Deterministic Processing Times Research Articles

The Impact of Processing Time Variations on Swap Sequence Performance in Dual-Armed Cluster Tools

The performance of a swap sequence is analyzed by assuming cyclic scheduling in dual-armed cluster tools with processing time variations. A dual-armed cluster tool consists of multiple processing modules (PMs), one material handling robot that can hold two wafers at the same time, and loadlocks where wafer cassettes are loaded or unloaded. The swap sequence in a dual-armed cluster tool is widely used in practice and known to be optimal with deterministic processing times when the bottleneck PM’s workload is larger than the robot workload. However, in practice, processing times on a PM can have a small variation, which leads to a different processing time of each wafer on the PM. Hence, when the processing time variation is introduced, the performance of the swap sequence needs to be analyzed. This paper first defines a fundamental cycle and analyzes its cycle time. It then proposes optimality conditions of the swap sequence and performs numerical experiments to show the effectiveness of the sequence. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A dual-armed cluster tool used for semiconductor manufacturing processes is usually operated with a swap sequence because it is simple, easy to control, and proven to be optimal with deterministic processing times. However, studies on the performance of the swap sequence are still limited with processing times varying in PMs which often occur in practice. Hence, this study shows the effectiveness of the swap sequence with the processing time variations by analyzing cycle times, optimality conditions, and performing numerical experiments.

A Markovian model of asynchronous multi-stage manufacturing lines fabricating discrete parts

Asynchronous serial manufacturing lines that fabricate discrete parts are traditionally used in mass production, which represents a key sector in the global economy. Recent technological solutions for the modularization and standardization of manufacturing stations have led to this type of manufacturing system being reconfigured more often than in the past. Therefore, synthetic but accurate performance-evaluation models have become relevant as kernels in decision supporting tools for the continuous improvement of manufacturing systems. This paper presents a novel analytical model for the performance evaluation of asynchronous unreliable manufacturing lines fabricating discrete parts with finite buffers and deterministic processing times. This approach is based on continuous-time continuous-flow Markov chains. The general concept of operational cycles in discrete production is integrated into the modeling. The proposed model was validated using a discrete event simulation. The results demonstrate the accuracy and robustness of this model in evaluating a wide set of performance measures. The advantages of using this approach with respect to a purely continuous model were demonstrated. The applicability of the model to actual industrial scenarios was also demonstrated in a use case involving a high-volume assembly line.

Flexible Job Shop Scheduling Problem with Fuzzy Times and Due-Windows: Minimizing Weighted Tardiness and Earliness Using Genetic Algorithms

The current requirements of many manufacturing companies, such as the fashion, textile, and clothing industries, involve the production of multiple products with different processing routes and products with short life cycles, which prevents obtaining deterministic setup and processing times. Likewise, several industries present restrictions when changing from one reference to another in the production system, incurring variable and sequence-dependent setup times. Therefore, this article aims to solve the flexible job shop scheduling problem (FJSSP) considering due windows, sequence-dependent setup times, and uncertainty in processing and setup times. A genetic algorithm is proposed to solve the FJSSP by integrating fuzzy logic to minimize the weighted penalties for tardiness/earliness. The proposed algorithm is implemented in a real-world case study of a fabric finishing production system, and it is compared with four heuristics adapted to the FJSSP such as earliest due date, critical reason, shortest processing time, and Monte Carlo simulation. Results show that the performance of the proposed algorithm provides efficient and satisfactory solutions concerning the objective function and computing time since it overperforms (more than 30%) the heuristics used as benchmarks.

Compensating for part arrival uncertainties in two-processing-machine, one-buffer flow lines: Inventory flexibility design based on the system transient performances

• A structured Markov process model for the proposed flow lines;. • Transition equation derivation for the flow lines;. • The algorithms for factoring a class of states to derive closed-form expressions;. • System transient performance analysis of the flow lines system;. • Discrete event dynamic system simulation and verification. In one-of-a-kind production (OKP), a flow line with two distinct deterministic processing time machines and one “flexible” storage buffer is studied from the perspective of manufacturing system design and transient behaviour analysis. This manufacturing process is disrupted by part arrival uncertainties and is considered a discrete dynamic stochastic system. The dynamic behaviour of the flow line is structured as a transfer line with multi-state machines and finite-storage buffers by a discrete-time, discrete-state Markov chain for the transient performance analysis, optimal design and efficient production operation. To assess the dynamic disruptions and further limit the cascading effects on the flow line, in the presented analytical model, the studies quantify the evolution of a basic serial production process over time; and meanwhile, we evaluate and optimize the manufacturing system transient performance to determine the optimal design of inventory flexibility as a function of the time and states. By factoring out a class of appropriate transient states associated with an initial state at a certain time slot and deriving closed-form expressions using the transition equations, we sought to determine the transient probabilities of the manufacturing system states to establish relationships between the variable system parameters and the performance measures. By embedding these practical results with quantitative precision in an optimal design process of inventory flexibility, we consider setting the storage buffer level between two processing machines for refined production optimization and control when the part arrival uncertainties and lack of synchronization constantly occur in this serial manufacturing system.

Memetic algorithm for unrelated parallel machine scheduling problem with grey processing times

PurposeThis paper aims to provide a promising memetic algorithm (MA) for an unrelated parallel machine scheduling problem with grey processing times by using a simple dispatching rule in the local search phase of the proposed MA.Design/methodology/approachThis paper proposes a MA for an unrelated parallel machine scheduling problem where the objective is to minimize the sum of weighted completion times of jobs with uncertain processing times. In the optimal schedule of the problem’s single machine version with deterministic processing time, the machine has a sequence where jobs are ordered in their increasing order of weighted processing times. The author adapts this property to some of their local search mechanisms that are required to assure the local optimality of the solution generated by the proposed MA. To show the efficiency of the proposed algorithm, this study uses other local search methods in the MA within this experiment. The uncertainty of processing times is expressed with grey numbers.FindingsExperimental study shows that the MA with the swap-based local search and the weighted shortest processing time (WSPT) dispatching rule outperforms other MA alternatives with swap-based and insertion-based local searches without that dispatching rule.Originality/valueA promising and effective MA with the WSPT dispatching rule is designed and applied to unrelated parallel machine scheduling problems where the objective is to minimize the sum of the weighted completion times of jobs with grey processing time.

A new mathematical formulation and a hybrid evolutionary algorithm for re-entrant flow-shop problem with release date

In this paper, we address the weighted multi-objective re-entrant flow-shop scheduling problem considering release dates in order to minimize makespan, total completion time, total tardiness, maximum idle time, and number of tardy jobs. Each job is taken into account with deterministic processing times, and release dates. The flow-shop comprised of two workshops in whose jobs are entered to the main workshop and after the first part of the processing, they are transferred to the second workshop and after this stage, the jobs are returned to the main workshop for the last part of the processing. We model the problem by a new mixed integer programming based on formulating sum of idle time as a new concept. Moreover, a hybrid evolutionary algorithm is proposed based on some dispatching rules, ant colony optimization, and genetic algorithm. The performance of the proposed algorithm on some test instances is compared to the mixed integer linear programming model as well as the state-of-the-art algorithms called genetic algorithm, tabu search, bio-geography based optimization, and artificial bee colony. The computational experiments show that our proposed approach outperforms other algorithms and the results indicate efficiency and capability of the proposed algorithm in comparison with the traditional algorithms.

A Secure Live Signature Verification with Aho-Corasick Histogram Algorithm for Mobile Smart Pad

There is a long history of using handwritten signatures to verify or authenticate a “signer” of the signed document. With the development of Internet technology, many tasks can be accomplished through the document management system, such as the applications of digital contracts or important documents, and more secure signature verification is demanded. Thus, the live handwriting signatures are attracting more interest for biological human identification. In this paper, we propose a handwriting signature verification algorithm by using four live waveform elements as the verification features. A new Aho-Corasick Histogram mechanism is proposed to perform this live signature verification. The benefit of the ACH algorithm is mainly its ability to convert time-series waveforms into time-series short patterns and then perform a statistical counting on the AC machine to measure the similarity. Since AC is a linearly time complexity algorithm, our ACH method can own a deterministic processing time. According to our experiment result, the proposed algorithm has satisfying performance in terms of speed and accuracy with an average of 91% accuracy.

Performance evaluation of asynchronous two-stage manufacturing lines fabricating discrete parts

Asynchronous systems with deterministic processing times are critical for fabricating discrete parts, especially in countries offering high salaries. Despite their widespread application, it is difficult to analyze these systems using conventional analytical modeling tools as commonly used hypotheses for these models consider different conditions compared to real behaviors. This paper presents a new analytical model for the performance evaluation of asynchronous two-stage manufacturing lines fabricating discrete parts with finite buffer capacity. A continuous-time Markov chain flow model that mimics the behavior of discrete asynchronous manufacturing systems by employing threshold-based control mechanisms is presented. The results obtained with the proposed model are compared with those using discrete event simulation, and they show good agreement. The model proposed in this paper can be used as a building block for the evaluation of longer asynchronous lines.

Regenerative scheduling problem in engineer to order manufacturing: an economic assessment

The dynamic production scheduling is a very complex process that may arise from the occurrence of unpredictable situations such as the arrival of new orders besides the ones already accepted. As a consequence, companies may often encounter several difficulties to make decisions about the new orders acceptance and sequencing along with the production of the existing ones. With this recognition, a mathematical programming model for the regenerative scheduling problem with deterministic processing times is formulated in the present paper to evaluate the economic advantage of accepting a new order in an engineer to order (ETO) manufacturing organization. The real case of an Italian ETO company which produces hydraulic marine and offshore cranes is afterwards presented.

A Markov Chain model for the performance evaluation of manufacturing lines with general processing times

This paper presents a Markov Chain approximation to model stations in manufacturing lines with general distributed processing times. The proposed Markov Chain approximation enables the use of continuous flow models for the performance evaluation of serial lines with finite buffers and mixed manual – automated operations. Each station in the line can consist of a highly automated machine with deterministic processing times, or of a human operator performing manual operations with general distributed processing times. Stations with random processing times are modelled through a continuous time – discrete state Markov Chain characterized by an operational state with a deterministic processing time, and by an auxiliary down state used to stochastically dilate the overall completion time of a part on the station. The Markov Chain parameters are defined through moments fitting of the probability distribution of the processing time of the original station. The resulting Markov Chain represents the behavior of the station in isolation and is then used as input in the decomposition techniques, based on continuous flow models, for the performance evaluation of serial lines. The model has been applied in the analysis of the production performances of a real assembly line.

Efficient scheduling of a stochastic no-wait job shop with controllable processing times

This work derives a novel effective and efficient algorithm for a stochastic no-wait job-shop scheduling problem with controllable processing times. Some of the processing times are stochastic and the proposed solution effectively minimizes the makespan and increases the robustness of the makespan against deviating processing times. Therefore, a no-wait job shop with controllable deterministic processing times is solved by a decomposition into timetabling and sequencing. During timetabling, extra safety margins are added to the scheduled processing times without delaying jobs. In the sequence optimization subproblem, an extra penalty term is added to the cost function which punishes uncertain tasks at positions that have an impact on the makespan. Simulation results based on real plant data and tailor-made benchmark problems show that these measures can reduce the standard deviation of the makespan dramatically. This significantly improves the prediction accuracy of the scheduling method.

Analysis of Backward Sequence for Single-Armed Cluster Tools With Processing Time Variations

This article analyzes the backward sequence for single-armed cluster tools with processing time variations. The backward sequence is popularly used to operate a single-armed cluster tool in practice, but its performance has not been analyzed when processing time variations are introduced. To address the problem, we first define a fundamental cycle and derive a formula for cycle time analysis considering processing time variations. We then develop conditions for which the backward sequence is optimal for a certain cycle or all cycles. We also analyze the upper bound of the average cycle time with the backward sequence. Finally, the performance of the backward sequence with processing time variations is investigated experimentally. Note to Practitioners —The backward sequence, which is widely used for scheduling single-armed cluster tools, is analyzed with processing time variations in processing modules (PMs). The backward sequence is proven to be optimal in many cases with deterministic processing times. However, in reality, the wafer processing time in a PM is not deterministic and varies within a given time range. With regard to this issue, we analyze the performance of the backward sequence with processing time variations. This study can be very helpful for not only tool engineers but also for researchers who are interested in scheduling automated manufacturing systems.

Minimizing makespan on a single machine with release dates and inventory constraints

We consider a single-machine scheduling problem with release dates and inventory constraints. Each job has a deterministic processing time and has an impact (either positive or negative) on the central inventory level. We aim to find a sequence of jobs such that the makespan is minimized while all release dates and inventory constraints are met. We show that the problem is strongly NP-hard even when the capacity of the inventory is infinite. To solve the problem, we introduce a time-indexed formulation and a sequence-based formulation, a branch-and-bound algorithm, and a dynamic-programming-based guess-and-check (GC) algorithm. From extensive computational experiments, we find that the GC algorithm outperforms all other alternatives.

Two-sided assembly line balancing that considers uncertain task time attributes and incompatible task sets

An assembly line is a serial production system that is meant to produce high-quality and usually complex products in mass quantities. Assembly lines play a crucial role in determining the profitability of a company, as they are utilised as the final stage of the system prior to shipping. In an assembly line balancing problem, the assembly tasks are allocated to workstations based on their processing times after considering the precedence relationships between them. There is a massive amount of research in the literature using deterministic task processing times, and many other works consider stochastic task times. This research utilises the uncertainty theory to model uncertain task times and considers incompatible task sets constraints. The problem is solved using a simulated annealing algorithm with problem-specific characteristics. Lower bounds are developed to accelerate the simulated annealing algorithm. A restart mechanism, which can escape the local optimum obtained by neighbourhood generation, is proposed. A repair mechanism is integrated to combine the workstations so as to further improve the quality of solutions. The numerical examples and experimental tests demonstrate the powerful solution-building capacity of the proposed simulated annealing algorithm over teaching–learning-based and genetic algorithms. The methodology proposed in this research is applicable to any industry (including the automotive industry) when the historical data on task processing times is very limited.

A multi-objective pigeon inspired optimization algorithm for fuzzy production scheduling problem considering mould maintenance

The fuzzy production scheduling problem considering mould maintenance (FPSP-MM) is studied. The processing time and the maintenance time are represented by triangular fuzzy numbers. When tasks are executed based on the sequence provided by the fuzzy schedule, the real duration of each task needs to be known so the posteriori solution with deterministic processing times can be obtained. Therefore, the concept of the schedule robustness needs to be considered for the fuzzy problem. The robustness is considered as the optimization objective except for the fuzzy makespan in this research. To optimize these two objective functions, a multi-objective pigeon inspired optimization (MOPIO) algorithm is developed. To extend the pigeon inspired optimization (PIO) algorithm from the single-objective case to the multi-objective case, non-dominated solutions are used as candidates for the leader pigeon designation and a special crowding distance is used to ensure a good distribution of solutions in both the objective space and the corresponding decision space. Furthermore, an index-based ring topology is used to manage the convergence speed. Numerical experiments on a variety of simulated scenarios show the excellent efficiency and effectiveness of the proposed MOPIO algorithm by comparing it with other algorithms.

Greed Works—Online Algorithms for Unrelated Machine Stochastic Scheduling

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work and depend linearly on an upper bound on the squared coefficient of variation of the jobs’ processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 6, respectively. As to the technical contribution, this paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.

Artificial immune system and particle swarm optimisation algorithms for an integrated production and distribution scheduling problem

This paper investigates an integrated production and distribution scheduling problem in a make to order supply chain. In the production part, manufacturing lots of different kinds of same product are produced on machines in a flow shop environment. All the products have a deterministic processing time and a sequence dependent setup time on each machine. In the distribution part, delivering of manufacturing lots to different customers are made by distribution centres having several modes of shipping. A mathematical model is developed and two algorithms, i.e., artificial immune system (AIS) and particle swarm optimisation (PSO) are proposed and illustrated. The proposed methodologies are evaluated for its solution quality by comparing with solutions obtained by CPLEX and CP solver. The comparison reveals that AIS algorithm generates better solution than PSO algorithm and CP and is capable of providing solution either equal or closer to lower bound value provided by CPLEX.

MODELING, OPTIMISATION AND ANALYSIS OF RE-ENTRANT FLOWSHOP JOB SCHEDULING WITH FUZZY PROCESSING TIMES

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.21

Closed-form formulae for moment, tail probability, and blocking probability of waiting time in a buffer-sharing deterministic system

Obtaining analytic expressions for characteristics in probabilistic systems with finite buffer capacities such as (higher) moments and tail probabilities of stationary waiting times, and blocking probabilities is by no means trivial. This is also true even for a system with deterministic processing times. By using the max–plus algebraic approach in this study, we introduce closed-form formulae for characteristics of stationary waiting time in a complete buffer-sharing m-node tandem system with constant processing times. Numerical examples are also provided.

Strategic WIP Inventory Positioning for Make‐to‐Order Production with Stochastic Processing Times

It is vital for make‐to‐order manufacturers to shorten the lead time to meet the customers’ requirements. Holding work‐in‐process (WIP) inventory at more stations can reduce the lead time, but it also brings about higher inventory holding cost. Therefore, it is important to seek out the optimal set of stations to hold WIP inventory to minimize the total inventory holding cost, while meeting the required due date for the final product at the same time. Since the problem with deterministic processing times at the stations has been addressed, as a natural extension, in this study, we address the problem with stochastic processing times, which is more realistic in the manufacturing environment. Assuming that the processing times follow normal distributions, we propose a solution procedure using genetic algorithm.