Unequal Times Research Articles

Evolution of nanoripples on silicon by gas cluster-ion irradiation

Si wafers of (100), (110) and (111) orientations were bombarded by gas cluster ion beam (GCIB) of 3000 Ar-atoms/cluster on average at a series of angles. Similar surface morphology ripples developed in different nanoscales. A simple scaling functional satisfactorily describe the roughness and wavelength of the ripple patterns as a function of dosage and angle of incidence. The ripples are formed orthogonal to the incident cluster-ions at large off-normal angles. An ellipsoidal pattern was created by two consecutive irradiations incident in mutually orthogonal directions with unequal exposure times between each irradiation, from 7:1 to 10:1, beyond which the original ripple imprints would be over-written. This work was inspired by use of the ripples to seed growth of controlled nanostructures without patterning by lithography or predeposition of catalysts.

The single-machine total tardiness problem with unequal release times and a linear deterioration

Recently, machine scheduling problems with deteriorating jobs have received more attention from the scheduling research community. In this paper we consider a single-machine scheduling problem with a linear deteriorating effect and unequal release times. The objective is to minimize the total tardiness. We propose a branch-and-bound algorithm incorporating with several dominance properties and two lower bounds to search for the optimal solution. In addition, we propose a marriage in honey-bees optimization algorithm (MBO) to provide a near-optimal solution. The computational experiment is also conducted to evaluate the impacts of the parameters over the performances of the proposed algorithms.

The burn-in test scheduling problem with batch dependent processing time and sequence dependent setup time

The burn-in test scheduling problem (BTSP) is a variation of the complex batch processing machine scheduling problem, which is also a generalisation of the liquid crystal injection scheduling problem with incompatible product families and classical identical parallel machine problem. In the case we investigated on the BTSP, the jobs are clustered by their product families. The product families can be clustered by different product groups. In the same product group, jobs with different product families can be processed as a batch. The batch processing time is dependent on the longest processing time of those jobs in that batch. Setup times between two consecutive batches of different product groups on the same batch machine are sequentially dependent. In addition, the unequal ready times are considered in the BTSP which involves the decisions of batch formation and batch scheduling in order to minimise the total machine workload without violating due dates and the limited machine capacity restrictions. Since the BTSP involves constraints on unequal ready time, batch dependent processing time, and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with compatible product families or incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Consequently, this paper proposes a mixed integer programming model to solve the BTSP exactly. In addition, two efficient solution procedures which solve the BTSP are also presented.

Single machine scheduling with unequal release times and idle insert for minimizing the sum of maximum earliness and tardiness

This paper addresses the problem of minimizing the sum of maximum earliness and tardiness on a single machine with unequal release times and idle insert as realistic assumptions and based on actual manufacturing environments. This problem is shown in the literature that is NP-hard in the strong sense, so there is no polynomial-time algorithm to solve it. Therefore, an exact branch-and-bound scheme is proposed to sequence the jobs by means of efficient dominance rules, lower and upper bounds. Moreover, a polynomial time algorithm to optimally minimize the objective function is developed to insert idle times and schedule the known sequence of jobs in each node of the search tree. To evaluate the efficiency of the proposed algorithm, 720 instances in nine series are randomly generated. Considering the complexity of the problem, the algorithm is capable of solving problems of up to 20 jobs. In addition, two evolutionary metaheuristic algorithms, genetic algorithm and particle swarm optimization, are provided and compared for large-job sizes. Computational results in 3420 randomly generated instances have shown that the proposed genetic algorithm improves the solutions in terms of both quality and time efficiency and that it would be capable of solving the problem of small to large sizes.

A Mixed Integer Mathematical Programming Optimization Model for the NP-Hard Industrial Processes Scheduling Problem

This paper investigates single machine scheduling problem with unequal release times and deterioration jobs where the objective function of it is minimal makespan. A mixed integer mathematical programming optimization model is developed for the problem which belongs to the NP-hard problem. The model is tested on examples and compared with a heuristic algorithm introduced by Lee et al.. Moreover, the branch-bound algorithm proposed by Lee et al. also can obtained optimal solutions the same as the results from CPLEX but the CPU time of it for 28 jobs even needs more than 2 hours, thus, the results between them are not compared. According to results of computational tests, it is showed that the proposed model is very effective in solving problems because it can obtain optimal solutions within a short time. Therefore, it is very useful and valuable for decision maker who requires the optimal solutions.

Spin, angular momentum and spin-statistics for a relativistic quantum many-body system**This paper is dedicated to the memory of Constantin Piron.

The adaptation of Wigner’s induced representation for a relativistic quantum theory making possible the construction of wave packets and admitting covariant expectation values for the coordinate operator xμ introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch–Gordan coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many-body systems and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are briefly discussed.

A study of the single-machine two-agent scheduling problem with release times

In many management situations, multiple agents compete on the usage of common processing resources. On the other hand, the importance of the ready times can be shown in Wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. However, research on scheduling with two-agent and ready time simultaneously is relatively unexplored. This paper addresses a single-machine two-agent scheduling problem with ready times. The aim is to find an optimal schedule to minimize the total completion time of the jobs of the first agent with the restriction that total completion time is allowed an upper bound for the second agent. To the best of our knowledge, the problem under study has not been considered. Firstly, we show that the proposed problem is strongly NP-hard. Following that, we then develop a branch-and-bound, an ant colony, and four genetic algorithms for an optimal and near-optimal solution, respectively. In addition, the extensive computational experiments are also given.

Role of PEDOT layer in polymeric LEDs

The effects of four kinds of poly(3,4-ethylenedioxythiophene) (PEDOT) dispersions in indium tin oxide/PEDOT/poly(9,9-dihexyl-9H-fluorene-2,7-diyl) (PF)/Al organic light emitting diodes have been tested: two PEDOT/polystyrene sulphonate blends and two poly3,4-ethylenedioxythiophene-co-polyethylene glycol copolymers. Current–voltage measurements and admittance spectra have revealed a strong dependence of the device current on the PEDOT conductivity rather than on the barrier height. The performed dynamic tests have given unequal relaxation times due to the different interface dipoles at the PEDOT/PF junction. The hypothesis of PEDOT Fermi level pinning and the device relaxation are analysed and discussed.

Scheduling identical parallel machines with machine eligibility restrictions to minimize total weighted flowtime in automobile gear manufacturing

In this paper, we address a scheduling problem for minimizing total weighted flowtime, observed in automobile gear manufacturing. Specifically, the bottleneck operation of the pre-heat treatment stage of gear manufacturing process has been dealt with in scheduling. Many real-life scenarios like unequal release times, sequence dependent setup times, and machine eligibility restrictions have been considered. A mathematical model taking into account dynamic starting conditions has been proposed. The problem is derived to be NP-hard. To approach the problem, a few heuristic algorithms have been proposed. Based on planned computational experiments, 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 the estimated optimal solution for large-size problem instances. Extensive computational analyses reveal that the proposed heuristic algorithms are capable of consistently yielding near-statistically estimated optimal solutions in a reasonable computational time.

Iterated hybrid metaheuristic algorithms for unrelated parallel machines problem with unequal ready times and sequence-dependent setup times

The problem considered in this paper involves a set of independent jobs on unrelated parallel machines with sequence-dependent setup times and unequal ready times, and the objective is to minimize the weighted number of tardy jobs. Iterated hybrid metaheuristic algorithms are proposed to address this problem. The algorithms begin with effective initial solution generators to generate initial feasible solutions; then, hybrid metaheuristics are applied to improve the initial solutions, integrating the principles of the variable neighborhood descent approach and tabu search. If the search becomes trapped at a local optimum, a perturbation operator is developed to help the search escape. To evaluate the performance of the suggested algorithms, heuristic rules and iterated local search algorithms are examined and compared. Computational experimental results show that the proposed algorithms outperform the other heuristics.

A simulated annealing algorithm to minimize makespan of parallel batch processing machines with unequal job ready times

A simulated annealing (SA) algorithm to minimize the makespan on a group of identical batch processing machines arranged in parallel is presented. We consider the case where each job has an arbitrary processing time, non-identical size, and non-zero ready time. Each machine can process simultaneously several jobs as a batch as long as the machine capacity is not exceeded. The batch processing time is equal to the largest processing time among those jobs in the batch. Similarly, the batch ready time is equal to the largest ready time among all the jobs in the batch. Random instances were used to compare the results of the SA approach against a lower bound, a mathematical model, and two heuristics published in the literature: the Modified Delay (MD) heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP). Computational experiments showed that the SA approach is comparable to GRASP with respect to solution quality, and less computationally costly. Both SA and GRASP comfortably outperformed the MD heuristic.

Heuristic algorithms for scheduling on uniform parallel machines with heads and tails

This paper considers the uniform parallel machine scheduling problem with unequal release dates and delivery times to minimize the maximum completion time. For this NP-hard problem, the largest sum of release date, processing time and delivery time first rule is designed to determine a certain machine for each job, and the largest difference between delivery time and release date first rule is designed to sequence the jobs scheduled on the same machine, and then a novel algorithm for the scheduling problem is built. To evaluate the performance of the proposed algorithm, a lower bound for the problem is proposed. The accuracy of the proposed algorithm is tested based on the data with problem size varying from 200 jobs to 600 jobs. The computational results indicate that the average relative error between the proposed algorithm and the lower bound is only 0.667%, therefore the solutions obtained by the proposed algorithm are very accurate.

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.

Semianalytical Solution for Nonequilibrium Sorption of Pollutant Transport in Streams

During pollutant transport in a stream, many pollutants get adsorbed in the streambed materials and are subsequently released. A conceptual hybrid-cells-in-series model for adsorption (HCIS-A), which consists of a plug flow zone and two thoroughly mixed zones of unequal residence times, has been developed to simulate adsorption-desorption in addition to advection and dispersion processes. Sorption processes governed by first-order mass exchange kinetics along with advection in the plug flow zone have been solved analytically using the Laplace transform technique. Analytical solutions have been derived for transport of pollutants through the first and second thoroughly mixed zones of the hybrid model considering sorption. Using the convolution technique and ramp kernel coefficients, the pollutants have been routed through all the zones to derive a semianalytical solution at the end of first hybrid unit. The advantages of this conceptual hybrid model are (1) the conversion of the second-order partial differential equation to a first-order ordinary differential equation; (2) the model’s capacity to incorporate variation of stream geometry and flow velocity in different stream reaches; and (3) the model’s capability to incorporate sorption kinetics. The responses of the hybrid model correspond to the finite-difference solutions of the partial differential equation (PDE) that accounts for advection, dispersion, and adsorption. The first arrival time of the pollutant downstream of a point disposal has been estimated. This is not clearly identified in other models. The effect of sorption on pollutant transport was studied and demonstrated in various C-t profiles as the pollutant moved downstream of a disposal point. The characteristics of the C-t profiles for a conservative pollutant in streams with adsorbing streambed were in the expected trend.

Simultaneous determination of lot size and production rate at capacity-constrained multiple-product systems

In the capacity constrained manufacturing systems where multiple product types are manufactured, the products are often produced in lots. Although the lot production may increase the system throughput by reducing changeover times, it may also increase production lead time because each item in a large lot has a long waiting time. Hence, a production manager should consider both throughput and lead time at the same time when deciding production lot sizes. This paper, which is an extension to the previous work done in Koo et al. (2007) that assumes homogeneous setup times, addresses a lot sizing problem in the system with multiple product types and unequal setup times. We develop a non-linear optimization model for simultaneous determination of throughput rate and lot size for each product. Since this optimization model cannot be solved analytically, we propose a heuristic solution procedure by analyzing the characteristics of the problem. Some numerical examples are presented to validate the proposed model, and finally the performance of the heuristic procedure is evaluated by comparison with the results of simulation experiments.

The liquid crystal injection scheduling problem (LCISP)

In this paper, the liquid crystal injection scheduling problem (LCISP) involving the constraints on limited maximum waiting times, unequal ready times, and machine setup times is considered to form the batches with incompatible product families and to sequence those batches on identical parallel batch processing machines. The batch scheduling problem, LCISP, has many applications, especially in thin film transistor liquid crystal display (TFT-LCD) factories at the cell assembly stage. In the LCISP, the objective is to minimise the total machine workload without violating the limited maximum waiting time restriction. Furthermore, machine setup times that are sequence dependent for two consecutive batches classified into different product families on the same machine are also considered. Since the LCISP involves constraints on limited maximum waiting times and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Therefore, this paper proposes a mixed integer programming model to solve the LCISP exactly. In addition, two efficient solution procedures which solve the LCISP are also presented.

Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times

In scheduling of batch processing machines in the diffusion and oxidation areas of a wafer fabrication facility, it can be found that the processing times of these batching operations can be extremely long (10 h) when compared to other operations (1–2 h) in a wafer fab. Moreover, the jobs to be processed may have different priorities/weights, due dates and ready times. In the presence of unequal ready times, it would be better to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, repeated processing of similar tasks improves workers’ skills. Motivated by these observations, we consider a single-machine problem with the sum of processing times based learning effect and release times. The objective is to find a schedule to minimize the total completion times. We first develop a branch-and-bound algorithm for the optimal solution. Then we propose a simulated-annealing heuristic algorithm for a near-optimal solution. Finally, we conduct a computational experiment to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 24 jobs, and the average error percentage of the simulated-annealing algorithm is less than 0.1482%.

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.

Branch-and-bound and simulated annealing algorithms for a total weighted completion time scheduling with ready times and learning effect

The importance of the ready times can be found in wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations, it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, scheduling with learning effect has received growing attention nowadays. However, research with learning and ready times is relatively unexplored. Motivated by this observation, we consider a single-machine problem with learning effect and ready times where the objective is to minimize the total weighted completion time. We develop a branch-and-bound algorithm and a simulated annealing algorithm for the problem. The results show that the branch-and-bound algorithm can solve instances up to 15 jobs, and the average error percentage of the simulated annealing algorithm is less than 0.25%.

Minimizing the makespan on a single machine with learning and unequal release times

The importance of the ready times can be found in Wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, there is a significant involvement of humans in scheduling environments; the amount of learning activities is high. Hence it seems to be reasonable to consider learning in scheduling environments. However, research with learning and release times is relatively unexplored. Motivated by this observation, this paper deals with a single-machine problem with the learning effect and release times where the objective is to minimize the makespan. This paper proposes a branch-and-bound algorithm and three two-stage heuristic algorithms for the problem. The computational experiments show that the branch-and-bound algorithm can solve instances up to 25 jobs, and the best one with the average error percentage of the proposed heuristics is less than 0.05%.