussed in the literature in sufficient detail. This study is a response to this research gap. It compares 17 heuristic priority rules and seeks the best performing heuristic priority rule. This is the first study ever that compares heuristic priority rules by considering combinations of variations in (1) resource allocation procedures, (2) number of activities, (3) number of resource constraints, and (4) resource supply levels. The objective is to understand the relative merits of heuristic rules used in solving the RCPS problem. The findings indicate that the “minimum late finish time” rule generates the shortest predicted project duration when used in parallel resource allocation, whereas the “minimum late start time”, “minimum late finish time”, and the “highest rank of positional weight 2” rules perform best in serial resource allocation. It was also found that parallel resource allocation is slightly superior to serial resource allocation in most instances.

A characterization for tropical polynomials being the minimum finishing time of project networks

A tropical polynomial is called $R$-polynomial if it can be realized as the minimum finishing time of a project network. $R$-polynomials satisfy the term extendability condition, and correspond to simple graphs. We give a characterization of $R$-polynomials in terms of simple graphs.

Proposal and evaluation of a selection procedure for cast parts

The design of casting components is a complex activity, which is usually based on guidelines scattered in the literature, or based on the designer’s accumulated experience. A single failure in the casting process selection can increase design and production time and, in critical cases, result in a collapse of the manufacturing and assembly of components. Nowadays the selection is made by prioritizing the features of the casting process, but this action could be carried out during the product development stage, assisting the designer. This could allow the project to adjust to a more viable casting process. In this context, our goal is to propose a selector for casting processes to be used during the early stages of the embodiment design. It was achieved through the use of quality function deployment and design for manufacturing (DFM) principles. Our proposal relates the component’s main functions with each process characteristic (mass, minimum section thickness, draft angle, surface finish, dimensional tolerances, minimum lot and lead time) through a correlation matrix, resulting in importance indexes for these characteristics. Furthermore, the importance indices obtained are related to the capability of each casting process discussed, providing a process rating. A checklist based on DFM principles is also provided to guide the designer when a need for improvement is observed or no processes are suited for producing the desired part. For validation, two ferrous and two nonferrous cast parts were analyzed. The results were compared with other selectors described in the literature and with processes actually used in the industry. Thus, they have shown a good relation with the other methods, especially regarding the quantitative classification determined by the proposed selector.

Development of a New Internal Finishing of Tube by Magnetic Abrasive Finishing Process Combined with Electrochemical Machining

The research proposes a new internal surface magnetic abrasive finishing (MAF) process, which compounded with electrochemical machining (ECM) to decrease machining time. The electrochemical process changes the morphology of the aluminum tube internal surface, producing an oxidation film. Then, we removed the film by magnetic abrasive finishing, results in minimized surface roughness in a significantly reduced processing time when compared to the conventional MAF. In this research, a new experimental set up with a tool that capable of magnetic abrasive finishing and electrochemical finishing was designed and developed to study the machining feasibility. The newly developed finishing method demonstrated simultaneous process of aluminum oxide film formation by ECM and its removal by MAF. This process plays a significant role in preventing the deepening of the pit during ECM and speed up the planarization. The method was developed step by step; firstly, ECM and MAF were conducted in two separate processes. In the second experiment, we modified the finishing conditions to facilitate one-stage finishing method. An investigation of the finishing surface is focusing on the pit size that formed by ECM. The pit size indicated the residue of oxide film because it is a part of the oxidation film construction. Pits morphology changes were observed for certain finishing time to determine the minimum finishing time for its removal. Surface roughness and SEM photograph of the finishing surface were recorded and studied.

Performance Evaluation of Matrix Multiplication on a Network of Work Stations with Communication Delay

Network-based multicomputer systems merge as a potential economical candidate to replace supercomputers. Despite enormous effort to evaluate the performance of those systems, we still lack a complete performance model to analyze distributed computing systems. The model is complete if all system parameters, network parameters, communication overhead parameters, and application parameters are considered explicitly in the solution. In this paper we develop a closed form solution for a finish time of executing a matrix-multiplication on a distributed network of processors (cloud computing). Matrix multiplication represents a paradigm of divisible jobs, which has a wide area of applications. The closed form solution is derived considering one-dimensional decomposition and two-dimensional decomposition of the matrices involved in the operation. The analytical results combine all system parameters, network parameters, and matrix dimension in the solution, which helps the designer to study the effect of each individual parameter on the overall system performance. This then becomes a tool for a designer of a multicomputer system to mange limited resources in an optimal manner paying attention only to those parameters that are most critical. The results show the superiority of the row-wise one-dimensional decomposition. We also show that, because of the communication overhead, adding more processors will not incessantly improve the system performance. We derived a closed form solution for the optimum number of processors (nodes) to be used to obtain the maximum speed up (equally the minimum finish time). Process allocation tradeoff is very important for optimizing the multicomputer system performance.

Scheduling directed a-cyclic task graphs on a bounded set of heterogeneous processors using task duplication

In a distributed computing environment, the schedule by which tasks are assigned to processors is critical to minimizing the overall run-time of the application. However, the problem of discovering the schedule that gives the minimum finish time is NP-Complete. This paper addresses static scheduling of a directed a-cyclic task graph (DAG) on a heterogeneous, bounded set of distributed processors to minimize the makespan. By combining several innovative techniques, including insertion-based scheduling and multiple task duplication, we present a new heuristic, known as Heterogeneous N-predecessor Decisive Path (HNDP), for scheduling directed a-cyclic weighted task graphs (DAGs) on a set of heterogeneous processors. We compare the performance of HNDP, under a range of varying input conditions, with two of the best existing heterogeneous heuristics namely HEFT and STDS. The results presented in this paper show that HNDP outperforms the two heuristics in terms of finish time and the number of processors employed over a wide range of parameters. The complexity of HNPD is O ( v 2 . p ) vs. O ( v 2 . p ) of HEFT and O ( v 2 ) of STDS where v is the number of nodes in the DAG.

Toward an analytical solution to task allocation, processor assignment, and performance evaluation of network processors

Message-passing network-based multicomputer systems emerge as a potential economical candidate to replace supercomputers. Despite enormous effort to evaluate the performance of those systems and to determine an optimum scheduling algorithm (which is known as an NP-complete), we still lack a complete and a good performance model to analyze distributed computing systems. The model is complete if all system parameters, network parameters, communication overhead parameters, and application parameters are considered explicitly in the solution. A good performance model, like a good scientific theory, should be able to explain all normal behavior, predict any abnormality in the system, and allow the designer to adjust some of the parameters, while abstracting unimportant details. In this paper, we develop a good and complete performance model, which predicts a minimum finish time, equally the maximum speed up. In addition, we develop a closed form solution which forecasts the optimum share of the parallel job (task) that has to be assigned to each processor (node). Task assignment may then be undertaken in a distributed manner, which enhances the distributive nature of the system and, thus, improve system performance. Most importantly, our analytical solution presents a mechanism to select, based on system and application parameters, the optimum number of processors (nodes) that has to be assigned to a given parallel job. The model helps the designer to study the effect of each individual parameter on the overall system performance. This then becomes a tool for a designer of a multicomputer system to manage limited resources in an optimal manner paying attention only to those parameters that are most critical.

Heuristic Load Balancing for CFD Codes Executed in Heterogeneous Computing Environments

A graph partitioning-based heuristic load-balancing algorithm known as the Largest Task First with Minimum Finish Time and Available Communication Costs is modified to take into account the dynamic nature and heterogeneity of current large-scale distributed computing environments, like Grids. The modified algorithm is applied to facilitate load balancing of a known CFD code used to model crystal growth.

DPS: dynamic priority scheduling heuristic for heterogeneous computing systems

Scheduling a parallel program is a crucial step in effectively harnessing the computing power of a heterogeneous computing system. Obtaining a minimum finish time schedule for a set of precedence constrained tasks is a well known NP-complete problem. Heterogeneity in parallel systems introduces an additional degree of complexity to the scheduling problem, i.e. varying speed of processors. A non-preemptive, compile-time scheduling heuristic has been developed, designated as DPS, that uses dynamic priorities based on the difference between b-level and t-level to map and schedule directed acyclic graphs (DAGs) onto heterogeneous processors, with the objective of minimising the schedule length. In the case of homogeneous processors, it is not difficult to compute the b-level and t-level, since the task execution costs are fixed. However, in the case of heterogeneous processors, as each task has a different execution cost on each processor, the b-level and t-level lose their traditional meaning. The b-level and t-level have been computed in a different and effective way that captures the changes which occurred in the DAG during scheduling. Dynamic priorities are thus determined during the scheduling process in order to avoid scheduling less important tasks before the more important ones. Moreover, the effect of changing the task execution cost to compute the b-level and t-level has also been studied. The effectiveness of the algorithm is demonstrated by comparing it against two of the existing closely related algorithms for randomly generated graphs. DPS outperforms both algorithms by a considerable margin and has a reasonable time complexity.

Optimal divisible job load sharing for bus networks

Optimal load allocation for load sharing a divisible job over N processors interconnected in bus-oriented network is considered. The processors are equipped with front-end processors. It is analytically proved, for the first time, that a minimal solution time is achieved when the computation by each processor finishes at the same time. Closed form solutions for the minimum finish time and the optimal data allocation for each processor are also obtained.

Static and Dynamic Processor Scheduling Disciplines in Heterogeneous Parallel Architectures

Most parallel jobs cannot be fully parallelized. In a homogeneous parallel machine-one in which all processors are identical-the serial fraction of the computation has to be executed at the speed of any of the identical processors, limiting the speedup that can be obtained due to parallelism. In a heterogeneous architecture, the sequential bottleneck can be greatly reduced by running the sequential part of the job or even the critical tasks in a faster processor. This paper uses Markov chain based models to analyze the performance of static and dynamic processor assignment policies for heterogeneous architectures. Parallel jobs are assumed to be described by acyclic directed task graphs. A new static processor assignment policy, called Largest Task First Minimum Finish Time (LTFMFT), is introduced. The analysis shows that this policy is very sensitive to the degree of heterogeneity of the architecture, and that it outperforms all other policies analyzed. Three dynamic assignment disciplines are compared and it is shown that, in heterogeneous environments, the disciplines that perform better are those that consider the structure of the task graph, and not only the service demands of the individual tasks. The performance of heterogeneous architectures is compared with cost-equivalent homogeneous ones taking into account different scheduling policies. Finally, static and dynamic processor assignment disciplines are compared in terms of performance.

Analysis of scheduling parallel tasks on hypercubesystems

The problem of scheduling independent parallel tasks with the consideration of setup time on a d-dimensional hypercube system is investigated. The objective of this problem is to find a schedule with minimum finish time; such a scheduling problem is NP-hard. Therefore, a heuristic algorithm is proposed and its performance bound derived. >

Closed form solutions for bus and tree networks of processors load sharing a divisible job

Optimal load allocation for load sharing a divisible job over processors interconnected in either a bus or a tree network is considered. The processors are either equipped with front-end processors or not so equipped. Closed form solutions for the minimum finish time and the optimal data allocation for each processor are obtained. The performance of large symmetric tree networks is examined by aggregating the component links and processors into a single equivalent processor. This allows an easy examination of large tree networks. In addition, it becomes possible to find a closed form solution for the optimal amount of data that is to be assigned to each processor in the tree network in order to achieve the minimum finish time.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Efficient scheduling algorithm for divisible and indivisible tasks in loosely coupled multiprocessor systems

In this paper, we investigate a scheduling problem in loosely coupled multiprocessor systems. This problem has been addressed by many researchers because it has a substantial effect on the performance of multiprocessor systems. Previous work considered only one class of tasks to be scheduled. In this paper, we propose an algorithm to schedule two classes of tasks, indivisible and divisible tasks, among the available processors in the system. The objective is to find the best scheduling that gives a minimum finish time. The divisible class of tasks, considered here for the first time in a scheduling algorithm, has important applications in signal-processing, image-processing and Kalman filtering. The proposed algorithm answered many important questions that arise when the two classes of divisible and indivisible tasks are considered. Applications of the algorithm include all operating systems with multiprocessor support, such as the Mach operating system. Although two classes of tasks are considered, the complexity of the algorithm stays in a reasonable order.

Performance of scheduling algorithms for no-wait flowshops with parallel machines

We study the performance of scheduling algorithms for a manufacturing system, called the ‘no-wait flowshop’, which consists of a certain number of machine centers. Each center has one or more identical parallel machines. Each job is processed by at most one machine in each center. The problem of finding the minimum finish time schedule is considered here in a flowshop consisting of two machine centers. Heuristic algorithms are presented and are analyzed in the worst case performance context. For the case of two centers, one with a single machine and the other with m, two heuristics are presented with tight performance guarantees of 3 − (1/ m) and 2. When both centers have m machines, a heuristic is presented with an upper bound performance guarantee of 8 3 − 2/(3m) . It is also shown that this bound can be reduced to 2(1 + ϵ). For the flowshop with any number of machines in each center, we provide a heuristic algorithm with an upper bound performance guarantee that depends on the relative number of machines in the centers.

Scheduling on a hypercube

We present a Θ( n 2) worst-case-time algorithm to determine the minimum finishing time for a preemptive schedule of n independent jobs on a hypercube of fixed dimension.

Scheduling algorithms for flexible flowshops: Worst and average case performance

We discuss the performance of scheduling algorithms for a certain kind of manufacturing environment, called the “Flexible Flowshop”, which consists of a certain number of machine centers. Each center has one or more identical parallel machines. Each part is processed by at most one machine in each center. The problem of finding minimum finish time schedules is considered. Heuristic algorithms are presented and are studied in the worst and average case performance contexts.

Optimal scheduling of unit-time tasks on two uniform processors under tree-like precedence constraints

An O(n 3/(b+1)) time algorithm to obtain a minimum finish time schedule subject to tree-like precedence constraints for unit-time tasks on two uniform processors is obtained. It is assumed that the slower processor takesb time units for each one taken by the speedier one, for some integerb. It is also noted that a slight modification of this schedule yields a minimum mean flow time schedule.

Scheduling of a Two-machine Flowshop with Processing Time Linearly Dependent on Job Waiting-time

This paper deals with the problem of finding the minimum finish-time schedule in a two-machine flowshop, where the processing times of jobs are linearly dependent on the job waiting-times. The problem is shown to be NP-hard. A heuristic algorithm is presented, and the worst-case bounds are derived for the different variations of the algorithm.

Complexity of Scheduling Shops with No Wait in Process

We show that obtaining minimum finish time schedules with no wait in process is NP-Hard for flow shops, job shops and open shops. Specifically, it is shown that the two processor job and open shop problems are NP-Hard even when jobs are restricted to have no task of length zero. The two processor flow shop problem is NP-Hard if jobs with only one task are permitted. Note that Gilmore and Gomory (Gilmore, P., R. Gomory. 1964. Sequencing a one state-variable machine: A solvable case of the travelling salesman problem. Oper. Res. 12 655–679.) have obtained a polynomial time algorithm for the two processor flow shop for the case where every job has two tasks. The 4-sum and 2-pair problems are also shown NP-Hard.