Internal energy minimization in biarc interpolation

The problem of scheduling n multioperation jobs on a single machine such as the flexible manufacturing system is considered. Each job comprises up to F operations, which belong to several distinct families, and a sequence-independent setup time is incurred whenever an operation is to be processed following an operation of a different family. A job completes when all of its operations have been processed. Two variants with maximum lateness and total completion time as optimality criterion are considered. The problems are denoted as $1\left| {s_f ,{\text{assembly}},GT} \right|L_{\max } $ and $1\left| {s_f = 1,{\text{assembly}},GT,p_{ij} = 0\,{\text{or}}\,1} \right|\sum {C_j } $ . The decision is to sequence all the families in order to minimize the predefined criterion. This environment has a variety of real world applications such as flexible manufacturing systems scheduling and food industry scheduling. A heuristic is presented and a branch and bound is developed for benchmarking. Experimental results show that the heuristic provides good results and the branch and bound procedure is efficient. These results may narrow down the gap between easy and hard cases of the general problem.     

A hybrid cuckoo search and variable neighborhood descent for single and multiobjective scheduling problems

Cuckoo search (CS) is a relatively new meta-heuristic that has proven its strength in solving continuous optimization problems. This papers applies cuckoo search to the class of sequencing problems by hybridizing it with a variable neighborhood descent local search for enhancing the quality of the obtained solutions. The Lévy flight operator proposed in the original CS is modified to address the discrete nature of scheduling problems. Two well-known problems are used to demonstrate the effectiveness of the proposed hybrid CS approach. The first is the NP-hard single objective problem of minimizing the weighted total tardiness time ( \(1|| \sum {T_{w}}\) ) and the second is the multiobjective problem of minimizing the flowtime \(\overline {C}\) and the maximum tardiness T _{m a x} for single machine ( \(1|| (\frac {1}{n}\sum {C}, T_{max})\) ). For the first problem, computational results show that the hybrid CS is able to find the optimal solutions for all benchmark test instances with 40, 50, and 100 jobs and for most instances with 150, 200, 250, and 300 jobs. For the second problem, the hybrid CS generated solutions on and very close to the exact Pareto fronts of test instances with 10, 20, 30, and 40 jobs. In general, the results reveal that the hybrid CS is an adequate and robust method for tackling single and multiobjective scheduling problems.     

Single-machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning

The paper deals with some single-machine scheduling problems with setup time considerations where the processing time of a job is given as a function of its starting times and position in a sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth ( $ \delta \geqslant 0 $ ) power of job completion times, the total weighted completion time, the maximum lateness and the number of tardy jobs. We show that the makespan minimization problem, the total completion time minimization problem, and the sum of the δth power of job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

工件加工随机调度中优先约束问题的研究

讨论工件加工时间为任意随机分布的随机变量的单机随机调度问题,设工件间的约束为树优先约束,目标函数为极小化加权完工时间和的数学期望.这一模型在机械设计与制造行业中的多个元器组件加工,以及钢铁板坯轧制等众多实际生产制造领域中都具有广泛的应用背景.证明了工件加工时间为任意随机分布的随机变量的情况下,最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的调度为最优调度,给出了最优多项式算法,该算法可以被推广应用于实际的生产中,具有较强的实际应用性.     

Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

In this paper, we consider the single-machine setup times scheduling with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the total completion time, and the sum of the $\mathit{\delta}$ th ( ${\mathit{\delta}} \geq 0$ ) power of job completion times are polynomially solvable. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

Flow shop scheduling with deteriorating jobs under dominating machines to minimize makespan

In this paper, we consider an n-job, m-machine flow shop scheduling problem with deteriorating jobs. By deteriorating jobs, we mean jobs whose processing times are an increasing function of their execution starting time. A simple linear deterioration function is assumed. When some dominant relationships between m???1 machines can be satisfied, we show that the makespan minimization problem can be solved in polynomial time.     

Makespan minimization of a flowshop sequence-dependent group scheduling problem

The flowshop sequence dependent group scheduling problem with minimization of makespan as the objective (F _m |fmls, S _plk, prmu|C _max ) is considered in this paper. It is assumed that several groups with different number of jobs are assigned to a flow shop cell that has m machines. The goal is to find the best sequence of processing the jobs in each group and the groups themselves with minimization of makespan as the objective. A mathematical model for the research problem is developed in this paper. As the research problem is shown to be NP-hard, a hybrid ant colony optimization (HACO) algorithm is developed to solve the problem. A lower bounding technique based on relaxing a few constraints of the mathematical model developed for the original problem is proposed to evaluate the quality of the HACO algorithm. Three different problem structures, with two, three, and six machines, are used in the generation of the test problems to test the performance of the algorithm and the lower bounding technique developed. The results obtained from the HACO algorithm and those that have appeared in the published literature are also compared. The comparative results show that the HACO algorithm has a superior performance compared to the best available algorithm based on memetic algorithm with an average percentage deviation of around 1.0% from the lower bound.     

A note on single-machine total completion time problem with general deteriorating function

In this paper, we consider the single-machine scheduling problem with a deteriorating function. By the deteriorating function, we mean that the actual job processing time is a function of jobs already processed. We show that the total completion time minimization problem for a?≥?1 remains polynomially solvable under the proposed model, where a denotes the deterioration rate. For the case of 0?<?a?<?1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times. We use the classical smallest processing time first rule as a heuristic algorithm for the case of 0?<?a?<?1 and analyze its worst-case bound.     

Improved feature-based test statistic for assessing suitability of the preliminary samples for constructing control limits of \bar{X} chart

In spite of using a large number of subgroups (m) of small samples (n), the estimated control limits of $ \bar{X} $ chart in phase I can be erroneous unless the preliminary samples are drawn from a stable process. As a result, the performance of the chart in phase II can be significantly affected. The pattern in the $ \bar{X} $ chart, exhibited by the plots of the subgroup averages of the preliminary samples, will be different depending on stability and instability of the process while the preliminary samples were collected. Based on this concept, a new feature-based test statistic (FTS) is proposed for evaluating suitability of the preliminary samples for the designing of the $ \bar{X} $ chart. The FTS, for given m, approximately follows $ N[1,{\text{ SD(}}m{)]} $ , where SD(m) is a function of m. The goodness of the approximation and effectiveness of the test are evaluated using simulated data. The results show that both are satisfactory for m?>?=48. The proposed statistic is also quite effective in detecting unstable process condition resulting in a cyclic pattern. The computation of FTS involves some complexities. However, now-a-days computers are widely available and so computation difficulty may not be a problem.     

Optimization of cutting conditions of YG15 on rough and finish cutting in WEDM based on statistical analyses

In this paper, the effects and the optimization of cutting parameters on surface roughness (Ra) and material removal rate (MRR) in the wire electrical discharge machining (WEDM) of high hardness tool steel YG15 are analyzed. In the WEDM process, the key process parameters, such as pulse-on time, pulse-off time, power, cutting feed rate, wire tension, wire speed, and water pressure, are optimized. Experimental data were initially collected based on the Taguchi method of experimental design, which are $L_{18}\left (2^1\times 3^5\right )$ and $L_{18}\left (2^1\times 3^4\right )$ Taguchi standard orthogonal array on rough and finish cutting experiments, respectively. The level of importance of the cutting parameters on the Ra and MRR was determined on both finish and rough cutting by using statistical analyses; average gap voltage is discussed in order to balance cutting efficiency and stability on both finish and rough cutting. In addition, comparative analysis of finish and rough cutting is drawn to analyze the difference between rough cutting and finish cutting. Then, regression models and signal-to-noise ratio are used to obtain the optimum cutting parameter combination. Finally, the results present the optimized MRR and Ra of the rough and finish process, respectively, and confirm the efficiency and abilities of the model.     

Effect of gate dimension on micro injection molded weld line strength with polypropylene (PP) and high-density polyethylene (HDPE)

As a defect of micro injection molding parts, weld line is unfavorable since it will influence the surface quality and mechanical properties of micro parts. Therefore, the investigation on the developing process of weld line would be a significant issue for improving the quality of micro injection molded parts. In this study, one injection mold with four micro tensile sample cavities was designed and constructed. Every cavity responses to various gate dimensions, which is marked as Gate $ {\text{Nr}}.1\left( {1.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.2\left( {1.0 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.3\left( {1.0 \times 0.05 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , and $ {\text{Nr}}.4\left( {0.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ . The effects of gate dimension of the mold on mechanical properties of weld line have been studied by experiments in different processing parameters. The tensile test was used to characterize the micro injection molded weld line strength. The results for polypropylene show that with the changing of injection pressure and mold temperature, Gate Nr.3 is corresponding to the strongest weld strength; the next is Gate Nr.2; Gates Nr.4 and Nr.1 are in the end. The difference between them is not obvious. For high-density polyethylene, Gate Nr.1 is not able to be completely filled, which is due to the blocking of stick materials and dirt based on the simulation analysis. The investigation was only carried out for the other three gate sizes; results present that Gate Nr.3 always gives the best weld line strength whatever the processing parameters are, Gate Nr.4 is next and then Gate Nr.2. There are always middle optimal values for processing parameters leading to strongest weld line strength, when injection pressure is 80 MPa, injection speed is 90 cm³/s, melt temperature is 200°C, and mold temperature is 130°C. Higher and lower processing parameters result in reduced weld line strength.     

Scheduling stochastic job shop subject to random breakdown to minimize makespan

The problem of scheduling stochastic job shop subject to breakdown is seldom considered. This paper proposes an efficient genetic algorithm (GA) for the problem with exponential processing time and non-resumable jobs. The objective is to minimize the stochastic makespan itself. In the proposed GA, a novel random key representation is suggested to represent the schedule of the problem and a discrete event-driven decoding method is applied to build the schedule and handle breakdown. Probability stochastic order and the addition operation of exponential random variables are also used to calculate the objective value. The proposed GA is applied to some test problems and compared with a simulated annealing and a particle swarm optimization. The computational results show the effectiveness of the GA and its promising advantage on stochastic scheduling.     

Job scheduling and management of wearing tools with stochastic tool lifetimes

The problem of scheduling jobs using wearing tools is studied. Tool wearing is assumed to be stochastic and the jobs are processed in one machining centre provided with a limited capacity tool magazine. The aim is to minimize the expected average completion time of the jobs by choosing their processing order and tool management decisions wisely. All jobs are available at the beginning of the planning period. This kind of situation is met in production planning of CNC-machines. Previous studies concerning this problem have either assumed deterministic wearing for the tools or omitted the wearing completely. In our formulation of the problem, tool wearing is stochastic and the problem becomes very hard to solve analytically. A heuristic based on genetic algorithms is therefore given for the joint problem of job scheduling and tool management. The algorithm searches the most beneficial job sequence when the tool management decisions are made by a removal rule taking into account the future planned usage of the tools. The cost of each job sequence is evaluated by simulating the job processing. Empirical tests with heuristics indicate that by taking the stochastic information into account, one can reduce the average job processing time considerably.     

A branch and bound procedure for the reentrant permutation flow-shop scheduling problem

This investigation considers a reentrant permutation flow-shop (RPFS) scheduling problem whose performance criterion is makespan. A reentrant flow-shop (RFS) refers to situations in which every job must be processed on machines in the order, M ₁, M ₂, ..., M _m , M ₁, M ₂, ..., M _m , ..., and M ₁, M ₂, ..., M _m . Every job can be decomposed into several layers each of which starts on M ₁ and finishes on M _m . In the RFS case, if the job ordering is the same on any machine at each layer, then no passing is said to be allowed, since no job is allowed to pass any former job. The RFS scheduling problem in which no passing is allowed, is called an RPFS problem. A branch and bound algorithm is presented and an example is also given to illustrate the solution procedure. To compare the proposed algorithm, a series of computational experiments are done on randomly generated test problems and the results show that the developed algorithm is efficient.     

The curved wall jet over a circular cylinder before the interaction of two opposing curved wall jets

A curved wall jet before the interaction of two identical curved wall jets over a circular cylinder was investigated experimentally. Using hot-wire anemometry, the mean velocity, Reynolds stresses, and high order moments of the fluctuating velocity were measured. The turbulent kinetic energy and shear stress budgets were evaluated using the measured data. The correlation coefficient, ${{\overline {uv} } \mathord{\left/ {\vphantom {{\overline {uv} } {u'v'}}} \right. \kern-0em} {u'v'}}$ , the normal stress ratio, ${{\overline {v^2 } } \mathord{\left/ {\vphantom {{\overline {v^2 } } {\overline {u^2 } }}} \right. \kern-0em} {\overline {u^2 } }}$ , and the principal direction of the Reynolds stress are presented. The effects of curvature and adverse pressure gradient on these diistributions are also discurssed. The turbulent kinetic energy and shear stress budgets in two regions before the interaction are analyzed in detail to illuminate the effect of the adverse pressure gradient on the turbulent transport.     

Meta-heuristics to solve single-machine scheduling problem with sequence-dependent setup time and deteriorating jobs

This paper tackles the single-machine scheduling problem in which there are sequence-dependent setup times and deteriorating jobs. In this regard, a mathematical model has been formulated to minimize makespan (C _max). Afterwards, genetic and tabu search algorithms have been developed. Since the population diversity is a very important issue in preventing neighborhood search from trapping in a local optimum, some methods have been applied to genetic algorithm in order to maintain population diversity, and the final results show the effectiveness of these methods. The calibration of genetic algorithm parameters and operators is performed using design of experiments. Finally, several examples are produced to illustrate the proposed approach.     

Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models

The worker assignment scheduling problem involves both the decisions of job scheduling and worker assignment. In this research, only the performance measure of total tardiness is investigated in the model of identical parallel machines with nonpreemptive jobs. Since the worker assignment scheduling problem in the selected model can be shown to be NP-complete, heuristics have been developed for minimising the total tardiness. The worker assignment scheduling problem is solved in two phases of job scheduling and worker assignment. The SES (SPT, EDD, SLACK) heuristic is used for the phase of job scheduling. For the phase of worker assignment, the largest marginal contribution (LMC) procedure is used to minimise the total tardiness. From the simulation conducted, 88 out of 100 simulated problems yielded optimal solutions while the others also obtained very good results. In conclusion, the heuristics developed have shown very impressive results in both effectiveness and efficiency aspects.Notation n Total number of jobs waiting to be processed - m Total number of machines available to process the above jobs - J _i A set of n jobs are to be processed, i=1, ..., n - M _j A set of m machines are used to process these n jobs, j=1, ..., m - t _i (W _j ) The processing time needed for job J _i processed on machine M _j , where W _j workers have been assigned to M _j - t _j,[k](W _j ) The processing time function of the k ^th job assigned to machine M _j , where W _j workers have been assigned to M _j - d _i The due date of job J _i - d _j,[k] The due date of the k ^th job assigned to machine M _j - r _i the ready time of job J _i - C _i The completion time of job J _i - C _j,[k](W _j ) The completion time function of the k ^th job assigned to machine M _j , where W _j workers have been assigned to M _j ; - F _i The flow time of job J _i , F _i =C _{i –} r _i - L _i The lateness of job J _i , L _i =C _{i –} d _i - T _i The tardiness of job J _i , T _i =max{0, L _i } - T _j,[k] The tardiness of the k ^th job assigned to machine M _j , T _j,[k]=max{0, C _j,[k](W _j )–d _j,[k]} - N _j The number of jobs assigned to machine M _j - W _j The number of workers assigned to machine M _j - W The total number of workers     

Studies of chipping mechanisms for dicing silicon wafers

The purpose of this study was to investigate the chipping modes produced in the die edges of dicing silicon wafer using the thin diamond blades. The effects of dicing directions and different wafer types on the chipping size were studied. Furthermore, scratching tests were also used to assist the analysis of studying chipping conditions of the silicon wafer. The experimental results showed that the trace behaviors produced by the diamond indenter in the scratching test of silicon wafer can be divided into the three stages: rubbing, plastic deformation, cracking. The plastic pile up and crack of the scratching traces on the wafer mainly propagate along the development of the easiest slip direction family <110>. The chipping modes produced in dicing silicon wafer can be broadly classified as four types: (1) 30° chipping; (2) 60° chipping; (3) 90° chipping; (4) irregular chipping, which causes these mechanisms of chipping modes due to the meeting between the radial cracks of 30°, 60°, and 90° along the easiest slip direction family <110> and the lateral cracks along the easiest cleavage plane family {111}. When using the thin diamond blade diced on the (111) silicon wafer along the $ {\left[ {\overline{1} 10} \right]} $ direction, the size of top chipping produced was smaller than that of along the $ {\left[ {11\overline{2} } \right]} $ direction. Besides, for the (100) plane of silicon wafer, the size and the distribution of the chipping modes produced along the $ {\left[ {\overline{1} 10} \right]} $ and $ {\left[ {\overline{1} \overline{1} 0} \right]} $ directions were similar.     

A calorimeter for detecting hadrons with energies of 10–100 GeV

A calorimeter for detecting hadrons in the energy range 10–100 GeV is described. It is used at CERN in the NA58 (COMPASS) experiment aimed at studying the nucleon structure and spectroscopy measurements of charmed particles. The calorimeter is composed of 480 modules with a cross section of 15×15 cm², assembled in a matrix with dimensions of 4.2×3 m² and a central window of area 1.2×0.6 m². In each module are 40 iron and scintillator layers of a total thickness of 4.8 interaction lengths. The energy resolution of the calorimeter for hadrons (pions) and electrons and the spatial resolution, determined on the test beams, are $\frac{{\sigma _\pi (E)}}{{E[GeV]}} = \frac{{59.4 \pm 2.9}}{{\sqrt E }} \oplus (7.6 \pm 0.4)\% ;\frac{{\sigma _e (E)}}{{E[GeV]}} = \frac{{24.6 \pm 0.7}}{{\sqrt E }} \oplus (0.7 \pm 0.4)\% $ , and σ _x,y ≈ 15 mm, respectively. The average value of the e/π ratio that characterizes the amplitude responses of the calorimeter to electrons and pions with equal energies from the above range is 1.2 ± 0.1. This study was performed at the JINR Laboratory for Particle Physics.