Critical path scheduling of task systems with resource and processor constraints (Extended Abstract)

The Garey–Johnson algorithm is a well known polynomial-time algorithm constructing an optimal schedule for the maximum lateness problem with unit execution time tasks, two parallel identical processors, precedence constraints and release times. The paper is concerned with the worst-case analysis of a generalization of the Garey–Johnson algorithm to the case of arbitrary number of processors. In contrast to other algorithms for the maximum lateness problem, the tight performance guarantee for the even number of processors differs from the tight performance guarantee for the odd number of processors.

Project implementation can be successful when existing resources are used effectively and efficiently. One attempt to use the critical path (CPM) method is a project scheduling method that uses project planning analysis and fixed tim e estimates for each activity. In other words, this method can help solve the scheduling problem by determining the timing of the longest production process schedules in the project so that the company can effectively and efficiently determine how long a project can be completed. Optimization must be done to restore the project duration to the actual schedule. The data processing results are performed to determine the project control methods applied by the CV. NBW. ID and obtain a comparison of completion time between scheduling using the CPM (Critical Path Method) method and actual CV results. NBA. ID. To shorten the life of the project, it can be used CPM. The result of using the program on the project with the CPM method is that the project may be completed with a duration of 108 hours or approximately 13 days for one project at a cost of Rs 2.255.903,00 with a time difference of 18 hours.

This paper studies the effects of overheads in massively parallel processing. The execution times for tasks on individual processors are modeled as independent and identically but arbitrarily distributed random variables. The time to execute a process fork is assumed to be distributed exponentially. The main result bounds (in expectation) the overhead time in forking a large number of tasks across n machines and then waiting for the join event. The model used is appropriate for massive parallelism (when n is large): in fact, the bound serves as a heavy traffic limit approached as n→ ∞ and for task times that are large in comparison to the time to execute a fork. In this model, the expected total time to reach the final join consists of a forking overhead that grows linearly with the number of processors n, a time for parallel execution of tasks that decreases in n, and finally a synchronization delay that is a concave sublinear function of ρ = EX/EA, which is the ratio of expected task time to the expected time needed to fork a new process. This overhead function is typically no worse than o(ρ). An interesting aspect of the analysis is that the original problem reduces to a previously studied problem in queueing theory: estimating total end-to-end delay in an infinite-server resequencing system. The new results thus provide new bounds and heavy-traffic approximations (in distribution and in expectation) for the theory of M/GI/∞ resequencing queues. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Preemptive scheduling with variable profile, precedence constraints and due dates

We consider the problem of scheduling tasks on multiprocessor architectures in the presence of communication delays. Given a set of dependent tasks, the scheduling problem is to allocate the tasks to processors such that the pre-specified precedence constraints among the tasks are obeyed and certain cost-measures (such as the computation time) are minimized. Several cases of the scheduling problem have

Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family.

Two extensions of the classical scheduling model with two parallel identical machines and a partially ordered set of unit execution time tasks are considered. It is well known that the Coffman—Graham algorithm constructs for this model a so-called ideal schedule: that is, a schedule which is optimal for both makespan and total completion time criteria simultaneously. The question of the existence of such a schedule for the extension of this model, where each task has a release time, has remained open over several decades. The paper gives a positive answer to this question and presents the corresponding polynomial-time algorithm. Another straightforward generalization of the considered classical model is obtained by the introduction of multiprocessor tasks. It is shown that, despite the fact that a slightly modified Coffman-Graham algorithm solves the makespan problem with multiprocessor tasks for arbitrary precedence constraints, generally an ideal schedule does not exist and the problem with the criterion of total completion time turns out to be NP-hard in the strong sense even for in-trees.

A parallelizable (or malleable) task is one which can be run on an arbitrary number of processors, with a task execution time that depends on the number of processors allotted to it. Consider a system of M independent parallelizable tasks which are to be scheduled without preemption on a parallel computer consisting of P identical processors. For each task, the execution time is a known function of the number of processors allotted to it. The goal is to find (1) for each task i, an allotment of processors β, and (2) overall, a non-preemptive schedule assigning the tasks to the processors which minimizes the average response time of the tasks. Equivalently, we can minimize the flow time which is the sum of the completion times of each of the tasks. In this paper we tackle the problem of finding a schedule with minimum average response time in the special case where each task in the system has sublinear speedup. This natural restriction on the task execution time means simply that the efficiency of a task decrease or remains constant as the number of processors allotted to it increases. The scheduling problem with sublinear speedups has been shown to be NP-complete in the strong sense. We therefore focus on finding a polynomial time algorithm whose solution comes within a fixed multiplicative constant of optimal. In particular, we given algorithm which finds a schedule having a response time that is within 2 times that of the optimal schedule and which runs in O(M(M2 + P)) time.

With the advent of multi-core processors, parallel execution of multiple tasks has become a common practice. Various scheduling algorithms have addressed this issue considering multiprocessor systems. Most of these algorithms target application level parallelism. Task level parallelism within an application can be exploited using shared memory architecture such as multi-core processor or in a distributed computing environment. In this paper, we propose a static scheduling algorithm that generates a schedule that can be optimized for one or all parameters including execution time, number of processors, and efficiency of processors. The input to this scheduler is a task dependency matrix is generated using dependency analysis technique. Efficiency of this scheduler is high because it uses multiple parameters such as task wait time, number of tasks whose dependency gets resolved by scheduling a task, and task execution time. The paper concludes with an example of applying this technique to a set of tasks.

Steel construction activities are often undertaken in an environment with limited climate control. Both hot and cold temperatures can physically and psychologically affect construction workers, thus decreasing their productivity. Temperature and humidity are two factors that constantly exert forces on workers and influence their performance and efficiency. Previous studies have established a relationship between labor productivity and temperature and humidity. This research is built on the existing body of knowledge and develops a framework of integrating building information modeling (BIM) with a lower level critical path method (CPM) schedule to simulate the overall impact of temperature and humidity on a healthcare facility’s structural steel installation project in terms of total man hours required to build the project. This research effort utilized historical weather data of four cities across the U.S., with each city having workable seasons year-round and conducted a baseline assessment to test if various project starting dates and locations could significantly impact the project’s schedule performance. It was found that both varied project start dates and locations can significantly contribute to the difference in the man hours required to build the model project and that the project start date and location can have an interaction effect. This study contributes to the overall body of knowledge by providing a framework that can help practitioners better understand the overall impact of a productivity influencing factor at a project level, in order to facilitate better decision making.

Index to volume 19 (1995)

Construction projects are constrained by time, cost, and quality, thus requiring effective control methods to ensure successful implementation. This study aims to compare the Critical Path Method and the Precedence Diagram Method in controlling project duration and costs on the Rehabilitation Project of TK Kartika IX-15 Teachers’ Room, which had a normal duration of 45 days. The research employed a quantitative approach using secondary data such as the project time schedule, budget plan, and progress reports. The analysis involved developing project networks using Critical Path Method and Precedemce Diagram Method, calculating forward pass, backward pass, total float, and conducting acceleration simulations through the addition of overtime work. The findings indicate that Critical Path Method shortens the project duration to 37 days, resulting in an 8-day acceleration with a cost slope of Rp1,058,867.59. Meanwhile, Precedence Diagram Method produces a shorter duration of 29 days, equivalent to a 16-day acceleration, with a lower cost slope of Rp928,354.77. These results demonstrate that Precedence Diagram Method offers better flexibility in managing activity relationships, enabling more efficient cost savings and schedule compression. Therefore, Precedence Diagram Method is considered more effective than Critical Parh Method in optimizing both time and cost control for this project. Keywords : Construction Project, Critical Path Method, Precedence Diagram Method, Project Scheduling, Cost Slope

The project scheduling establish the time sequence of various activities which has a certain time limit, this means that the project must be completed before or exactly at the specified time. The delay effect and result in delays to the completion of the overall project. The purpose of study is to analyze the scheduling of the project to find out how long a project can be completed, determine the critical path as well as optimize the time of execution of the project. Research methods used for the project implementation analysis of Clubhouse building construction using critical path method (CPM) and program evaluation and review technique (PERT). Results of the discussion and calculations obtained that the completion of the project still in accordance with the schedule that has been determained, with the critical path method (CPM) is 321 days, and the program evaluation and review technique (PERT), time most quickly resolved is 312 days (value of Z= 0,22%), the slowest time is 339 days (value of Z= 99,87%) and the most probable time is 325 days (value of Z= 49,20%). Be aware of the activities which constitute the critical path is the activities: A, B1, B2, B3, B4, C1, C2, C3, C4, C6, C5, C7, C8, D, and obtained the optimization of project completion time with the CPM method is 48 days, PERT method, time most quickly is 57 days,the slowest time is 30 days, and the most possible time is 44 days.

A malleable task is a computational unit which may be executed on any arbitrary number of processors, its execution time depend- ing on the amount of resources allotted to it. According to the standard behavior of parallel applications, we assume that the mal- leable tasks are monotonic, i.e. that the execution time is decreas- ing with the number of processors while the computational work increases. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guar- antee of for the minimization of the parallel execution time, or makespan. It improves all other existing practical results includ- ing the two-phases method introduced by Turek et al. The main idea is to transfer the difficulty of a two phases method from the scheduling part to the allotment selection. We show how to formu- late this last problem as a knapsack optimization problem. Then, the scheduling problem is solved by a dual-approximation which leads to a simple structure of two consecutive shelves.

Samarinda City has a total of 123 housing estates with 20 subsidized housing (MBR) and 4 mixed housing. Project scheduling in construction greatly determines the project's success because it is a benchmark that the project is successful within the allotted time. CPM (Critical Path Method). CPM is a method that introduces an element of project time by using a predefined activity time estimate. This method is used for crushing the Bukit Mulya housing project, which only applies to the implementation of crash time. From the analysis results, the initial scheduling time, which was originally 87 days, was trimmed by 9 days using CPM, the optimal time was 78 days.