考虑学习效应的最小化延误总时间的单机批次排序问题

一些生产场景中,工件以批次作业的形式被安排生产,工件批量大、加工工序基本相同,所以标准工时相同,而且实际加工时间会受到学习效应的影响.为此,讨论学习效应的最小化延误总时间的单机批次排序问题,对该问题建立数学模型.该问题属于NP-hard问题,采用动态规划算法(DP)和模拟退火算法(SA)求解该问题,通过实验分析不同规模时DP的执行时间与SA的执行时间和求解误差的变化趋势,比较SA与其他实践中常用的经典规则的求解效果.最后得出DP适合批次数小于13的小规模问题,可以得到精确解;与经典规则相比,SA至少可以使目标函数降低20%,表明SA算法具有有效性.SA解决大规模问题时效果较优,并得出SA的执行时间和误差随着控制参数改变的变化趋势.     

Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times

In this article, we consider a single-machine scheduling problem with one unavailability period, with the aim of minimizing the weighted sum of the completion times. We propose three exact methods for solving such a problem: a branch-and-bound method based on new properties and lower bounds, a mixed integer programming model, and a dynamic programming method. These methods were coded and tested on randomly generated instances, and their performances were analyzed. Our numerical experiments show that the branch-and-bound method and the dynamic programming method are complementary. Using these approaches, we are able to solve problems with up to 3000 jobs within a reasonable computation time.     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

Single machine scheduling with controllable processing times to minimize total tardiness and earliness

In most deterministic scheduling problems job processing times are considered as invariable and known in advance. Single machine scheduling problem with controllable processing times with no inserted idle time is presented in this study. Job processing times are controllable to some extent that they can be reduced or increased, up to a certain limit, at a cost proportional to the reduction or increase. In this study, our objective is determining a set of compression/expansion of processing times in addition to a sequence of jobs simultaneously, so that total tardiness and earliness are minimized. A mathematical model is proposed firstly and afterward a net benefit compression–net benefit expansion (NBC–NBE) heuristic is presented so as to acquire a set of amounts of compression and expansion of jobs processing times in a given sequence. Three heuristic techniques in small problems and in medium-to-large instances two meta-heuristic approaches, as effective local search methods, as well as these heuristics are employed to solve test examples. The single machine total tardiness problem (SMTTP) is already NP-hard, so the considered problem is NP-hard obviously. The computational experiments demonstrate that our proposed heuristic is efficient approach for such just-in-time (JIT) problem, especially equipped with competent heuristics.     

Single CNC machine scheduling with controllable processing times to minimize total weighted tardiness

Advanced manufacturing technologies, such as CNC machines, require significant investments, but also offer new capabilities to the manufacturers. One of the important capabilities of a CNC machine is the controllable processing times. By using this capability, the due date requirements of customers can be satisfied much more effectively. Processing times of the jobs on a CNC machine can be easily controlled via machining conditions such that they can be increased or decreased at the expense of tooling cost. Since scheduling decisions are very sensitive to the processing times, we solve the process planning and scheduling problems simultaneously. In this study, we consider the problem of scheduling a set of jobs on a single CNC machine to minimize the sum of total weighted tardiness, tooling and machining costs. We formulated the joint problem, which is NP-hard since the total weighted tardiness problem (with fixed processing times) is strongly NP-hard alone, as a nonlinear mixed integer program. We proposed a DP-based heuristic to solve the problem for a given sequence and designed a local search algorithm that uses it as a base heuristic.     

Parallel-machine scheduling with an availability constraint

e consider two parallel machines scheduling problem where one machine is not available in a specified time period. The unavailable time period is fixed and known in advance. The objective is to minimize the total weighted completion time. The problem is known to be NP-hard. We give a fully polynomial-time approximation scheme (FPTAS) for the problem. We then generalize the results to the case with m parallel machines.     

Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness

We present an Iterated Local Search (ILS) algorithm for solving the single-machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness. The proposed ILS algorithm exhibits several distinguishing features, including a new neighborhood structure called Block Move and a fast incremental evaluation technique, for evaluating neighborhood solutions. Applying the proposed algorithm to solve 120 public benchmark instances widely used in the literature, we achieve highly competitive results compared with a recently proposed exact algorithm and five sets of best solutions of state-of-the-art metaheuristic algorithms in the literature. Specifically, ILS obtains the optimal solutions for 113 instances within a reasonable time, and it outperforms the previous best-known results obtained by metaheuristic algorithms for 34 instances and matches the best results for 82 instances. In addition, ILS is able to obtain the optimal solutions for the remaining seven instances under a relaxed time limit, and its computational efficiency is comparable with the state-of-the-art exact algorithm by Tanaka and Araki (Comput Oper Res 40:344–352, 2013). Finally, on analyzing some important features that affect the performance of ILS, we ascertain the significance of the proposed Block Move neighborhood and the fast incremental evaluation technique.     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

Single-machine scheduling to minimize total convex resource consumption with a constraint on total weighted flow time

In this paper, we consider single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function. The objective is to minimize the total amount of resource consumed subject to a constraint on total weighted flow time. The optimal resource allocation is obtained for any arbitrary job sequence. The computational complexity of the general problem remains an open question, but we present and analyze some special cases that are solvable by using polynomial time algorithms. For the general problem, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions. The results show that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%.     

Parallel-machine scheduling to minimize tardiness penalty and power cost

Traditional research on machine scheduling focuses on job allocation and sequencing to optimize certain objective functions that are defined in terms of job completion times. With regard to environmental concerns, energy consumption becomes another critical issue in high-performance systems. This paper addresses a scheduling problem in a multiple-machine system where the computing speeds of the machines are allowed to be adjusted during the course of execution. The CPU adjustment capability enables the flexibility for minimizing electricity cost from the energy saving aspect by sacrificing job completion times. The decision of the studied problem is to dispatch the jobs to the machines as well as to determine the job sequence and processing speed of each machine with the objective function comprising of the total weighted job tardiness and the power cost. We give a formal formulation, propose two heuristic algorithms, and develop a particle swarm optimization (PSO) algorithm to effectively tackle the problem. Since the existing solution representations do not befittingly encode the decisions involved in the studied problem into the PSO algorithm, we design a tailored encoding scheme which can embed all decisional information in a particle. A computational study is conducted to investigate the performances of the proposed heuristics and the PSO algorithm.     

Single-machine scheduling with periodic and flexible periodic maintenance to minimize maximum tardiness

This paper considers a single-machine scheduling problem with several maintenances periods. Specifically, two situations are investigated. In the first one, maintenance periods are periodically fixed: maintenance is required after a periodic time interval. In the second one, the maintenance is not fixed but the maximum continuous working time of the machine which is allowed is determined. The objective is to minimize the maximum tardiness. These problems are known to be strongly NP-hard. We propose some dominance properties and an efficient heuristic. Branch-and-bound algorithms, in which the heuristics, the lower bounds and the dominance properties are incorporated, are proposed and tested computationally.     

A heuristic procedure to minimize number of tardy jobs and total tardiness in single machine scheduling

Moore has suggested an optimizing algorithm for minimizing the number of tardy jobs in single machine scheduling. This article explores the possibility of modifying the Moore's algorithm so that total tardiness is minimized while keeping the number of tardy jobs minimum. A heuristic procedure based on the Moore's original algorithm is presented and its performance is evaluated. A simple extension of the algorithm to parallel machine scheduling is also provided.     

Heuristics for two-machine no-wait flowshop scheduling with an availability constraint

In this paper we study the two-machine no-wait flowshop problem with an availability constraint. The problem has been shown to be NP-hard, and some heuristics with a worst-case error bound of 2 have been developed for it. We provide two improved heuristics for the problem, and show that each has a worst-case error bound of 5/3.     

Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness

In many realistic production situations, a job processed later consumes more time than the same job when it is processed earlier. Production scheduling in such an environment is known as scheduling with deteriorating jobs. However, research on scheduling problems with deteriorating jobs has rarely considered explicit (separable) setup time (cost). In this paper, we consider a single-machine scheduling problem with deteriorating jobs and setup times to minimize the maximum tardiness. We provide a branch-and-bound algorithm to solve this problem. Computational experiments show that the algorithm can solve instances up to 1000 jobs in reasonable time.     

Scheduling linear deteriorating jobs to minimize makespan with an availability constraint on a single machine

The scheduling problem with deteriorating jobs to minimize the makespan on a single machine where the facility has an availability constraint is studied in this paper. By a deteriorating job we mean that the processing time for the job is a function of its starting time. Even with the introduction of the availability to a facility, the linear deteriorating model can be solved using the 0-1 integer programming technique if the actual job processing time is proportional to the starting time.     

Family scheduling with batch availability in flow shops to minimize makespan

This paper addresses a batch scheduling problem in flow shop production systems, where job families are formed based on setup similarities. In order to improve setup efficiency, we consider batching decisions in our solution procedure. Due to its high practical relevance, the batch availability assumption is also adopted in this study. In the presence of sequence-dependent setup times, it is proved that a permutation flow shop is generally not optimal. Therefore, our objective is to determine solutions with inconsistent batches, which essentially lead to non-permutation schedules, to minimize makespan. After examining structural properties, we develop a tabu search algorithm with multiple neighbourhood functions. Computational results confirm the remarkable benefits of batching decisions. Our algorithm also outperforms some well-known and well-performing approaches.     

Tabu search for scheduling on identical parallel machines to minimize mean tardiness

This paper presents a tabu search approach for scheduling jobs on identical parallel machines with the objective of minimizing the mean tardiness. Initially, we consider a basic tabu search that uses short term memory only. Local search is performed on a neighborhood defined by two types of moves. Insert moves consist of transferring each job from one machine to another and swap moves are those obtained by exchanging each pair of jobs between two machines. Next, we analyze the incorporation of two diversification strategies with the aim of exploring unvisited regions of the solution space. The first strategy uses long term memory to store the frequency of the moves executed throughout the search and the second makes use of influential moves. Computational tests are performed on problems with up to 10 machines and 150 jobs. The heuristic performance is evaluated through a lower bound given by Lagrangean relaxation. A comparison is also made with respect to the best constructive heuristic reported in the literature.