Job Flow Time Research Articles

Parallel machine scheduling with batch deliveries to minimize total flow time and delivery cost

AbstractMotivated by the flow of products in the iron and steel industry, we study an identical and parallel machine scheduling problem with batch deliveries, where jobs finished on the parallel machines are delivered to customers in batches. Each delivery batch has a capacity and incurs a cost. The objective is to find a coordinated production and delivery schedule that minimizes the total flow time of jobs plus the total delivery cost. This problem is an extension of the problem considered by Hall and Potts, Ann Oper Res 135 (2005) 41–64, who studied a two‐machine problem with an unbounded number of transporters and unbounded delivery capacity. We first provide a dynamic programming algorithm to solve a special case with a given job assignment to the machines. A heuristic algorithm is then presented for the general problem, and its worst‐case performance ratio is analyzed. The computational results show that the heuristic algorithm can generate near‐optimal solutions. Finally, we offer a fully polynomial‐time approximation scheme for a fixed number of machines. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 492–502, 2016

A Hungarian penalty-based construction algorithm to minimize makespan and total flow time in no-wait flow shops

This paper presents a penalty-based construction algorithm for the no-wait flow shop scheduling problem with the objective of minimizing makespan and total flow time of jobs. The proposed method, derived from Hungarian penalty method originally used for the classic assignment problem is employed to generate an initial schedule of jobs, which is further improved by an insertion technique to obtain an optimal or near-optimal schedule. The results of computational experiments on a large number of test problems show that the proposed method performs significantly better than the state-of-the-art procedures while requiring comparable computational effort.

A note on efficient sequences with respect to total flow time and number of tardy jobs

AbstractFor the single‐machine scheduling problem with the objective of simultaneously minimizing total flow time and number of tardy jobs, a lower bound on the number of efficient sequences is known. However, the proof thereof, which makes use of a modified version of Smith's algorithm, is unduly lengthy and sophisticated. Adopting a totally new point of view, we present in this short article a much simpler proof based on the naive idea of pairwise interchange. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 346–348, 2016

Optimization for Speculative Execution in Big Data Processing Clusters

A big parallel processing job can be delayed substantially as long as one of its many tasks is being assigned to an unreliable or congested machine. To tackle this so-called straggler problem, most parallel processing frameworks such as MapReduce have adopted various strategies under which the system may speculatively launch additional copies of the same task if its progress is abnormally slow when extra idling resource is available. In this paper, we focus on the design of speculative execution schemes for parallel processing clusters from an optimization perspective under different loading conditions. For the lightly loaded case, we analyze and propose one cloning scheme, namely, the Smart Cloning Algorithm (SCA) which is based on maximizing the overall system utility. We also derive the workload threshold under which SCA should be used for speculative execution. For the heavily loaded case, we propose the Enhanced Speculative Execution (ESE) algorithm which is an extension of the Microsoft Mantri scheme to mitigate stragglers. Our simulation results show SCA reduces the total job flowtime, i.e., the job delay/ response time by nearly $6$ percent comparing to the speculative execution strategy of Microsoft Mantri. In addition, we show that the ESE Algorithm outperforms the Mantri baseline scheme by $71$ percent in terms of the job flowtime while consuming the same amount of computation resource.

A NSGA-II and NSGA-III comparison for solving an open shop scheduling problem with resource constraints

This paper presents an open shop scheduling problem based on a real mechanical workshop made of m machines that process n jobs. It deals with different resource constraints related to the tools allocation and the multi-skills staff assignment. Resource skills and their availability are required to execute one process task. In this work, we expose a multi-objective problem where the idea is to minimize three objectives simultaneously. The first one considers the minimization of the total flow time of jobs in the production system, then the workload balancing concerning both, humans and machines is addressed. We propose and compare two multi-objective methods: NSGA-II and NSGA-III. Computational experiments are designed according to the literature, we expose the small and large sized instances to present the general performance of these algorithms using the hyper-volume metric to compare them.

Solving Multi Objective Job Shop Scheduling Problems Using Artificial Immune System Shifting Bottleneck Approach

Scheduling problems are usually solved using heuristics to get optimal or near optimal solutions because problems found in practical applications cannot be solved to optimality using reasonable resources in many cases. Scheduling problems vary widely according to specific production tasks but most are NP-hard problems. Optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered in this work. The Artificial Immune System Shifting Bottleneck Approach is used for finding optimal makespan, mean flow time, mean tardiness values of two benchmark problems. In this Artificial Immune System Shifting Bottleneck Approach (AISSB), initial sequences are generated with Artificial Immune System Algorithm (AIS) and Shifting Bottleneck Algorithm (SB) is used for finding final solutions. The results show that the AISSB Approach is effective algorithm that gives better results than literature results. The proposed AISSB Approach is an efficient problem-solving technique for multi objective job shop scheduling problem.

Minimizing average flow-time under knapsack constraint

We give the first logarithmic approximation for minimizing average flow-time of jobs in the subset parallel machine setting (also called the restricted assignment setting) under a single knapsack constraint. In a knapsack constraint setting, each job has a profit, and the set of jobs which get scheduled must have a total profit of at least a quantity Π. Our result extends the work of Gupta et al. (2009) [8] who considered the special case where the profit of each job is unity. Our algorithm is based on rounding a natural LP relaxation for this problem. In fact, we show that one can use techniques based on iterative rounding.

Single-machine batch scheduling of linear deteriorating jobs

We consider the problem of scheduling jobs in batches on a single machine where the processing time of each job is a simple increasing linear function of its waiting time, i.e., the time between the starting time of processing the batch to which the job belongs and the starting time of processing of the job. The objective is to minimize the sum of the total job flow time and the batching cost. We first show that the case with a given number of batches is strongly NP-hard and we present a fully polynomial-time approximation scheme (FPTAS) for this case. We then show that the case with an arbitrary number of batches is also strongly NP-hard and there is no polynomial-time approximation algorithm with a constant upper bound for this case unless P=NP.

Family-based dispatching with parallel machines

Family-based dispatching heuristics seek to lower set-up frequencies by grouping similar types of jobs for joint processing. Hence, job flow times may be improved as less time is spent on set-ups. So far, family-based dispatching with parallel machines received little attention in literature. We address the perceived gap by proposing extensions to existing family-based dispatching heuristics. Main extensions concern improved rules for family priority settings and for coordinating the number of machines in use by a single family. Extended heuristics are tested by an extensive simulation study. Significant performance gains for extended heuristics vs. existing heuristics are found. Performance gains are largest for high set-up to run-time ratios.

A Hybrid ILS-VND Based Hyper-heuristic for Permutation Flowshop Scheduling Problem

In this paper an iterated local search (ILS) is embedded with a variable neighborhood Descent (VND) hyper-heuristic. The proposed hyper-heuristic combines low-level heuristics. Several variants from the literature within the proposed ILS were implemented and tested. This article conducts an empirical study involving hard combinatorial optimization problems, permutation flowshop scheduling problem (PFSP) with the objectives of minimizing makespan and the total flowtime of jobs. The proposed ILS based hyper-heuristic proved its general and applicable across the studied problems.

Integrated process planning and scheduling: an enhanced ant colony optimization heuristic with parameter tuning

This study develops an enhanced ant colony optimization (E-ACO) meta-heuristic to accomplish the integrated process planning and scheduling (IPPS) problem in the job-shop environment. The IPPS problem is represented by AND/OR graphs to implement the search-based algorithm, which aims at obtaining effective and near-optimal solutions in terms of makespan, job flow time and computation time taken. In accordance with the characteristics of the IPPS problem, the mechanism of ACO algorithm has been enhanced with several modifications, including quantification of convergence level, introduction of node-based pheromone, earliest finishing time-based strategy of determining the heuristic desirability, and oriented elitist pheromone deposit strategy. Using test cases with comprehensive consideration of manufacturing flexibilities, experiments are conducted to evaluate the approach, and to study the effects of algorithm parameters, with a general guideline for ACO parameter tuning for IPPS problems provided. The results show that with the specific modifications made on ACO algorithm, it is able to generate encouraging performance which outperforms many other meta-heuristics.

Simulation-based experimental design and statistical modeling for lead time quotation

In a produce-to-order environment, it is of substantial interest to be able to quote a tight and reliable lead time for a new job (or order) upon its arrival to a manufacturing system. This work developed a simulation-based statistical approach to provide responsive and high-quality prediction of a new job's flow time through the system, which renders the capability of accurately quoting lead times in real time. The approach integrates analytical queueing analysis, design of experiments, and statistical modeling to quantify the dependence of a new job's flow time distribution upon the shop status “seen” by that job. To the best of our knowledge, this is the first attempt to design simulation experiments in the space spanned by a complete set of shop status factors for the thorough investigation of the possible impacts those factors may have on the distribution of a new job's flow time. The method has been applied on a scaled-down semiconductor manufacturing system, and the quality of the quoted lead time has been evaluated based on a large and well-designed validation data set in terms of the six commonly used performance criteria.

A New GT Heuristic for Solving Multi Objective Job Shop Scheduling Problems

The n-job, m-machine Job shop scheduling (JSP) problem is one of the general production scheduling problems in manufacturing system. Scheduling problems vary widely according to specific production tasks but most are NP-hard problems. Scheduling problems are usually solved using heuristics to get optimal or near optimal solutions because problems found in practical applications cannot be solved to optimality using reasonable resources in many cases. In this paper, optimization of three practical performance measures mean job flow time, mean job tardiness and makespan are considered. New Game theory based heuristic method (GT) is used for finding optimal makespan, mean flow time, mean tardiness values of different size problems. The results show that the GT Heuristic is an efficient and effective method that gives better results than Genetic Algorithm (GA). The proposed GT Heuristic is a good problem-solving technique for job shop scheduling problem with multi criteria.

IMPACT OF GENETIC ALGORITHM OPERATORS ON ITS PERFORMANCE IN SOLVING FLOW SHOP SCHEDULING PROBL

The primary objective of flow shop scheduling is to obtain the best sequence which optimizes various objectives such as makespan, total flow time, total tardiness, or number of tardy jobs, etc. Due to the combinatorial nature of the flow shop problem (FSP) there is a lot of artificial intelligence methods proposed to solve it. The Genetic Algorithm (GA), one of these methods, is considered a valuable search algorithm capable of finding a reasonable solution in a short computational time. GA operators, (selection, crossover and mutation process), give different forms that can be combined to give various GAs. In this paper we investigate the impact of selection, crossover and mutation process on the quality of the GA solution in solving the flow shop scheduling problems. In this study, four selection methods, seventeen crossover methods and eight mutation methods are investigated. The computational results show that there are significant differences among the investigated methods on the performance of the proposed GA.

A heuristic algorithm to minimise the total flowtime of jobs in permutation flowshops

A heuristic algorithm with six implementations (HA-I to HA-VI) is presented in this paper, and it is used to solve the permutation flowshop scheduling problem to minimise the total flowtime of jobs. These implementations have been evaluated by using the 90 benchmark flowshop scheduling problem instances, and the solutions yielded are compared with the solutions reported in the literature. The comparison shows that the implementations all together have produced better solutions for 28 problem instances and same solutions for 29 problem instances, out of 90 problem instances considered with respect to the solutions by Iterated Local Search algorithm proposed by Dong et al. (2009). They have also produced better solutions for 50 problem instances and the same solutions for 19 problem instances, out of 90 problem instances considered with respect to the solutions by PSOvns algorithm proposed by Tasgetiren et al. (2007), as reported in Dong et al. (2009).

A counterexample to a proposed dynamic programming algorithm for optimal bid construction in an auction-based fully distributed manufacturing system

The paper by Veeramani and Wang (Int J Adv Manuf Technol 28:541–550, 2006) published in this journal offers a general bid construction scheme for minimizing the job flow time in auction-based manufacturing control and claims the optimality of the procedure. The purpose of this note is to provide a small example, in which their proposed new method fails to produce an optimal solution. We also address efficient correct algorithms so as to protect the readers from mistakenly believing that their new procedure is a better way of computing solutions.

A discrete artificial bee colony algorithm with composite mutation strategies for permutation flow shop scheduling problem

The Permutation Flow Shop Scheduling Problem (PFSSP) is an NP-hard problem of wide engineering and theoretical background. In this paper, a kind of discrete artificial bee colony with composite mutation strategies is presented to compensate the defects of the single mutation scheme that is easy to get into the local best for PFSSP, named CDABC. Firstly, to make ABC suitable for PFSSP, we regard each discrete job permutation as a food source and apply discrete operations to generate a new neighbourhood food source for different bees. Secondly, the Nawaz-Enscore-Ham (NEH) heuristic is combined with the random initialization to initialize the population with a certain quality and diversity. Thirdly, the composite mutation strategies are proposed to enable the DABC to solve the permutation flow shop scheduling. Finally, the fast local search is used for enhancing the best individual. Within our knowledge, there are few papers to discuss artificial bee colony algorithm about PFSSP with the objective of minimizing total flow time and maximum lateness of jobs. In this sense, our work can be viewed as a start point for researchers to develop ABC-based algorithms to solve PFSSP. Additionally, simulations and comparisons based on PFSSP benchmarks are carried out, which shows that our algorithm is very competitive. We have also evaluated our algorithm with the well known DMU problems. For the problems with the objective of minimizing makespan, the algorithm CDABC obtains 26 new upper bounds of the 40 instances, and for the problems with the objective of maximum lateness, CDABC obtains 137 new upper bounds of the 160 instances. These new upper bounds can be used for future algorithms to compare their results with ours.

Setup-oriented dispatching rules – a survey

This paper provides a survey of dispatching rules that explicitly take into account setup times in their decision making. Rules are classified into the categories of purely setup-oriented, composite and family-based rules, and the most promising rules from the three categories are identified from the literature. These rules are then compared empirically on various job shop problems with sequence-dependent setup times for their performance regarding mean setup time, mean flow time, mean tardiness and proportion of tardy jobs. The setup times are modelled using setup time matrices, and five different types of matrices are applied to assess the influence of this factor on the relative performance of a setup-oriented dispatching rule. Experimental results indicate that the choice of the best rule is often dependent on the setup time matrix structure. While good family-based rules exist for reducing the mean setup time and mean flow time, they are clearly outperformed by effective composite rules for due date-related criteria. Moreover, the better rules all seem to rely on queue information rather than only job attributes.

A multi-agent-based negotiation approach for parallel machine scheduling with multi-objectives in an electro-etching process

Electro-etching is a critical process in producing aluminium foil, and it always involves many parallel machines with three distinct voltages. Therefore, production scheduling involves these parallel machines and their eligibility. In this paper, an agent-based negotiation approach is proposed to develop a distributed parallel machine scheduling application in this manufacturing environment. The agent-based system consists of types of agent, i.e. job agents, machine agents and management agents, to represent jobs, machines and supervisors, respectively. To establish job allocations, job agents and machine agents have to bid interactively. Negotiation protocol and bid decision models are developed for negotiations between job agents and machine agents. The management agent plays a centralised controller and system coordinator role. The main function of the management agent is to manage the negotiation process between job agents and machine agents to ensure that the global objectives of the system, such as minimising total job tardiness and flow time, balancing machine loading and maximising total revenue, can be achieved. Experiments are conducted to evaluate the performance of the proposed system. The results show that the proposed agent-based scheduling mechanism will provide an integrated process plan and parallel eligible machine scheduling solutions with better global performance.

A Pareto-Optimal Solution for a Multi-Objective Scheduling Problem with Periodic Maintenance Requirement

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.