Shortest Processing Time First Research Articles

Coordinated Scheduling of Two-Agent Production and Transportation Based on Non-Cooperative Game

A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers. The jobs of two agents compete for the processing position on a machine, and after the processed, they compete for the transport position on a transport vehicle to be transported to two agents. The two agents have different objective functions. The objective function of the first agent is the sum of the makespan and the total transportation time, whereas the objective function of the second agent is the sum of the total completion time and the total transportation time. Given the competition between two agents for machine resources and transportation resources, a non-cooperative game model with agents as game players is established. The job processing position and transportation position corresponding to the two agents are mapped as strategies, and the corresponding objective function is the utility function. To solve the game model, an approximate Nash equilibrium solution algorithm based on an improved genetic algorithm (NE-IGA) is proposed. The genetic operation based on processing sequence and transportation sequence, as well as the fitness function based on Nash equilibrium definition, are designed based on the features of the two-agent production and transportation coordination scheduling problem. The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes. When compared to heuristic rules such as the Longest Processing Time first (LPT) and the Shortest Processing Time first (SPT), the objective function values of the two agents are reduced by 4.3% and 2.6% on average.

Anarchy in the UJ: Coordination mechanisms for minimizing the number of late jobs

We consider the distributed scheduling problem on parallel machines with the central objective of maximizing the number of on-time jobs. Jobs are self-interested utility-maximizers that can choose the machines they are processed on and are exclusively interested in reducing their own private objective function. Each machine processes the jobs according to a local policy. We discuss Nash equilibria in the resulting schedules and perform a thorough analysis of the resulting (absolute) prices of anarchy for various parallel machine environments, utilities of the agents, and local policies of the machines. We show that local policies that are based on simple sorting-based procedures like shortest processing time first (SPT) and earliest due date first (EDD) lead to big losses in welfare compared to the global optimum. However, when employing Moore-Hodgson’s algorithm as a local policy, we can prove a price of anarchy of (2m−1)/m for identical machines and a price of anarchy of 2 for related and unrelated parallel machines. Moreover, we show how these results can be used to prove approximation ratios for greedy scheduling algorithms. This paper is the first to prove approximation ratios for two greedy scheduling procedures, turning them from simple heuristics into actual approximation ratios with a provable approximation ratio.

Flit Scheduling for Cut-Through Switching: Towards Near-Zero End-to-End Latency

Achieving low end-to-end latency with high reliability is one of the key objectives for future mission-critical applications, like the Tactile Internet and real-time interactive Virtual/Augmented Reality (VR/AR). To serve the purpose, cut-through (CT) switching is a promising approach to significantly reduce the transmission delay of store-and-forward switching, via flit-ization of a packet and concurrent forwarding of the flits belonging to the same packet. CT switching, however, has been applied only to well-controlled scenarios like network-on-chip and data center networks, and hence flit scheduling in heterogeneous environments (e.g., the Internet and wide area network) has been given little attention. This paper tries to fill the gap to facilitate the adoption of CT switching in the general-purpose data networks. In particular, we first introduce a packet discarding technique that sheds the packet expected to violate its delay requirement and then propose two flit scheduling algorithms, f EDF (flit-based Earliest Deadline First) and f SPF (flit-based Shortest Processing-time First), aiming at enhancing both reliability and end-to-end latency. Considering packet delivery ratio (PDR) as a reliability metric, we performed extensive simulations to show that the proposed scheduling algorithms can enhance PDR by up to 30.11% (when the delay requirement is 7 ms) and the average end-to-end latency by up to 13.86% (when the delay requirement is 10 ms), against first-in first-out (FIFO) scheduling.

Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion

The problem of minimising total absolute deviation of job completion times in a two-machine no-wait proportionate flow shop has been recently studied. It was shown that the LPT (largest processing time first) job sequence is optimal if the number of jobs n does not exceed 7, and that the LPT sequence is not optimal for instances with . We prove that there exists an optimal semi-V-shaped job sequence, in which the first job has the largest processing time, a certain number, greater than n / 2, of the following jobs appear in the LPT order, and jobs following job with the minimum processing time are sequenced in the SPT (shortest processing time first) order. We also present an time dynamic programming algorithm to find the best V-shaped job sequence, in which the jobs on the left of the job with the minimum processing time are sequenced in the LPT order and those on the right of this job are sequenced in the SPT order.

Modeling and solving static m identical parallel machines scheduling problem with a common server and sequence dependent setup times

This paper addresses the static m identical parallel machines scheduling problem with a common server and sequence dependent setup times. Initially, a mixed integer linear programming (MILP) model is presented for the problem to minimize the makespan. Due to the complexity of the problem, simulated annealing (SA) and genetic algorithm (GA) based solution approaches are developed. Subsequently, the performance of the proposed MILP model, SA and GA based solution approaches are compared with the performance of basic dispatching rules such as, shortest processing time first (SPT) and longest processing time first (LPT) over a set of randomly generated problem instances. The results of the computational experiments indicate that the proposed GA is generally more effective and efficient in solving this problem when it is compared to the proposed MILP model, SA, SPT and LPT.

Dispatching Rule에 기반한 능동 위상 배열 다기능 레이더의 빔 스케줄링 기법

능동 위상 배열레이더(AESA radar: Active Electronically Scanned Array radar)는 전자적으로 빔을 조향함으로써 빔 조향 시간이 비약적으로 빨라져, 기존의 기계식 빔 조향 레이더에 비해 레이더에서 수행할 수 있는 다중 임무처리 능력이 크게 향상되었다. 이러한 다중 임무 처리 능력을 최대화하면서 레이더의 전체 성능을 향상하기 위해, 레이더에 주어진 시간, 에너지, 처리 능력 등의 한정된 자원을 실시간으로 효율적으로 관리, 운용할 수 있는 레이더 자원 관리 기술의 중요성이 크게 대두되었다. 그 중 레이더 빔 스케줄링 기술은 레이더 자원 관리의 핵심적인 요소라 할 수 있다. 본 논문에서는 레이더 빔 스케줄링을 위한 다양한 dispatching rule을 비교 분석하고, 특히 빔의 처리 시간 지연 정도에 따라 SPF(Shortest Processing time First)와 ERF(Earliest Request time First)를 차등적으로 적용하여 빔의 우선 순위를 정하는 dispatching rule을 제안, 그 성능의 우월성을 입증하였다. AESA radar is able to instantaneously and adaptively position and control the beam, and such adaptive beam pointing of AESA radar enables to remarkably improve the multi-mission capability, compared with mechanically scanned array radar. AESA radar brings a new challenges, radar resource management(RRM), which is a technique efficiently allocating finite resources, such as energy and time to each task in an optimal and intelligent way. Especially radar beam scheduling is the most critical component for the success of RRM. In this paper, we proposed the several dispatching rules for radar beam scheduling, and compared the performance on the multi-function radar scenario. We also showed that the dispatching rule which differently applying SPF(Shortest Processing time First) and ERF(Earliest Request time First) according to beam processing latency is the most efficient.

Single machine scheduling with a learning effect and discounted costs

In this paper, we consider a single machine scheduling problem with a learning effect and discounted costs. The learning effect of a job is assumed to be a function of its position. We show that discounted total completion time is minimized by the classical shortest processing time first (SPT) rule. For the following objective function, discounted total weighted completion time, we show by an example that the optimal schedule of the classical discounted weighted shortest processing time first (WDSPT) rule is not optimal in the presence of a learning effect. But for some special cases, we prove that the WDSPT rule can construct the optimal sequence. We give the worst-case error bound for the WDSPT rule in the general case. Some extensions of the problem are also given.

Parallel machine scheduling with multiple unloading servers

We study a parallel machine scheduling problem with multiple unloading servers. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. Only after unloading, the machine is available for processing the next job. The model is motivated by the milk run operations of a logistics company that faces limited unloading docks at the warehouse. Our interest is to minimize the total completion time of the jobs. We show that the shortest-processing-time-first (SPT) algorithm has a worst-case bound of 2. We also develop other improved heuristic algorithms as well as a branch-and-bound algorithm to solve the problem. Computational experiments show that our algorithms are efficient and effective.

Single-machine scheduling problems with the time-dependent learning effect

In this paper, three single-machine scheduling problems with time-dependent learning effect model to minimize the sum of weighted completion times, the sum of the k th powers of completion times and the maximum lateness are investigated. We show that the shortest processing time first (SPT) rule is an optimal solution for the problem to minimize the sum of the k th powers of completion times. Some polynomial time solutions are provided for the other two problems under certain conditions, respectively.

Priority Auctions and Queue Disciplines That Depend on Processing Time

We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before or after service). In both schemes, a customer obtains priority over all customers, waiting in the queue or arriving while he is waiting, who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue discipline (i.e., shortest-processing-time-first (SPT), longest-processing-time-first (LPT)) arising in a bidding equilibrium.

A note on the SPT heuristic for solving scheduling problems with generalized due dates

Two NP-hard scheduling problems on parallel identical machines with generalized due dates are studied. We focus on two objectives: (i) minimizing maximum tardiness and (ii) minimizing total tardiness. In both cases, we introduce a shortest processing time first (SPT)-based heuristic and simple lower bounds on the optimal cost. Our numerical study indicates that the SPT heuristic performs extremely well in all settings. Scope and purpose In traditional scheduling literature, due dates are job dependent, i.e., a specific job has to be completed by a given due date. When generalized due dates are considered, a certain number of jobs must be completed by each specified due date. The identity of the jobs is immaterial. In this note, we address two hard multi-machine scheduling problems with generalized due dates. We introduce a simple and efficient heuristic, which is shown numerically to produce very close to optimal schedules.

Efficiency versus Fairness in Priority Control: Waterway Lock Case

Delay at a congested service facility, such as a waterway lock, depends on the control policy used. The shortest processing time first (SPF) policy, which is a promising priority control policy, can significantly reduce the average delay/barge compared to the normally used first come first served (FCFS) policy. SPF tends to favor large groups of barges, i.e., tows, at the expense of smaller ones. This paper modifies the SPF policy to consider fairness among tows in queues. One modified algorithm, called fairer SPF (FSPF), limits the number of tows allowed to pass any particular tow. The case study indicates that FSPF can yield most of the benefits of SPF without greatly sacrificing fairness. Compared with FCFS, FSPF can reduce barge delay up to 53.89%. When tow sizes (and thus service times) are similar, the benefits from resequencing tows are limited. Results confirm that larger tow size variance yields larger barge-delay savings. The barge-delay savings for FSPF compared to FCFS range from 6.68% for constant tow size to 60.74% in a high-variance case. The results indicate that significant delay reductions are achievable without significantly compromising fairness.

On the Asymptotic Optimality of the SPT Rule for the Flow Shop Average Completion Time Problem

Consider a flow shop with M machines in series, through which a set of jobs are to be processed. All jobs have the same routing, and they have to be processed in the same order on each of the machines. The objective is to determine such an order of the jobs, often referred to as a permutation schedule, so as to minimize the total completion time of all jobs on the final machine. We show that when the processing times are statistically exchangeable across machines and independent across jobs, the Shortest ProcessingTime first (SPT) scheduling rule, based on the total service requirement of each job on all M machines, is asymptotically optimal as the total number of jobs goes to infinity. This extends a recent result of Kaminsky and Simchi-Levi (1996), in which a crucial assumption is that the processing times on all M machines for all jobs must be i.i.d.. Our work provides an alternative proof using martingales, which can also be carried out directly to show the asymptotic optimality of the weighted SPT rule for the Flow Shop Weighted Completion Time Problem.

Simulation Analysis of Order and Kanban Sequencing Rules in a Kanban-Controlled Flow Shop

This paper presents a simulation study of several customer order and kanban sequencing/selection rules in a kanban-controlled flow shop. Kanbans are used to authorize production within a work center and withdrawals from previous work cen ters. In addition to single queue sequencing rules such as first-come, first-served (FCFS) and shortest processing time first (SPT), a set ofmul tiple queue selection rules are defined for produc tion kanbans. Furthermore, assuming that the orders wait in separate queues determined by part type, single queue sequencing rules are ap plied to customer orders within each queue. A simulation model is developed to investigate the effect of kanban-order sequencing rule combina tions on performance measures such as mean order cycle time, lateness, and tardiness. The re sults indicate that the shortest processing time first-smallest order quantity combination (SPT- SOQ) is the best operating policy.

Effects of Tow Sequencing on Capacity and Delay at a Waterway Lock

This paper presents several heuristic methods for sequencing tows through waterway locks, including locks with two dissimilar chambers. Two algorithms are proposed for obtaining good initial solutions. Of these, the shortest processing time first (SPF) algorithm gives priority to tows with lower processing time per barge, while maximum saving (SAVE) favors tows with the highest relative advantage at particular chambers. The resulting improvements in delays and capacity are evaluated by comparing these algorithms with a first come first served (FCFS) operation. Delay savings of up to 75.85% with SAVE and up to 79.73% with SPF are projected at congested locks. A pairwise exchange algorithm is used to improve the initial solutions obtained with SPF and SAVE. The improved methods, SPF with exchange (SPFX) and SAVE with exchange (SAVEX), further reduce the average barge delay. While SPFX does not improve much on SPF, SAVEX reduces average barge delay by up to 26.5% compared to SAVE. Among all these methods, SPFX yields the smallest barge delay (up to 79.8% less than FCFS). The delay savings can be even greater when upstream and downstream flows are unequal.

The Two-Stage Flowshop Scheduling Problem with M Machines at each Stage

Abstract In the following article the two-stage flowshop problem with an identical number of machines at the two stages is discussed. A new lower bound calculation for the makespan is introduced, and the performance of a Johnson’s type ordering is evaluated, This method of job sequencing is shown to be superior to random and SPT (shortest processing time first) orderings over a wide variety of problem sizes involving differing numbers of jobs to be processed and machines available at the two stages.

Evaluation of the Optimal SRPT Strategy with Overhead

Considering queueing systems in data networks, one can identify a special feature of the communication system: the service time, which is proportional to message length, is known in advance. This is a precondition for queueing strategies such as SPT (shortest processing time first) or SRPT (shortest remaining processing time first), which offers the shortest mean delay time among all conceivable strategies. For a practical evaluation of these strategies it is essential to include the influence of overhead time, especially for the Preemptive SRPT strategy. This paper analyzes SRPT with constant overhead time CV modified by a constant preemption gap <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CP \gcong CV</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M/G/1</tex> systems. The comparison of strategies for FIFO, SPT, SRPT, and RR (round robin) using different service time distributions with coefficients of variation >1 and overhead shows, for SRPT and for a combination of SRPT and RR, a considerable reduction of the mean delay time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overline{TD}</tex> , especially for service time distributions with high coefficients of variation. This result indicates the potential advantages of these strategies in data network applications.