共查询到10条相似文献,搜索用时 156 毫秒
1.
Liron Yedidsion 《Journal of Scheduling》2012,15(6):665-679
We analyze two single machine scheduling problems for the case where job processing times are controllable, by allocating continuous and non-renewable resources to the processing operations. The first problem to analyze is constructing the trade-off curve between maximum lateness and total resource consumption; an O(n 2) computational time optimization algorithm was constructed to solve this problem. This algorithm was extended to solve the second problem, which is to construct the trade-off surface between maximum lateness, makespan, and total resource consumption. As part of this algorithm we identify a plane in the 3D field that is formed by the three criteria, which is parallel only to the maximum lateness, and calculate the optimal makespan and total resource consumption as functions of points on this plane. The extended algorithm keeps the same complexity of O(n 2) time. Both algorithms are very robust as they solve the problem for a very large set of resource consumption functions which has to follow only some mild (and commonly acceptable) conditions. Moreover, as far as we know, this is the first research of its kind in the field of multi-objective scheduling to present an algorithm that constructs a 3D trade-off surface. 相似文献
2.
We consider single-machine batch delivery scheduling with an assignable common due date and controllable processing times, which vary as a convex function of the amounts of a continuously divisible common resource allocated to individual jobs. Finished jobs are delivered in batches and there is no capacity limit on each delivery batch. We first provide an O(n5) dynamic programming algorithm to find the optimal job sequence, the partition of the job sequence into batches, the assigned common due date, and the resource allocation that minimize a cost function based on earliness, tardiness, job holding, due date assignment, batch delivery, and resource consumption. We show that a special case of the problem can be solved by a lower-order polynomial algorithm. We then study the problem of finding the optimal solution to minimize the total cost of earliness, tardiness, job holding, and due date assignment, subject to limited resource availability, and develop an O(nlog n) algorithm to solve it. 相似文献
3.
In many resource allocation problems in physical or economic systems, a linear resource consumption function is commonly considered, and job processing times are assumed to be fixed parameters. However, the former assumption fails to reflect the law of diminishing returns, and the latter may be controlled by changing the allocation of resources to jobs. Motivated by these observations, we provide a unified model for solving single-machine scheduling problems in which each job's processing time is a function of its starting time and convex resource allocation. The objective is to find the optimal sequence of jobs subject to a limited resource consumption. We first show how this unified model can be useful in solving scheduling problems under due date assignment considerations. We analyze the problem with four different due date assignment methods, and our objective function includes costs for earliness, tardiness and due date assignments. We also consider scheduling problems without involving due date assignment decisions. The objective function is to minimize the makespan, total completion time, total absolute variation in completion times, and total absolute variation in waiting times. We show that several existing well-known problems can be reduced to a special case of our unified model and solved in O(nlogn) time. 相似文献
4.
We consider two single machine scheduling problems with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. In the first problem, the objective is to minimize the total resource consumption with a constraint on the sum of job completion times. We show that a recognition version of the problem is NP-complete. In the second problem, the objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. We provide some optimality conditions and show that the problem is polynomially solvable. 相似文献
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6.
In this paper, we consider a single-machine scheduling problem with release dates. The aim is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose two new lower bounds that can be, respectively, computed in O(n2) and in O(nlogn) time where n is the number of jobs. We prove a sufficient and necessary condition for local optimality, which can also be considered as a priority rule. We present an efficient heuristic using such a condition. We also propose some dominance properties. A branch-and-bound algorithm incorporating the heuristic, the lower bounds and the dominance properties is proposed and tested on a large set of instances. 相似文献
7.
This paper studies a bicriteria scheduling problem on a series-batching machine with objective of minimizing makespan and total completion time simultaneously. A series-batching machine is a machine that can handle up to b jobs in a batch and the completion time of all jobs in a batch is equal to the finishing time of the last job in the batch and the processing time of a batch is the sum of the processing times of jobs in the batch. In addition, there is a constant setup time s for each batch. For the problem we can find all Pareto optimal solutions in O(n2) time by a dynamic programming algorithm, where n denotes the number of jobs. 相似文献
8.
We consider a problem to schedule a set of jobs on a single machine under the constraint that the maximum job completion time does not exceed a given limit. Before a job is released for processing, it must undergo some preprocessing treatment which consumes resources. It is assumed that the release time of a job is a positive strictly decreasing continuous function of the amount of resources consumed. The objective is to minimize the total resource consumption. We show that ordering jobs in nonincreasing processing times yields an optimal solution. We then consider a bicriterion approach to the problem in which the maximum job completion time and the resource consumption are simultaneously minimized and present a polynomial time solution algorithm. Finally, we consider a related problem in which the job release times are given but the processing times are functions of the amount of resource consumed. We show that ordering jobs in nondecreasing release times gives an optimal solution and that the problem to minimize both the maximum completion time and resource consumption is polynomially solvable 相似文献
9.
Marek Cygan Marcin Pilipczuk Michał Pilipczuk Jakub Onufry Wojtaszczyk 《Algorithmica》2014,68(3):692-714
In a scheduling problem, denoted by 1|prec|∑C i in the Graham notation, we are given a set of n jobs, together with their processing times and precedence constraints. The task is to order the jobs so that their total completion time is minimized. 1|prec|∑C i is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2 n n O(1) time, and whether there exists an algorithms solving 1|prec|∑C i in O(c n ) time for some constant c<2 was an open problem posted in 2004 by Woeginger. In this paper we answer this question positively. 相似文献