有关单机两代理排序问题的两个结果

研究了两个单机两代理排序问题. 在第一个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化最大工件费用. 在第二个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化所有工件的最大完工时间. 证明了第一个问题是强NP-难的, 改进了已有的一般意义NP-难的结果; 对第二个问题给出了一个与现有的动态规划算法不同的动态规划算法.     

极小化最大完工时间的单机分批加工问题

本文考虑极小化最大完工时间的单机分批加工问题．设有n个工件和一台批加工机器．每个工件有一个释放时间和一个加工时间．批加工机器可以同时加工b(b相似文献   

Single-machine scheduling problems with actual time-dependent and job-dependent learning effect

In this study, we introduce an actual time-dependent and job-dependent learning effect into single-machine scheduling problems. We show that the complexity results of the makespan minimization problem and the sum of weighted completion time minimization problem are all NP-hard. The complexity result of the maximum lateness minimization problem is NP-hard in the strong sense. We also provide three special cases which can be solved by polynomial time algorithms.     

Minimizing weighted mean absolute deviation of job completion times from their weighted mean

We address a single-machine scheduling problem where the objective is to minimize the weighted mean absolute deviation of job completion times from their weighted mean. This problem and its precursors aim to achieve the maximum admissible level of service equity. It has been shown earlier that the unweighted version of this problem is NP-hard in the ordinary sense. For that version, a pseudo-polynomial time dynamic program and a 2-approximate algorithm are available. However, not much (except for an important solution property) exists for the weighted version. In this paper, we establish the relationship between the optimal solution to the weighted problem and a related one in which the deviations are measured from the weighted median (rather than the mean) of the job completion times; this generalizes the 2-approximation result mentioned above. We proceed to give a pseudo-polynomial time dynamic program, establishing the ordinary NP-hardness of the problem in general. We then present a fully-polynomial time approximation scheme as well. Finally, we report the findings from a limited computational study on the heuristic solution of the general problem. Our results specialize easily to the unweighted case; they also lead to an approximation of the set of schedules that are efficient with respect to both the weighted mean absolute deviation and the weighted mean completion time.     

Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect

In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single-machine scheduling problems with an actual time-dependent deterioration

In this paper, we consider the single machine scheduling problems with an actual time-dependent deterioration effect. By the actual time-dependent deterioration effect, we mean that the processing time of a job is defined by increasing function of total actual processing time of jobs in front of it in the sequence. We show that even with the introduction of an actual time-dependent deterioration to job processing times, makespan minimization problem, total completion time minimization problem, the total lateness, and the sum of the quadratic job completion times minimization problem remain polynomially solvable, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, and the total tardiness minimization problem can be solved in polynomial time under certain conditions.     

Single machine scheduling with a general exponential learning effect

In this paper we consider the scheduling problem with a general exponential learning effect and past-sequence-dependent (p-s-d) setup times. By the general exponential learning effect, we mean that the processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the δ ? 0th power of completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

A solvable case of the variance minimization problem

An algorithm is derived, which solves the completion time variance (CTV) problem with equal processing times in O(n log n) time. This result indicates that the special case formulated by Merten and Muller [1] is well solvable.     

Single-machine scheduling with a sum-of-actual-processing-time-based learning effect

In this paper we consider the single-machine scheduling problems with a sum-of-actual-processing-time-based learning effect. By the sum-of-actual-processing-time-based learning effect, we mean that the processing time of a job is defined by a function of the sum of the actual processing time of the already processed jobs. We show that even with the introduction of the sum-of-actual-processing-time-based learning effect to job processing times, the makespan minimization problem, the total completion time minimization problem, the total completion time square minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem remain polynomially solvable, respectively.     

Scheduling on same-speed processors with at most one downtime on each machine

We consider the problem of scheduling a set of independent tasks on multiple same-speed processors with planned shutdown times with the aim of minimizing the makespan. We give an LPT-based algorithm, LPTX, which yields a maximum completion time that is less than or equal to 3/2 the optimal maximum completion time or 3/2 the time that passes from the start of the schedule until the latest end of a downtime. For problems where the optimal schedule ends after the last downtime, and when the downtimes represent fixed jobs, the LPTX maximum completion time is within 3/2 of the optimal maximum completion time. In addition, we show that this result is asymptotically tight for the class of polynomial algorithms assuming that P≠NP. We also show that the bound obtained previously for a similar problem, when no more than half of the machines are shut down at the same time, for the LPT algorithm is asymptotically tight in the class of polynomial algorithms if P≠NP.     

Total completion time minimization in two-machine job shops with unit-time operations

We study the problem of minimizing total completion time in two-machine job shop with unit-time operations. We propose an efficient algorithm for the problem. The algorithm is polynomial with respect to a succinct encoding of the problem instances, where the number of bits necessary to encode a job with k operations is O(log(k + 1)). This result answers a long standing open question about the complexity of the problem.     

Single machine scheduling with general time-dependent deterioration, position-dependent learning and past-sequence-dependent setup times

The paper deals with single machine scheduling problems with setup time considerations where the actual processing time of a job is not only a non-decreasing function of the total normal processing times of the jobs already processed, but also a non-increasing function of the job’s position in the sequence. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the δth (δ ≥ 0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the δ th (δ ≥ 0) power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Branch and bound based solution algorithms for the budget constrained discrete time/cost trade-off problem

The time/cost trade-off models in project management aim to reduce the project completion time by putting extra resources on activity durations. The budget problem in discrete time/cost trade-off scheduling selects a time/cost mode for each activity so as to minimize the project completion time without exceeding the available budget. There may be alternative modes that solve the budget problem optimally and each solution may have a different total cost value. In this study we consider the budget problem and aim to find the minimum cost solution among the minimum project completion time solutions. We analyse the structure of the problem together with its linear programming relaxation and derive some mechanisms for reducing the problem size. We solve the reduced problem by branch and bound based optimization and heuristic algorithms. We find that our branch and bound algorithm finds optimal solutions for medium-sized problem instances in reasonable times and the heuristic algorithms produce high quality solutions very quickly.     

The Sudoku completion problem with rectangular hole pattern is NP-complete

The sudoku completion problem is a special case of the latin square completion problem and both problems are known to be NP-complete. However, in the case of a rectangular hole pattern–i.e. each column (or row) is either full or empty of symbols–it is known that the latin square completion problem can be solved in polynomial time. Conversely, we prove in this paper that the same rectangular hole pattern still leaves the sudoku completion problem NP-complete.     

V-shape property for job sequences that minimize the expected completion time variance

We consider the problem of sequencing n jobs with random processing time on a single machine so as to minimize the expected variance of job completion times. Our main result is a new sufficient condition for an optimal sequence to be V-shaped in terms of the mean processing times when n ⩾ 3. We show that this condition is satisfied by a wide variety of problem instances, including those in which the processing times follow different patterns of distributions. This result relaxes a condition proposed before.     

Minimizing the total completion time on a single machine with the learning effect and multiple availability constraints

This paper considers a single machine scheduling problem with the learning effect and multiple availability constraints that minimizes the total completion time. To solve this problem, a new binary integer programming model is presented, and a branch-and-bound algorithm is also developed for solving the given problem optimally. Since the problem is strongly NP-hard, to find the near-optimal solution for large-sized problems within a reasonable time, two meta-heuristics; namely, genetic algorithm and simulated annealing are developed. Finally, the computational results are provided to compare the result of the binary integer programming, branch-and-bound algorithm, genetic algorithm and simulated annealing. Then, the efficiency of the proposed algorithms is discussed.     

Note on “A note on single-machine group scheduling problems with position-based learning effect”

In a recent paper, Lee and Wu [W.-C. Lee, C.-C. Wu, A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model. 33 (2009) 2159–2163] proposed a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. They investigate the makespan and the total completion time minimization problems on a single-machine. As for the total completion time minimization problem, they assumed that the numbers of jobs in each group are the same and the group normal setup and the job normal processing times are agreeable. Under the assumption conditions, they showed that the total completion time minimization problem can be optimally solved in polynomial time solution. However, the assumption conditions for the total completion time minimization problem do not reflect actual practice in many manufacturing processes. Hence, in this note, we propose other agreeable conditions and show that the total completion time minimization problem remains polynomially solvable under the agreeable conditions.     

Minimizing total completion time and total deviation of job completion times from a restrictive due-date

We study a single-machine scheduling problem with the objective of minimizing a linear combination of total job completion times and total deviation of job completion times from a common due-date. The due-date is assumed to be restrictive, i.e., it may be sufficiently small to have an impact on the optimal sequence. When more weight is allocated to total job completion times, the problem is shown to have a polynomial time solution. When more weight is allocated to total completion time deviations from the due-date, the problem is NP-hard in the ordinary sense. For the latter case, we introduce an efficient dynamic programming algorithm, which is shown numerically to perform well in all our tests.     

Optimal streaming of a single job in a two-stage flow shop

Lot streaming is moving some portion of a process batch ahead to begin a downstream operation. The problem to be considered in this paper is the following: a single job consisting of U units is to be processed on two machines in the given order. Given a fixed number of possible transfer batches between the two machines, the problem is to find the timing and the size of the transfer batches (or, sublots) so as to optimize a given criterion. The schedules can be evaluated based on job completion, sublot completion, or item completion times. In the single job lot streaming problem, minimizing job completion time corresponds to minimizing the makespan, for which formulas for optimal sublot sizes are available. In this paper, the results for the sublot and item completion time models are presented.     

考虑产品与单元匹配的单元装配系统构建模型

针对日本式单元生产过程中流水装配线向单元装配系统转换的决策优化问题,本文以最小化总完工时间和工人总工时为目标,同时考虑产品与单元的匹配关系,构建了单元装配系统多目标优化模型,基于NSGA-II算法设计了适用于该问题的三段染色体的编码方式。通过算例分析了产品与单元匹配关系变化对总完工时间和工人总工时的影响,结果表明,在工人数不变的情况下,产品与单元匹配关系变化会导致总完工时间产生较大差异,随着工人数增多,这种差异逐渐变小。