Deterministic Processing Times Research Articles

Scheduling assembly tasks with caterpillar precedence constraints on dedicated machines

In this work, we address the problem of scheduling a set of n non-preemptive tasks on m dedicated machines in order to minimise the makespan. For each task deterministic processing times and a specific processing machine are given, moreover a set of precedence constraints among the tasks are known. We present a heuristic and some lower bounds on the minimum makespan for a relevant case in manufacturing applications, namely when the precedence constraints form a caterpillar graph. A caterpillar is a directed tree consisting of a single directed path and leaf nodes each of which is incident to the directed path by exactly one incoming arc. A number of computational experiments are also performed in order to test the performance of the proposed solution algorithm.

Lawler’s minmax cost problem under uncertainty

The well-known \(O(n^2)\) minmax cost algorithm of Lawler (Manag Sci 19(5):544–546, 1973) was developed to minimize the maximum cost of jobs processed by a single machine under precedence constraints. We first develop a fast updating algorithm to obtain optimal solutions for two neighboring instances. This method will be used throughout this article. Then we consider job cost functions that depend on the completion time and on one or more additional numerical parameters. The parameters are uncertain and take values from given intervals. Under the uncertainty, we apply the minmax regret criterion for choosing a solution. We generalize results by Brauner et al. (J Sched, 2015) for decomposable cost functions with deterministic processing times and a single uncertain parameter to general cost functions. We describe different conditions, under which minmax regret solutions can be obtained with the time complexity \(O(n^3)\) or \(O(n^2)\). Then the updating algorithm is applied to the lateness model by Kasperski (Oper Res Lett 33:431–436, 2005) where both the processing time and the due date of each job are uncertain. The original \(O(n^4)\) running time is improved to the time complexity \(O(n^3)\). Finally, we extend the cost functions with a single uncertain parameter to those with a vector of additional uncertain parameters, improve one of the complexity results by Volgenant and Duin (Comput Oper Res 37:909–915, 2010) and solve some new problems.

Generation of Look-Up Tables for Dynamic Job Shop Scheduling Decision Support Tool

Majority of existing scheduling techniques are based on static demand and deterministic processing time, while most job shop scheduling problem are concerned with dynamic demand and stochastic processing time. As a consequence, the solutions obtained from the traditional scheduling technique are ineffective wherever changes occur to the system. Therefore, this research intends to develop a decision support tool (DST) based on promising artificial intelligent that is able to accommodate the dynamics that regularly occur in job shop scheduling problem. The DST was designed through three phases, i.e. (i) the look-up table generation, (ii) inverse model development and (iii) integration of DST components. This paper reports the generation of look-up tables for various scenarios as a part in development of the DST. A discrete event simulation model was used to compare the performance among SPT, EDD, FCFS, S/OPN and Slack rules; the best performances measures (mean flow time, mean tardiness and mean lateness) and the job order requirement (inter-arrival time, due dates tightness and setup time ratio) which were compiled into look-up tables. The well-known 6/6/J/Cmax Problem from Muth and Thompson (1963) was used as a case study. In the future, the performance measure of various scheduling scenarios and the job order requirement will be mapped using ANN inverse model.

Mathematical modeling and a memetic algorithm for the integration of process planning and scheduling considering uncertain processing times

The integration of process planning and scheduling is important for an efficient utilization of manufacturing resources. However, the focus of existing works is mainly on deterministic constraints of jobs. This article proposes a novel memetic algorithm for the integrated process planning and scheduling problem with processing time uncertainty based on processing time scenarios. First, a mathematical model for the stochastic integrated process planning and scheduling problem based on the network graph is established. Due to the nonlinearity in the model and the complexity of the problem, a memetic algorithm is then suggested for this problem. A novel local search (variable neighborhood search) algorithm is incorporated into the memetic algorithm. Two effective neighborhood structures are employed in the variable neighborhood search algorithm to improve the overall performance of the population. Furthermore, for the uncertainty in processing times, a set of scenarios have been generated to evaluate each individual. Finally, two performance measures—the expected performance measure and the worst-case deviation measure—are introduced and compared. In the experimental studies, the proposed memetic algorithm is tested on typical benchmark instances. Computational results show that the expected makespan measure performs better than the worst-case deviation measure and the proposed method exhibits high performance especially for large-scale instances. In addition, the results obtained by the proposed memetic algorithm are more satisfactory than those obtained by the algorithm that considers deterministic processing times only.

A factory-level dynamic operator allocation policy: the bubble allocation

In this paper, we propose a factory-level dynamic operator allocation policy called the bubble allocation policy. This policy is commonly implemented in labour-intensive industries in the presence of different operator speeds, high labour turnover, and learning effects. We prove the optimality of bubble allocation in several typical scenarios under deterministic and exponential processing time and different operator speed assumptions. When labour turnover and learning effects were considered, the effects of the bubble allocation were verified through simulation. Bubble allocation had a more significant positive effect on system throughput than the passive operator allocation policy. The positive effects of bubble allocation are enhanced with a larger production system scale (more parallel lines and more stations), higher turnover rate and slower learning process. Compared with active allocation policies such as work-sharing policy, bubble allocation policy has no requirements for additional cross-training and is not sensitive to the switching time of tasks. The bubble allocation policy stands out when the system is large and the flow line is designed in a balanced way.

Buffer clustering policy for sequential production lines with deterministic processing times

Buffer clustering policy for sequential production lines with deterministic processing times

Analysis of two-machine lines with finite buffer, operation-dependent and time-dependent failure modes

An analytical model for evaluating the throughput of two-machine lines, characterised by intermediate buffer with finite capacity, deterministic processing times and multiple failure modes for each machine is presented in this paper. Both operation-dependent failure and time-dependent failure are captured in a unique model as extension of the existing literature that was dealing with either one of them. Each machine has two failure modes, one is operation-dependent and the other is time-dependent. Time to failure and time to repair are assumed to be geometrically distributed. The presented method calculates the steady-state probabilities of the manufacturing system with a computational effort that depends only on the number of failure modes and not on the buffer capacity. A performance comparison of the proposed model with existing techniques is also reported, the aim is to show the error introduced by an analytical model that considers the operation-dependent failure mode as approximation of the time-dependent one.

The throughput rate of serial production lines with deterministic process times and random setups

We conduct exact analysis of serial production lines with deterministic service durations and various classes of random state-dependent setups between customers. Our focus is on assessing the produ...

An Approximate Analytical Method to Evaluate the Performance of Multi-product Assembly Manufacturing Systems

The automotive industry is characterized by the continuous and frequent adoption of cutting edge technologies in manufacturing. The introduction of new technology often entails a system level investigation to determine whether it meets expected production requirements. Many system design alternatives are usually considered at this stage, and a fast performance evaluation tool is desired to quickly obtain the optimum system configuration. In this paper, we introduce an analytical tool that was developed for this specific purpose.The investigated manufacturing system is a multi-product, automated, assembly production line composed of unreliable machines decoupled by finite buffers. Each product is an assembly of two components that are produced in sub-assembly lines before being assembled at an assembly machine. The performance of this system needs to be evaluated for different configurations that arise mainly due to the integration of a remote laser welding technology. This new technology promises, among other advantages, a much faster assembly than existing technologies. This makes it feasible to share assembly among many products with different possible production policies. The processing machines including the assembly machine are liable to fail randomly in operation thereby necessitating an evaluation method capable of accounting for stochastic behavior.To solve this problem, we develop a decomposition-based approximate analytical method. We use the continuous material flow approximation, which allows to model machines having deterministic but inhomogeneous processing times as in the investigated real system. We also account for multiple machine failure modes and introduce new techniques to incorporate the assembly of multiple products with different policies of switching between products. Comparison with simulation results shows the good accuracy of the model in estimating system throughput and work-in-progress. The model has been successfully utilized to evaluate the performance of an automotive door assembly manufacturing system and the main results of this case study are reported.

Sequenciamento de máquinas paralelas não-relacionadas com tempos de setup dependentes das tarefas

Este artigo propõe uma heurística para sequenciamento de tarefas em um ambiente de manufatura composto por máquinas paralelas não-relacionadas com tempos de setup dependentes da sequência de processamento das tarefas. As funções-objetivo consideradas são a minimização da soma do tempo ponderado de processamento e a minimização do atraso ponderado das tarefas. O método proposto acrescenta uma etapa ao procedimento de duas etapas de Bank e Werner (2001), para solução de problemas NP-hard, e é executado em três etapas: (i) ordenação inicial das tarefas, (ii) alocação das tarefas às máquinas, e (iii) aprimoramento da solução final através da ferramenta de otimização Tabu Search. O desempenho da heurística é comparado à solução ótima obtida por enumeração total. Ao ser aplicada em um ambiente de manufatura de componentes eletrônicos composto por duas máquinas paralelas não-relacionadas com tempos de processamento e de setup, a heurística proposta resulta em um desvio de 1,1% em relação ao valor ótimo da soma do tempo ponderado de processamento e 4,6% do mínimo atraso ponderado das tarefas em tempo computacional inferior a dez minutos.

SpaceWire-based thermal-infrared imager system for asteroid sample return mission HAYABUSA2

A thermal-infrared (TIR) imager system is developed for HAYABUSA2, which is planned to be launched in 2014 and aims at sample-return from a C-class near-Earth asteroid 162173 (1999JU3) considered to contain organic or hydrated materials. The system consists of a TIR imager and digital electronics, which are used not only for the scientific investigation of physical properties of the asteroid surface, but also for the assessment of landing site selection and safe descent operation onto the asteroid surface with in situ measurement. TIR adopts an uncooled bolometer. Image operations such as multiple images summation, dark image subtraction, and the compensation of dead pixels are processed onboard. A processing module is connected to sensor interfaces through SpaceWire in order to provide deterministic processing time. Data compression is also provided to reduce the restriction of transmission time, which provides the equivalent compression ratio as JPEG2000 in 1/30 processing time in average. A high-speed data recorder is connected through SpaceWire in order to record TIR data in parallel with other sensor data. The modularity of SpaceWire enables us to use these as built devices for TIR and inherits the same design as the long-wavelength infrared imager developed for the Venus climate orbiter Akatsuki.

The throughput rate of serial production lines with deterministic process times and random setups: Markovian models and applications to semiconductor manufacturing

We conduct exact analysis of serial production lines with deterministic service durations and various classes of random state-dependent setups between customers. Our focus is on assessing the production rate, or just-in-time (JIT) throughput. We demonstrate that such systems can be modeled as a Markov chain and consider various types of setups inspired by clustered photolithography tools in semiconductor manufacturing. We deduce when exact closed form expressions for the production rate are possible and when a numeric solution to the Markov chain balance equations are required. As these systems have shown promise for modeling process bound clustered photolithography tools, we study their accuracy versus detailed simulation for predicting the tool throughput. Various practical features such as the capacity of a pre-scan buffer and batch customers (to model wafer lots) are investigated.

Scheduling tasks with comb precedence constraints on dedicated machines

A set of n nonpreemptive tasks are to be scheduled on m dedicated machines in order to minimize the overall makespan. Precedence constraints among the tasks, deterministic processing times and processing machine of each task are given. We present lower bounds of the minimum makespan and heuristic algorithms for two relevant cases in manufacturing applications, namely when the precedence constraints form a comb or a caterpillar. Promising preliminary computational tests are also reported proving the efficiency and effectiveness of the proposed solution algorithm.

Solving type-2 assembly line balancing problem with fuzzy binary linear programming

This paper deals with the use of fuzzy set theory as a viable alternative method for modelling and solving the stochastic assembly line balancing problem. This paper presents a fuzzy extension of the simple assembly line balancing problem of type 2 SALBP-2 with fuzzy job processing times since uncertainty, variability, and imprecision are often occurred in real-world production systems. The job processing times are formulated by triangular fuzzy membership functions using their statistical distributions. This study proposes to solve a Fuzzy Binary Linear Problem FBLP with fuzzy coefficients in the objective function and in a constraint. Finally, the effect of the unbalancing of a station in a real case study has been investigated in order to consider different scenarios. In particular, four different scenarios were studied considering the balanced and unbalanced line with deterministic and stochastic job processing times. The results obtained showed that the use of a fuzzy approach allows to take in account the effect of the job processing time variability demonstrating the validity of the proposed model.

Stochastic flow-shop scheduling with minimizing the expected number of tardy jobs

In this research, minimizing the expected number of tardy jobs in a dynamic m machine flow-shop scheduling problem, i.e., \( {F_m}\left| {{r_j}\left| {{\text{E}}\left[ {\sum {{U_j}} } \right]} \right.} \right. \) is investigated. It is assumed that the jobs with deterministic processing times and stochastic due dates arrive randomly to the flow-shop cell. The due date of each job is assumed to be normally distributed with known mean and variance. A dynamic method is proposed for this problem by which the m machine stochastic flow-shop problem is decomposed into m stochastic single-machine sub-problems. Then, each sub-problem is solved as an independent stochastic single-machine scheduling problem by a mathematical programming model. Comparison of the proposed method with the most effective rule of thumb for the proposed problem, i.e., shortest processing time first rule shows that the proposed method performs 23.9 % better than the SPT rule on average for industry-size scheduling problems.

Parallel dedicated machines scheduling with chain precedence constraints

A set of n nonpreemptive tasks are to be scheduled on m parallel dedicated machines with a regular criterion. Chain precedence constraints among the tasks, deterministic processing times and processing machine of each task are given.We present computational complexity results and solution algorithms for some special cases. When the precedence relations among the tasks are given by two chains, we provide efficient solution algorithms for the minimization of the weighted sum of task completion times and the number of tardy jobs. Moreover, we show that when minimizing the sum of non-decreasing functions of the completion times of the tasks, a pseudopolynomial time algorithm and a fully polynomial time approximation scheme (FPTAS) exist. Indeed, when the objective is the minimization of the weighted number of tardy jobs or total weighted tardiness the problem is NP-hard in the ordinary sense.Finally, we consider slightly more general precedence structures and show that, even when the precedence constraints form a comb, makespan minimization problem turns out to be strongly NP-hard.

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.

Analysis of berth allocation and inspection operations in a container terminal

Nowadays, approximately 90 per cent of the world's cargoes are moved by vessels, and the majority of general cargoes are transported in containers. Accordingly, a container terminal becomes one of the important nodes in the global supply chain network and it is important to make container terminals operate efficiently. Meanwhile, after the terrorist attack on September 11, 2001, the US Government has proposed and implemented several approaches to improve security systems, including container security inspection operations. These operations may make an inspection center a bottleneck in container terminal operations. In this article, we analyze the container terminal berth allocation and inspection operation systems to find out a proper service rate so that potential bottlenecks can be avoided. We derive lower bounds of the service rate of the inspection center for the deterministic processing time case and perform simulation experiments to validate the lower bounds under stochastic processing time settings.

A decomposition approximation for three-machine closed-loop production systems with unreliable machines, finite buffers and a fixed population

This paper describes an approximate analytical method for evaluating the average values of throughput and buffer levels of closed three-machine production systems with finite buffers. The method includes a new set of decomposition equations and a new building block model. The machines have deterministic processing times and geometrically distributed probabilities of failure and repair. The numerical results of the method are close to those from simulation. The method performs well because it takes into account the correlation among the numbers of parts in the buffers. Extensions to larger systems are discussed. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix of additional numerical results]

Completion time variance minimization in single machine and multi-machine systems

In this paper we consider the problem of minimizing the completion time variance of n jobs on a single machine with deterministic processing times. We propose a new heuristic and compare the results with existing popular heuristics for the problem. We also propose a method based on genetic algorithms to solve the problem. We present the worst case performance analysis of the proposed heuristic. We also consider the problem of minimizing the completion time variance of n jobs on m identical parallel machines in both restricted and unrestricted versions. A heuristic method and a method based on genetic algorithms are presented for both the cases and results of computational testing are provided. It is concluded that the proposed methods provide better results compared to existing methods for the single machine case as well as for the multi-machine case.