Total Flow Time Research Articles

Financial analyses of on-line preemption-restart scheduling subject to cost penalties

This paper considers the on-line production order scheduling problem where each preemption causes a penalty, and the net profit is the total revenues of completed jobs minus the total penalties caused by preemptions. We discuss a preemptive version of the single-machine scheduling problem with the total flow time criterion. Two models with different kinds of preemption cost penalties are considered in this paper. In the first model, cost penalties are constant. In the second model, the preemption penalties are proportional to the lost part of the preempted job. Uncertain release times and processing times are modeled by an M/M/1 queue system. We calculate a lower bound probability for preemption of each job. Also, some financial analyses of the models are presented.

Performance evaluation of proposed Differential Evolution and Particle Swarm Optimization algorithms for scheduling m-machine flow shops with lot streaming

We consider n-job, m-machine lot streaming problem in a flow shop with equal size sub lots where the objective is to minimize the makespan and total flow time. Lot streaming (Lot sizing) is a technique that splits a production lot consisting of identical items into sub lots to improve the performance of a multi stage production system by over lapping the sub lots on successive machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. To solve this problem, we propose a Differential Evolution Algorithm (DEA) and Particle Swarm Optimization (PSO) to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set up time. In this research, we propose the DEA and PSO algorithms for discrete lot streaming with equal sub lots. The proposed methods are tested and the performances were evaluated. The computational results show that the proposed algorithms are very competitive for the lot streaming flow shop scheduling problem.

Single machine batch scheduling with two competing agents to minimize total flowtime

We study a single machine scheduling problem, where two agents compete on the use of a single processor. Each of the agents needs to process a set of jobs in order to optimize his objective function. We focus on a two-agent problem in the context of batch scheduling. We assume identical jobs and identical (agent-dependent) setup times. The objective function is minimizing the flowtime of one agent subject to an upper bound on the flowtime of the second agent. As in many real-life applications, we restrict ourselves to settings where the batches of the second agent must be processed continuously. Thus, the batch sizes are partitioned into three parts, starting with a sequence of the first agent, followed by a sequence of the second agent, and ending by another sequence of the first agent. In an optimal schedule, all three are shown to be decreasing arithmetic sequences. We introduce an efficient O ( n 3 2 ) solution algorithm (where n is the total number of jobs).

Congestion analysis of waterborne, containerized imports from Asia to the United States

A queuing model is introduced for estimating container flow times through port terminals as a function of infrastructure, staffing, and import volume. The model is statistically calibrated on industry data. Flow-time estimates of the model are aggregated with estimates from models previously developed for rail networks to develop estimates of the total container flow times from West Coast ports to inland distribution centers. Integrated with a supply-chain optimization model, the queuing formulas are used to predict import flows by port and landside channel in scenarios of total import growth, varying all-water rates, and a higher import share for nation-wide importers.

Scheduling with Bully Selfish Jobs

In job scheduling with precedence-constraints, i≺j means that job j cannot start being processed before job i is completed. In this paper we consider selfish bully jobs who do not let other jobs start their processing if they are around. Formally, we define the selfish precedence-constraint where i≺ s j means that j cannot start being processed if i has not started its processing yet. Interestingly, as was detected by a devoted kindergarten teacher whose story is told below, this type of precedence-constraints is very different from the traditional one, in a sense that problems that are known to be solvable efficiently become NP-hard and vice-versa.The work of our hero teacher, Ms. Schedule, was initiated due to an arrival of bully jobs to her kindergarten. Bully jobs bypass all other nice jobs, but respect each other. This natural environment corresponds to the case where the selfish precedence-constraints graph is a complete bipartite graph. Ms. Schedule analyzed the minimum makespan and the minimum total flow-time problems for this setting. She then extended her interest to other topologies of the precedence-constraints graph and other special instances with uniform length jobs and/or release times.

Efficient Heuristics for Flowshop Scheduling for Minimizing the Makespan and Total Flowtime of Jobs

The problem of scheduling in permutation flowshops has been extensively investigated by many researchers. Recently, attempts are being made to consider more than one objective simultaneously and develop algorithms to obtain a set of Pareto-optimal solutions. Varadharajan et al. (2005) presented a multi-objective simulated-annealing algorithm (MOSA) for the problem of permutation-flowshop scheduling with the objectives of minimizing the makespan and the total flowtime of jobs. The MOSA uses two initial sequences obtained using heuristics, and seeks to obtain non-dominated solutions through the implementation of a probability function, which probabilistically selects the objective of minimizing either the makespan or the total flowtime of jobs. In this paper, the same problem of heuristically developing non-dominated sequences is considered. We propose an effective heuristics based on simulated annealing (SA), in which the weighted sum of the makespan and the total flowtime is used. The essences of the heuristics are in selecting the initial sequence, setting the weight and generating a solution in the search process. Using a benchmark problem provided by Taillard (1993), which was used in the MOSA, these conditions are extracted in a large-scale experiment. The non-dominated sets obtained from the existing algorithms and the proposed heuristics are compared. It was found that the proposed heuristics drastically improved the performance of finding the non-dominated frontier.

A fast hybrid particle swarm optimization algorithm for flow shop sequence dependent group scheduling problem

A Particle Swarm Optimization (PSO) algorithm for a Flow Shop Sequence Dependent Group Scheduling (FSDGS) problem, with minimization of total flow time as the criterion (Fm|fmls,Splk,prmu|∑Cj), is proposed in this research. An encoding scheme based on Ranked Order Value (ROV) is developed, which converts the continuous position value of particles in PSO to job and group permutations. A neighborhood search strategy, called Individual Enhancement (IE), is fused to enhance the search and to balance the exploration and exploitation. The performance of the algorithm is compared with the best available meta-heuristic algorithm in literature, i.e. the Ant Colony Optimization (ACO) algorithm, based on available test problems. The results show that the proposed algorithm has a superior performance to the ACO algorithm.

Batch scheduling on uniform machines to minimize total flow-time

The solution of the classical batch scheduling problem with identical jobs and setup times to minimize flowtime is known for twenty five years. In this paper we extend this result to a setting of two uniform machines with machine-dependent setup times. We introduce an O(n) solution for the relaxed version (allowing non-integer batch sizes), followed by a simple rounding procedure to obtain integer batch sizes.

Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments

SUMMARYSpatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required. Copyright © 2011 John Wiley & Sons, Ltd.

A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops

Obtaining an optimal solution for a permutation flowshop scheduling problem with the total flowtime criterion in a reasonable computational timeframe using traditional approaches and optimization tools has been a challenge. This paper presents a discrete artificial bee colony algorithm hybridized with a variant of iterated greedy algorithms to find the permutation that gives the smallest total flowtime. Iterated greedy algorithms are comprised of local search procedures based on insertion and swap neighborhood structures. In the same context, we also consider a discrete differential evolution algorithm from our previous work. The performance of the proposed algorithms is tested on the well-known benchmark suite of Taillard. The highly effective performance of the discrete artificial bee colony and hybrid differential evolution algorithms is compared against the best performing algorithms from the existing literature in terms of both solution quality and CPU times. Ultimately, 44 out of the 90 best known solutions provided very recently by the best performing estimation of distribution and genetic local search algorithms are further improved by the proposed algorithms with short-term searches. The solutions known to be the best to date are reported for the benchmark suite of Taillard with long-term searches, as well.

Tabu Search with two approaches to parallel flowshop evaluation on CUDA platform

The introduction of NVidia’s powerful Tesla GPU hardware and Compute Unified Device Architecture (CUDA) platform enable many-core parallel programming. As a result, existing algorithms implemented on a GPU can run many times faster than on modern CPUs. Relatively little research has been done so far on GPU implementations of discrete optimisation algorithms. In this paper, two approaches to parallel GPU evaluation of the Permutation Flowshop Scheduling Problem, with makespan and total flowtime criteria, are proposed. These methods can be employed in most population-based algorithms, e.g. genetic algorithms, Ant Colony Optimisation, Particle Swarm Optimisation, and Tabu Search. Extensive computational experiments, on Tabu Search for Flowshop with both criteria, followed by statistical analysis, confirm great computational capabilities of GPU hardware. A GPU implementation of Tabu Search runs up to 89 times faster than its CPU counterpart.

Batch Scheduling Problem with Multiple Due-dates Constraints

This paper describes the issue of batch scheduling.In food production, the lead-time from produc-tion to sale should be decreased becausefreshness of the product is important. Products are shipped at diverse times depending on a demand of sellers, because the types of sellers has become diversified such as super-markets, convenience stores and etc. production of quantity demanded must be completed by time to ship it then. The authors consider a problem with due-dates constraints and construct the algorithm to find the opti-mal schedule that satisfy the due-dates constraint, batch size constraint, inventory time constraint and mini-mize total flow time.

Scheduling algorithms to minimise the total family flow time for job shops with job families

This paper considers the job scheduling problem in which jobs are grouped into job families, but they are processed individually. The decision variable is the sequence of the jobs assigned to each machine. This type of job shop scheduling can be found in various production systems, especially in remanufacturing systems with disassembly, reprocessing and reassembly shops. In other words, the reprocessing shop can be regarded as the job shop with job families since it performs the operations required to bring parts or sub-assemblies disassembled back to like-new condition before reassembling them. To minimise the deviations of the job completion times within each job family, we consider the objective of minimising the total family flow time. Here, the family flow time implies the maximum among the completion times of the jobs within a job family. To describe the problem clearly, a mixed integer programming model is suggested and then, due to the complexity of the problem, two types of heuristics are suggested. They are: (a) priority rule based heuristics; and (b) meta-heuristics. Computational experiments were performed on a number of test instances and the results show that some priority rule based heuristics are better than the existing ones. Also, the meta-heuristics improve the priority rule based heuristics significantly.

Scheduling jobs to consider physiological factors

AbstractWe studied scheduling jobs and breaks for a single worker. The processing time of jobs increases as the worker tires. In this study, we assume that conventional machine scheduling models do not always work for humans. So, while determining the break time, we consider the workers' physiological factors. The two objectives considered are the total flow time and makespan. An exact mathematical model and heuristic algorithm are developed to solve large problems. Numerical examples are presented for understanding and analyzing the performance of the mathematical model and the heuristic. © 2011 Wiley Periodicals, Inc.

Discrete harmony search algorithm for the no-wait flow shop scheduling problem with total flow time criterion

In this paper, a discrete harmony search algorithm (DHS) is developed for solving the no-wait flow shop scheduling problem with the objective to minimize total flowtime. Firstly, a harmony is represented as a discrete job permutation, and a new heuristic based on the well-known NEH method is proposed to initialize the harmony memory. Secondly, a novel pitch adjustment rule is employed in the improvisation to produce a new harmony. Thirdly, a local search is presented and embedded to enhance the algorithm's local exploitation ability. Extensive computational experiments are carried out based on a set of well-known benchmark instances. Computational results and comparison show the effectiveness of the presented DHS algorithm in solving the no-wait flow shop scheduling with total flowtime criterion.

Estimation of distribution algorithm for permutation flow shops with total flowtime minimization

In this paper, an Estimation of Distribution Algorithm (EDA) is proposed for permutation flow shops to minimize total flowtime. Longest Common Subsequence (LCS) is incorporated into the probability distribution model to mine good “genes”. Different from common EDAs, each offspring individual is produced from a seed, which is selected from the population by the roulette method. The LCS between the seed individual and the best solution found so far is regarded as good “genes”, which are inherited by offspring with a probability less than 100% to guarantee the population diversity. An effective Variable Neighborhood Search (VNS) is integrated into the proposed EDA to further improve the performance. Experimental results show that the inheritance of good “genes” obtained by LCS can improve the performance of the proposed EDA. The proposed hybrid EDA outperforms other existing algorithms for the considered problem in the literature. Furthermore, the proposed hybrid EDA improved 42 out of 90 current best solutions for Taillard benchmark instances.

Single Machine Scheduling With Fuzzy Preemption Penalties

In preemptive scheduling problems, processing of a job can be temporarily interrupted, and resumed at a later time. Conventionally, in the literature on preemptive scheduling, preempted jobs can simply be resumed from the point at which preemption occurred or restart from the beginning. However, this situation may not always be true in practice. It is likely that, in some cases, an imprecise or fuzzy part of jobs processing must be repeated, i.e., a fuzzy time penalty must be incurred. In this paper, we consider the single-machine scheduling problem of minimizing the total flow time subject to job release dates and fuzzy preemption penalties. We present a heuristic algorithm and validate it using some numerical examples.

Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and the schedule deviation measures. The efficiency measure is the total flow time, and the schedule deviation measure is the total disruption cost caused by the differences between the initial and current schedules. We provide polynomial-time solution methods to the following hierarchical optimization problems: minimizing total disruption cost among the minimum total flow time schedules and minimizing total flow time among the minimum total disruption cost schedules. We propose exponential-time algorithms to generate all efficient solutions and to minimize a specified function of the measures. Our extensive computational tests on large size problem instances have revealed that our optimization algorithm finds the best solution by generating only a small portion of all efficient solutions.

A multi-objective simulated annealing algorithm for permutation flow shop scheduling problem

Exact and heuristic algorithms have been proposed over the years for solving static permutation flow shop scheduling problems with the objectives of minimising makespan, total tardiness, and total flow time, etc. Of late, attempts are being made to consider more than one objective at a time, and develop algorithms in order to obtain a set of Pareto-optimal solutions. In such multi-objective scheduling problems, it is common to obtain a set of Pareto-optimal or efficient solutions such that at least one such solution is not inferior to any other given solution not contained in the set, and the solutions in that set does not dominate each other. In this paper, we consider a multi-objective permutation flow shop problem with the aim of generating non-dominated solutions with the aim of minimising makespan and maximum tardiness of jobs. A multi-objective simulated annealing (MOSA) algorithm has been developed towards this purpose. The proposed algorithm is evaluated using randomly generated problems. The effi...

Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem

We study the n–job two–parallel machines scheduling problem with the aim of minimising the total flow–time. In this problem, instead of allowing both machines to be continuously available as it is often assumed in the literature, we consider that one of the machines is available for a specified period of time after which it can no longer process any job. On the basis of the modification of an exact algorithm execution, we establish the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the above–mentioned problem.