A decomposition algorithm for the single machine total tardiness problem

The problem of sequencing jobs on a single machine to minimize total tardiness is considered. An algorithm, which decomposes the problem into subproblems which are then solved by dynamic programming when they are sufficiently small, is presented and is tested on problems with up to 100 jobs.     

A memetic algorithm for the total tardiness single machine scheduling problem

In this paper, a new memetic algorithm (MA) for the total tardiness single machine scheduling (SMS) problem with due dates and sequence-dependent setup times is proposed. The main contributions with respect to the implementation of the hybrid population approach are a hierarchically structured population conceived as a ternary tree and the evaluation of three recombination operators. Concerning the local improvement procedure, several neighborhood reduction schemes are developed and proved to be effective when compared to the complete neighborhood. Results of computational experiments are reported for a set of randomly generated test problems. The memetic approach and a pure genetic algorithm (GA) version are compared with a multiple start algorithm that employs the all-pairs neighborhood as well as two constructive heuristics.     

Dynamic programming and decomposition approaches for the single machine total tardiness problem

The problem of sequencing jobs on a single machine to minimize total tardiness is considered. General precedence constrained dynamic programming algorithms and special-purpose decomposition algorithms are presented. Computational results for problems with up to 100 jobs are given.     

On the single machine total tardiness problem

In this paper we study the single machine total tardiness problem. We first identify some optimality properties based on which a special case with a given number of distinct due dates is proved polynomially solvable. The results are then extended to the case with release dates.     

Some remarks on the decomposition properties of the single machine total tardiness problem

The note extends Lawler’s [E.L. Lawler, A pseudopolynomial algorithm for sequencing jobs to minimize total tardiness, Annals of Discrete Mathematics, 1 (1977) 331–342] fundamental decomposition theorem. This extension serves as a basis for alternate criteria that recognize when the problem is non-decomposable. It also shows that even relaxing a single criterion to a weak inequality may contradict Lawler’s (1977) decomposition theorem.     

A tabu search approach for the single machine mean tardiness problem

In this paper, a tabu search approach is proposed for solving the single machine mean tardiness scheduling problem. Simulation experiment results obtained from the tabu search approach and three other heuristics are compared. Although computation time is increased, the results indicate that the proposed approach provides a much better solution than the other three approaches.     

A tabu search algorithm for the single machine total weighted tardiness problem

In this study, a tabu search (TS) approach to the single machine total weighted tardiness problem (SMTWT) is presented. The problem consists of a set of independent jobs with distinct processing times, weights and due dates to be scheduled on a single machine to minimize total weighted tardiness. The theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is NP-hard, rendering it a challenging area for meta-heuristic approaches. This paper presents a totally deterministic TS algorithm with a hybrid neighborhood and dynamic tenure structure, and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search. The proposed TS approach yields very high quality results for a set of benchmark problems obtained from the literature.     

New insights on the single machine total tardiness problem

Virtually all algorithmic studies on the single machine total tardiness problem use Emmons’ theorems that establish precedence relations between job pairs. In this paper, we investigate these theorems with a geometric viewpoint. This approach provides a compact way of representing Emmons’ theorems and promotes better insights into dominance properties. We use these insights to differentiate between certain classes of easy and hard instances.     

Algorithms for single machine total tardiness scheduling with sequence dependent setups

We consider the problem of scheduling a single machine to minimize total tardiness with sequence dependent setup times. We present two algorithms, a problem space-based local search heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP) for this problem. With respect to GRASP, our main contributions are—a new cost function in the construction phase, a new variation of Variable Neighborhood Search in the improvement phase, and Path Relinking using three different search neighborhoods. The problem space-based local search heuristic incorporates local search with respect to both the problem space and the solution space. We compare our algorithms with Simulated Annealing, Genetic Search, Pairwise Interchange, Branch and Bound and Ant Colony Search on a set of test problems from literature, showing that the algorithms perform very competitively.     

Fast neighborhood search for the single machine total weighted tardiness problem

Most successful heuristics for solving 1||∑w_jT_j are based on swap moves. We present an algorithm which improves the complexity of searching the swap neighborhood from O(n³) to O(n²). We show that this result also improves the complexity of the recently developed dynasearch heuristics.     

单机排序中带可分配工期的总误工问题的应急管理

对于机器排序的应急管理问题,Qi Xiang-tong等人进行了系统分析,得出了较好的结果.此文则考虑带可分配工期的总误工问题的应急管理问题.对于不同模型,或给出其最优序,或给出其近似解.     

A new discrete particle swarm optimization approach for the single-machine total weighted tardiness scheduling problem with sequence-dependent setup times

In this paper we present a new Discrete Particle Swarm Optimization (DPSO) approach to face the NP-hard single machine total weighted tardiness scheduling problem in presence of sequence-dependent setup times. Differently from previous approaches the proposed DPSO uses a discrete model both for particle position and velocity and a coherent sequence metric. We tested the proposed DPSO mainly over a benchmark originally proposed by Cicirello in 2003 and available online. The results obtained show the competitiveness of our DPSO, which is able to outperform the best known results for the benchmark. In addition, we also tested the DPSO on a set of benchmark instances from ORLIB for the single machine total weighted tardiness problem, and we analysed the role of the DPSO swarm intelligence mechanisms as well as the local search intensification phase included in the algorithm.     

带有固定区间的单机双代理可中断总误工问题

研究带有固定区间的两个代理单机排序问题.第一个代理工件可中断,且工件到达时间与工期满足一致关系,目标函数为最小化总误工.第二个代理工件被安排在固定时间窗口.目标是寻找一个排序,使得满足第二个代理目标可行情况下,第一个代理目标函数值最小.在固定区间等于加工时间的情况下,利用分块原则,提出了一个伪多项式时间动态规划算法,并给出了固定区间大于加工时间情况下的时间复杂度分析.     

A simulated annealing approach for the one-machine mean tardiness scheduling problem

In this paper we propose a simulated annealing approach for solving the single machine mean tardiness scheduling problem. The results of a simulation experiment indicate that the proposed method provides much better solutions than two heuristics that gave good results in previous studies. More importantly, the solutions obtained are within less than 1% of optimal solutions.     

Grasp with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times

This paper addresses the problem of scheduling jobs in a single machine with sequence dependent setup times in order to minimize the total tardiness with respect to job due dates. We propose variants of the GRASP metaheuristic that incorporate memory-based mechanisms for solving this problem. There are two mechanisms proposed in the literature that utilize a long-term memory composed of an elite set of high quality and sufficiently distant solutions. The first mechanism consists of extracting attributes from the elite solutions in order to influence the construction of an initial solution. The second one makes use of path relinking to connect a GRASP local minimum with a solution of the elite set, and also to connect solutions from the elite set. Reactive GRASP, which probabilistically determines the degree of randomness in the GRASP construction throughout the iterations, is also investigated. Computational tests for instances involving up to 150 jobs are reported, and the proposed method is compared with heuristic and exact methods from the literature.     

Evaluation of leading heuristics for the single machine tardiness problem

A recent paper on the single machine tardiness problem by Panwalker, Smith and Koulamas [8] disputes experimental results of Holsenback and Russell [5] that indicated the Net Benefit of Relocation (NBR) heuristic provides significant improvement over the adjacent pairwise interchange (API) routine of Fry et al. [4], which in turn, was reported to show better solution quality than the Wilkerson-Irwin (W-I) heuristic ([13]). Panwalker et al. [8] claim that the P-S-K heuristic yields better results than the other methods over a wide range of problems and suggest that the NBR heuristic is not only inferior to the P-S-K heuristic, but also inferior to the API and W-I routines. This paper will shed new light on the quality of the experimentation of Panwalker et al. [8] and show that in general, the P-S-K heuristic is inferior to the NBR heuristic.     

Earliness and tardiness single machine scheduling with proportional weights

This paper presents the first efficient method to solve an earliness-tardiness single machine n job scheduling model with idle times permitted. In this model the earliness and tardiness penalties are proportional to the processing times of the jobs. A two stage decomposition process builds the optimal job arrangement as a sequence of single and multijob blocks. The arrangement of the jobs within each multijob block is unspecified since it depends on the start time of this block. This process is followed by a procedure that drastically reduces the number of candidate optimal n job sequences. Finally an available optimal timing algorithm is recommended and implemented to select the best schedule among those sequences. The solution procedure tested on a PC on 400 examples for n=40 and 50 proves to be very fast.