SPT Rule Research Articles

The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown

We consider the problem of scheduling jobs on a single machine subject to an uncertain breakdown to minimize the flowtime. Assuming the machine is unavailable during the breakdown, the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under these assumptions and starting from the perspective of statistical optimization, we first establish the scheduling problem HSONRP, which contains deterministic information, stochastic information, and online information and then define the expected competitive ratio of an algorithm to find the optimized solution of the problem HSONRP. In addition, then, we propose and prove certain results on the expected competitive ratio of the SPT rule. In particular, we prove the expected competitive ratio of SPT rule is less than 1+max{pi}2P when s is the uniform distribution on interval (0,P], where pi is the processing time of job i, P=∑i=1npi, and show that it is no more than 54 under a quite loose condition. Meanwhile, we also make some discussions about our studies. What we have performed will enrich and improve the research results on the area of scheduling to minimize flowtime and advance the development of online optimization and stochastic optimization.

Note on “A note on single machine scheduling with time-dependent deterioration and exponential learning effect”

A result in a recent paper Huang et al. (2010) is incorrect because job processing times are variable due to both deteriorating jobs and learning effects, which is not taken into account by the authors. In this note, we show by a counter-example that the published result is incorrect. From the counter-example, we know that the classical SPT rule or LPT rule cannot give an optimal solution for the problem 1pj[r]=pj(1+∑i=1r-1pi)aαr-1,wj=θpj∑wjCj, then we provide a revised model.

Approximation Algorithms for Multitasking Scheduling Problems

In this work, we incorporate human factors and real-life operations into newly proposed multitasking scheduling problems with periodic shift activities. It is motivated by personnel resource scheduling with periodic work shifts under the requirement of providing continuous service to customers. We model the problem as two identical parallel machine scheduling with complementary non-available time periods, and consider two models with the objectives of the makespan, i.e. the maximum completion time and respectively the total completion time. We then prove that the Greedy algorithm and SPT rule are of asymptotic and parametric approximation ratios for the two models, respectively.

Lower and upper bounds for scheduling multiple balancing vehicles in bicycle-sharing systems

Public bicycle-sharing systems have been implemented in many big cities around the world to face many public transport problems. The exploitation and the management of such transportation systems imply crucial operational challenges. The balancing of stations is the most crucial question for their operational efficiency and economic viability. In this paper, we study the balancing problem of stations with multiple vehicles by considering the static case. A mathematical formulation of the problem is proposed, and two lower bounds based on Eastman’s bound and SPT rule are developed. Moreover, we proposed four upper bounds based on a genetic algorithm, a greedy search algorithm and two hybrid methods that integrate a genetic algorithm, a local search method and a branch-and-bound algorithm. The developed lower and upper bounds are tested and compared on a large set of instances.

Heuristic algorithms for scheduling hybrid flow shops with machine blocking and setup times

We investigate a new variant of the hybrid flow shop problem (HFSP) considering machine blocking and both sequence-independent and sequence-dependent setup times. Since the HFSP is NP-hard, we propose heuristic algorithms along with priority rules based on the traditional SPT and LPT rules. We carried out computational experiments on simulated problem instances to test the performance of the priority rules. The objective function adopted was makespan minimization, and we used the rate of success and the relative deviation as performance criteria. The results indicate superiority of LPT-based rules. On instances with sequence-independent setup times, the LP rule, which is based on the non-increasing sorting of total processing times, outperformed other rules in most tested instances. In instances with sequence-dependent setup times, the LPS rule, which is based on the non-increasing sum of processing time and average setup times, outperformed other rules in most tested instances.

Optimized Three-Stage Strategy of Orderly Management of File Stream in Network Printing Workflow

Abstract This paper proposed the optimized three-stage strategy of orderly management of file stream in network printing workflow. In first stage the customer preflight was added to the conventional prepress preflight, which set quick-type, general-type, stable-type and comprehensive-type preflight scheme for customers by investigating the possibility of occurrence of errors of various preflight entries and customer relevancy. Based on four types of preflight schemes, four customer preflight applications were created by using Pitstop Pro and Connector You. Customers can select one of the appropriate applications for quick preflight before delivering to reduce the probability of returning the files back for correction when errors occur in preflight. Second stage is printing enterprise prepress preflight, which proposed the concept of the prepress preflight tolerance. In addition, according to the different requirements of printing technology and quality, this paper established the prepress preflight scheme based on the printing enterprises’ tolerance for preflight error. Third stage is to manage the optimized sorting of prepress file stream. To achieve it, the SPT rule and the 0-1 programming model were adopted, time spend of preflight, printing process and post-press finishing was also taken into account. Moreover, Enfocus Switch software was applied to establish automated network printing workflow and complete the file stream sorting. Finally, the result of simulation analysis of the optimized strategy shows that the optimized three-stage strategy can effectively shorten the file processing time.

Single Machine Scheduling Model with Total Tardiness Problem

Objectives: In this paper, Five Dispatching Rules and a Branch & Bound algorithm is introduced for Single Machine Total Tardiness Scheduling Problem (SMTTSP) to minimize the total (average) tardiness and number of tardy jobs. Methods/Statistical Analysis: We proposed five dispatching (priority) rules as Shortest Processing Time, Earliest Due Dates, Longest Processing Time, Minimum Slack Time and First Come First Serve for SMTTSP and compared the performance of all the proposed priority rules. Furthermore, a numerical illustrations is also provided to select the best dispatched rule of SMTTSP. Next, we developed a Branch & Bound Algorithm for SMTTSP using best selected dispatching rule. We also developed Branch Tree to understand the Lower bound process of the B& B Algorithm. Findings: The main aim to proposed these dispatching rules and a Branch and Bound Algorithm is to obtain the optimal sequence to optimize the total (average) tardiness and number of total tardy jobs. The comparative analysis of the dispatching rules shows that EDD rule is better than other dispatching rules for minimization of total tardy jobs and tardiness of the jobs while SPT rule is better for minimization of make span. But Dispatching rules do not have the guarantee to give an optimal solution. So in this study, an exact algorithm (Branch & Bound) was developed with EDD rule for finding the optimal solution for SMTTSP. The comparative study between dispatching rules and an exact (B&B) algorithm is being justified by numerical illustrations and we found that the EDD rule and B&B Algorithm give the same results. Hence it was concluded that EDD rule works as an Exact algorithm and gives the optimal solution for SMTTSP. Application/Improvements: The computational results of the proposed (B&B) algorithm and Dispatching rules show that our methodology is more useful than other optimal approach for SMTTSP and it provides an important tool for decision makers.

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.

Determination of Transportation Fleet Size using The Combination of Adjusted SPT Rule and Linear Programming Method

<p>In a very competitive industry, XYZ Ltd. needs to have an effective, efficient and reliable logistics fleet management. The fleets should be able to help the company serve the market demands and guarantee the distribution of its products. This research analyzed and determined the by-truck transportation fleet size of XYZ Ltd using the combination of adjusted SPT Rule and linear programming method. The results showed that the product delivery’s scheduling was arranged by operating a fleet of 13 tronton trucks and 25 trailer trucks, with the scheduling of delivery resulting in maximum makespan of 6.98 days and an average flow-time per shipment of 3.83 days. <br /><strong>Keywords</strong>: Fleet Management, Logistics Transportation, Adjusted SPT</p>

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.

Coordination mechanisms with hybrid local policies

We study coordination mechanisms for scheduling n jobs on m parallel machines where agents representing the jobs interact to generate a schedule. Each agent acts selfishly to minimize the completion time of his/her own job, without considering the overall system performance that is measured by a central objective. The performance deterioration due to the lack of a central coordination, the so-called price of anarchy, is determined by the maximum ratio of the central objective function value of an equilibrium schedule divided by the optimal value. In the first part of the paper, we consider a mixed local policy with some machines using the SPT rule and other machines using the LPT rule. We obtain the exact price of anarchy for the problem of minimizing the makespan and some bounds for the problem of minimizing the total completion time. In the second part of the paper, we consider parallel machine scheduling subject to eligibility constraints. We devise new local policies based on the flexibilities and the processing times of the jobs. We show that the newly devised local policies outperform both the SPT and the LPT rules.

Hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints

One of the common assumptions in the field of scheduling is that machines are always available in the planning horizon. This may not be true in realistic problems since machines might be busy processing some jobs left from previous production horizon, breakdowns or preventive maintenance activities. Another common assumption is the consideration of setup times as a part of processing times, while in some industries, such as printed circuit board and automobile manufacturing, not only setups are an important factor but also setup magnitude of a job depends on its immediately preceding job on the same machine, known as sequence-dependent setup times. In this paper, we consider hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints caused by preventive maintenance. The optimization criterion is the minimization of makespan. Since this problem is NP-hard in the strong sense, we propose three heuristics, based on SPT, LPT and Johnson rule and two metaheuristics based on genetic algorithm and simulated annealing. Computational experiments are performed to evaluate the efficiencies of the algorithms.

A two-stage multiple-machine assembly scheduling problem for minimizing sum of completion times

This paper considers a two-stage multiple-machine assembly scheduling problem for minimizing the sum of completion times. The first stage consists of two independent machines, each of which produces its own type of components. The second stage consists of two identical and independent parallel machines. The processing of the second stage cannot begin until the processing of the first stage is finished. Minimizing the sum of completion times at the second stage is considered as the scheduling measure. A lower bound based on the SPT rule is derived, which is then used to develop a branch-and-bound algorithm. An efficient simple heuristic algorithm is also developed.

Further study of minimizing total flowtime for the worker assignment scheduling problem in the identical parallel-machine models

Previously, minimizing total flow time in the model of an identical, parallel machines with nonpreemptive jobs has been investigated. Because the specific problem has been shown as NP-complete, heuristics have been developed for solving it. A shortest processing time for Ai part (SPT-A) heuristic is used for the job scheduling subproblem. In addition, the largest marginal contribution (LMC) procedure is used for the worker assignment subproblem and then minimizes the total flow time. Different values of W (number of workers) are used for further study of the performance of these heuristics developed. In conclusion, for the simplified processing time function, values of W have no significant influence when the heuristics are applied. In other words, no matter what value of W was used when SPT rule was applied, the heuristics generate the same, excellent results.

Scheduling with tool changes to minimize total completion time: A study of heuristics and their performance

AbstractThe machine scheduling literature does not consider the issue of tool change. The parallel literature on tool management addresses this issue but assumes that the change is due only to part mix. In practice, however, a tool change is caused most frequently by tool wear. That is why we consider here the problem of scheduling a set of jobs on a single CNC machine where the cutting tool is subject to wear; our objective is to minimize the total completion time. We first describe the problem and discuss its peculiarities. After briefly reviewing available theoretical results, we then go on to provide a mixed 0–1 linear programming model for the exact solution of the problem; this is useful in solving problem instances with up to 20 jobs and has been used in our computational study. As our main contribution, we next propose a number of heuristic algorithms based on simple dispatch rules and generic search. We then discuss the results of a computational study where the performance of the various heuristics is tested; we note that the well‐known SPT rule remains good when the tool change time is small but deteriorates as this time increases and further that the proposed algorithms promise significant improvement over the SPT rule. © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003

The Asymptotic Optimality of the SPT Rule for the Flow Shop Mean Completion Time Problem

In the flow shop mean completion time problem, a set of jobs has to be processed on m-machines. Every machine has to process each one of the jobs, and every job has the same routing through the machines. The objective is to determine a sequence of the jobs on the machines so as to minimize the sum of the completion times of all jobs on the final machine. In this paper, we prove the asymptotic optimality of the Shortest Processing Time algorithm for any continuous, independent, and identically distributed job processing times.

Simulation comparison of collaboration protocol-based testing models

This paper uses a stimulation modelling approach to investigate two collaboration protocols: timeout and frequent request collaboration protocols. The models presented here are very generic and can be adopted in general testing environments with a single tester shared by many types of jobs and with the repair process. This research presents different results from earlier studies, while addressing their misleading simplifying assumptions that are a common pitfall in practice. The two collaboration protocols are redefined based on the results. The timeout protocol improved system performance by collaborating with the SPT rule in the gamma repair time distributions with left biased shape. This collaboration is simple to implement and does not require the parameter estimation that is often a drawback of most heuristics for the combination of dispatching rules. The frequent service request (FSR) dispatching rule showed as good performance as the SPT rule with respect to overall mean flow time in this problem. Research is being continued to further investigate the properties of the timeout collaboration protocol with various factors.

IMPROVING JOB SHOP PERFORMANCE THROUGH PROCESS QUEUE MANAGEMENT UNDER TRANSFER BATCHING

This research investigated the value of protecting the continuity of release batchs in a transfer batching environment, by modifying the SPT rule. A simulation model of a job shop was used to test the modified SPT rule. The performance measures evaluated were mean flow time, flow time variance, and mean lateness. Conditions under which the SPT modification improved results were as follows: large number of transfer batches, small setup time to process time ratio, and large variation in process times from station to station. The results suggest that shop loading is not a significant factor affecting performance of the modified SPT rule.

Two-machine flowshop scheduling with bicriteria problem

This paper attempts to solve a two-machine flowshop bicriteria scheduling problem with release dates for the jobs, in which the objective function is to minimize a weighed sum of total flow time and makespan. To tackle this scheduling problem, an integer programming model with N 2+3 N variables and 5 N constraints where N is the number of jobs, is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, a heuristic scheduling algorithm is presented. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. The average solution quality of the heuristic algorithm is above 99% and is much better than that of the SPT rule as a benchmark. A 15-job case requires only 0.018 s, on average, to obtain an ultimate or even optimal solution. The heuristic scheduling algorithm is a more practical approach to real world applications than the integer programming model.

The sensitivity of jobshop due date lead time to changes in the processing time

This paper provides a procedure for calculating the sensitivity of the production lead time to the average job processing time for a single machine problem under a general priority rule using simulation. The aim of this work is to develop sensitivity routines, for queues with any non-preemptive priority rule, to calculate the sensitivity of the due date lead time to the average jobs processing time. Though GI/G/1 queuing model is given, the same methodology can be extended to GI/G/m queuing model. The new algorithm is valid for the SPT, LPT and FCFS priority rules.