Optimal Number Of Machines Research Articles

Machine interference model application in woven fabric production

In today’s production control and analysis in the weaving rooms is provided by a system which permits the automatic and immediate collection (in real time) of the data concerning the running of each weaving machine (stop, weft breakage, warp breakage). The result is the availability of objective and complete data which can build the base for the most appropriate choices and interventions aimed at improving the production of the weaving departments. Weaving is a stage where the yarn becomes a surface and it is the most important cost center due to operator density, machine density and energy consumption. In this study, an application is made on the machine interference problem on weaving plant in a factory producing woolen fabric. Further, a study has been conducted on how the number of operators allocated in order to eliminate these downtimes will provide optimum conditions. For this study, three of the most produced fabrics in the facility are selected and data on the loom group where these fabrics were produced are collected. The optimum number of machines that an operator should be serviced has been examined according to this collected data and production costs by using queuing theorem.

An $\mathcal{O}(\log {m})$-Competitive Algorithm for Online Machine Minimization

We consider the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a minimum number of machines. Our main result is a general $\mathcal{O}(\log {m})$-competitive algorithm for the online problem, where $m$ is the optimal number of machines used in an offline solution. This is the first improvement to an intriguing problem in nearly two decades. To date, the best known result is a $\mathcal{O}(\log (p_{\max}/p_{\min}))$-competitive algorithm by Phillips et al. [Optimal time-critical scheduling via resource augmentation, STOC, 1997] that depends on the ratio of maximum and minimum job sizes, $p_{\max}$ and $p_{\min}$. Even for $m=2$ no better algorithm was known. Our algorithm is in this case constant-competitive. When applied to laminar or agreeable instances, our algorithm achieves a competitive ratio of $\mathcal{O}(1)$ even independently of $m$. The following two key components lead to our new result. First, we derive a new lower bound on the optimum value that relates the laxity and the number of jobs with intersecting time windows. Then, we design a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.

The methodic of calculation for the need of basic construction machines on construction site when developing organizational and technological documentation

Economic indicators of construction work, particularly in high-rise construction, are directly related to the choice of optimal number of machines. The shortage of machinery makes it impossible to complete the construction & installation work on scheduled time. Rates of performance of construction & installation works and labor productivity during high-rise construction largely depend on the degree of provision of construction project with machines (level of work mechanization). During calculation of the need for machines in construction projects, it is necessary to ensure that work is completed on scheduled time, increased level of complex mechanization, increased productivity and reduction of manual work, and improved usage and maintenance of machine fleet. The selection of machines and determination of their numbers should be carried out by using formulas presented in this work.

P-DOT: a model of computation for big data

In response to the high demand of big data analytics, several programming models on large and distributed cluster systems have been proposed and implemented, such as MapReduce, Dryad and Pregel. However, compared with high performance computing areas, the basis and principles of computation and communication behaviour of big data analytics is not well studied. In this paper, we review the current big data computational model DOT and DOT Advanced, and propose a more general and practical model p-DOT (p-phases DOT). p-DOT is not a simple extension, but with profound significance: for general aspects, any big data analytics job execution expressed in DOT model or bulk synchronous parallel model can be represented by it; for practical aspects, it considers I/O behaviour to evaluate performance overhead. Moreover, we provide a cost function of p-DOT implying that the optimal number of machines is near-linear to the square root of input size for a fixed algorithm and workload, and certify that the processing paradigm of p-DOT is scalable and fault-tolerant. Finally, we demonstrate the effectiveness of the model through several experiments.

An Algorithm for an Optimal Staffing Problem in Open Shop Environment

The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as two- dimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal open- shop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Windows scheduling of arbitrary-length jobs on multiple machines

The generalized windows scheduling problem for n jobs on multiple machines is defined as follows: Given is a sequence, I=?(w 1,? 1),(w 2,? 2),?,(w n ,? n )? of n pairs of positive integers that are associated with the jobs 1,2,?,n, respectively. The processing length of job i is ? i slots where a slot is the processing time of one unit of length. The goal is to repeatedly and non-preemptively schedule all the jobs on the fewest possible machines such that the gap (window) between two consecutive beginnings of executions of job i is at most w i slots. This problem arises in push broadcast systems in which data are transmitted on multiple channels. The problem is NP-hard even for unit-length jobs and a (1+?)-approximation algorithm is known for this case by approximating the natural lower bound $W(I)=\sum_{i=1}^{n}(1/w_{i})$ . The techniques used for approximating unit-length jobs cannot be extended for arbitrary-length jobs mainly because the optimal number of machines might be arbitrarily larger than the generalized lower bound $W(I)=\sum_{i=1}^{n}(\ell_{i}/w_{i})$ . The main result of this paper is an 8-approximation algorithm for the WS problem with arbitrary lengths using new methods, different from those used for the unit-length case. The paper also presents another algorithm that uses 2(1+?)W(I)+logw max machines and a greedy algorithm that is based on a new tree representation of schedules. The greedy algorithm is optimal for some special cases, and computational experiments show that it performs very well in practice.

Resource Allocation, Batching and Dispatching in a Stochastic Flexible Job Shop

The problem of resource allocation and scheduling is considered for a flexible job shop composed of several work centers with multiple identical machines. Each machine has its own setup time that depends on the current and the arriving batch types. The optimal number of machines at each center and the optimal batch size for each job type is to be determined for several dispatching rule. The objective of the study is to assist the scheduler in selecting the best dispatching rule with respect to a desired performance measure along with its corresponding batch size and optimum number of machines in each center. Several measures are considered including the average flow time, sum of earliness and tardiness, and the number of tardy jobs. The simulation package ProModel is used to build the model and its optimization tool called SimRunner is used for optimization.

The shifting bottleneck procedure for job-shops with parallel machines

The shifting bottleneck (SB) heuristic has been successfully applied to the job-shop scheduling problem. In this paper, the shifting bottleneck heuristic has been extended to solve job-shop problems with parallel machine workcentres. The efficient shifting bottleneck heuristic was developed to reduce the number of subproblems and provide tradeoff results between the computation time and the solution quality. The effect of bottleneck machine selection and reoptimisation procedures on the computational time is discussed. Moreover, a procedure is developed to achieve the desired makespan with near optimal number of machines of each machine type. The tradeoff between the makespan and the minimal number of machines required to achieve the makespan is also illustrated on few job-shop problems.

Optimum machine selection in multistage manufacturing systems

Machine selection during the initial stages of facility planning is critical as most capital costs are incurred in the investment of new machines. This paper presents an approach for optimizing the number of machines acquired for batch processing in a multistage manufacturing system. Machines of the same type differ in their processing capabilities. Four cases of overlap in machine capabilities are examined. For each case, the problem is optimized with and without the time balance constraints between the stages. The output is the optimum number of machines of each type to be purchased for each stage, as well as the optimum time delay between the stages such that the system cost is minimized. The resulting multistage line is then simulated under specified conditions to observe its behaviour over time and to assess the viability of the developed model.

Single operation earliness—tardiness scheduling with machine activation costs

We consider a static, single operation, non-pre-emptive, deterministic scheduling problem in which a set of n jobs is to be processed on k identical machines. Jobs assigned to each machine have a common due date. The number of machines (k) is unknown. Activating a machine will require additional costs to be incurred. The objective is to find an optimal sequence, the optimal number of machines (k), and the respective due dates to minimize the weighted sum of earliness, tardiness, and machine activation costs. We propose a polynomial time algorithm to solve the problem.

Single operation earliness—tardiness scheduling with machine activation costs

We consider a static, single operation, non-pre-emptive, deterministic scheduling problem in which a set of n jobs is to be processed on k identical machines. Jobs assigned to each machine have a common due date. The number of machines (k) is unknown. Activating a machine will require additional costs to be incurred. The objective is to find an optimal sequence, the optimal number of machines (k), and the respective due dates to minimize the weighted sum of earliness, tardiness, and machine activation costs. We propose a polynomial time algorithm to solve the problem.

A machine requirements planning problem in the design of manufacturing systems

This paper considers the problem of determining the optimal number of machines for various machine groups in a manufacturing system. The technique of genetic algorithms is proposed as a means of solving such a problem. A mathematical model is developed to describe the characteristics of the system. The performance of the proposed solution procedure is illustrated by using numerical examples. Indeed, it is shown that the genetic search procedure proposed in this paper is a powerful but simple means of effecting the optimal machine requirements planning in the design of manufacturing systems.

A study on optimal task decomposition of networked parallel computing using PVM

A numerical study is performed to investigate the effect of task decomposition on networked parallel processes using Parallel Virtual Machine (PVM), In our study, a PVM program distributed over a network of workstations is used in solving a finite difference version of a one dimensional heat equation, where natural choice of PVM programming structure would be the master-slave paradigm with the aim of finding an optimal configuration resulting in least computing time including communication overhead among machines. Given a set of PVM tasks comprised of one master and five slave programs, it is found that there exists a pseudo optimal number of machines, which does not necessarily coincide with the number of tasks, that yields the best performance when the network is under a light usage. Increasing the number of machines beyond this optimal one does not improve computing performance since increase in communication overhead among the excess number of machines offsets the decrease in CPU time obtained by distributing the PVM tasks among these machines. However, when the network traffic is heavy, the results exhibit a more random characteristic that is explained by the random nature of data transfer time.

A stochastic approach to machine interference problems in robot-served manufacturing systems

This work investigates the machine interference problems in robot-served manufacturing systems using a stochastic approach for modelling the system. Two new parameters are introduced: the robot availability parameter and the machine stoppage. The problem is modelled for both priority and no-priority situations. The models are analysed to obtain an evaluation for the system's performance of machine efficiencies and robot utilizations that reflect the behaviour of the system under given conditions. Also, the models are evaluated to determine the optimum number of machines that can be located within a manufacturing cell.

Optimal assignment of priorities for the machine interference problems

This paper investigates multiple machine repair problems with one repairman. Each machine is subject to two modes of failure, major and minor. The machines are identical, with times to repair and the times to failure assumed to be negative exponentially distributed. In this paper we consider the problem: when there are i and j failed machines in modes 1 and 2, respectively, which mode of failure should be selected for repair? A profit model is developed and then, to achieve the optimal profit, we derive the optimal repair policy for the single repairman. In addition, we describe a procedure to determine the optimal number of machines which should be assigned to a repairman. Numerical examples are provided in which the system characteristics are evaluated and profits are analyzed.

A methodology for investigating effects of cell size on operational flexibility in flexible manufacturing systems

There are two aspects to cell formation in flexible manufacturing systems, cell sizing or deciding on the optimum number of machines to be allocated to each cell, and then allocation of specific machines to each cell. Although the latter problem has been investigated extensively there is a paucity of published work on the former. This paper discusses the effects of cell sizing on operational flexibility.

A solution methodolgy for optimal number of machines operated by a single worker

Abstract An optimal design problem is considered for a man-machine system, where a group of numerically controlled (NC) machines is operated by a single worker. The processing time at each machine and the service time by the worker are assumed to be random variables. The decision variable is the number of machines in the group and the optimal criterion is minimize the cost for producting a product. We propose an approximation method for obtaining the optimal number. Some numerical example are presented to show that the obtained number of machines is identical with the exact number when the coefficients of variations for service time and processing time distributions are greater than √0.25 and √0.5, respectively, although the method is approximate.

Machine assignments in production systems with manufacturing cells

SUMMARY In this paper we investigate flow shop production systems with manufacturing cells. We develop a procedure which enables us to determine the optimal number of machines for each operation, the optimal assignments of operations to manufacturing cells, and the optimal number of robots required in each cell such that the total production cost per unit is minimized.

Machine interference in automated cells

This paper presents a simulation and an analytical modeling of the machine interference problem in manufacturing cells. Each machine experiences two types of stoppage which are to be served by a robot. Several combinations of the distributions of the stoppages, service distributions, and service disciplines are studied. We determine the optimal number of machines assigned to the robot under different operating conditions such that the expected total cost of the manufacturing cell is minimized.

Human supervisory control in flexible manufacturing systems: Allocation of functions and system size

Abstract The objective of this study is to explore both the optimal allocation of tasks between the human supervisor and the computers in an FMS (flexible manufacturing sysytem) and the optimal number of machines in which a supervisor should control such a system. It is proposed that there is an interaction effect between the number of machines and the task allocation level and that an optimal level of machines exists for the operator to monitor. These hypotheses have been tested in a statistically balanced experimental design using 30 subjects with three independent variables: number of machines, task allocation, and sequence of task presentation. Physiological measures (electrocardiogram and respiratory rate), response time, and two subjective stress questionnaires were used as indices of arousal. The results revealed that the inverted‐U function for response time as a function of machine level was not supported but the effect of allocation level was significant for both performance and subjective stres...