A preemptive single-machine scheduling problem with a late work criterion and convex resource consumption functions

Pareto-scheduling of two competing agents with their own equal processing times

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.

A survey of scheduling problems with late work criteria

Scheduling theory is concerned with problems of the allocation of resources to perform a set of activities in order to achieve a certain goal. The purpose of the scheduling process could be attained by finding a feasible solution of the considered problem as well as by determining the best solution in the reference to a given optimality criterion. There are a few classical performance measures broadly studied such as schedule length, mean or mean weighted flow time, maximum lateness etc. However, trying to cover more realistic problems, new parameters and criteria must be considered. The performance measure based on the amount of late work in the system is an example of such a non-classical criterion involving due dates. Classical criteria such as e.g. maximum lateness or mean tardiness calculate the penalty for late tasks with respect to the time of their completion, whereas in some applications, the penalty should be determined with the reference to the amount of the late work independently of the time of its completion. The criteria based on late work were first proposed in the context of parallel processors and then applied in a one machine scheduling problem. In the paper, new results are presented concerning general complexity of scheduling problems with the late work criteria and some special cases in the shop environment.

We consider a single-machine scheduling problem such that the processing time of each job is inversely proportional to the power of the amount of resource consumption. The objective is to minimize the sum of the total resource consumption cost and the total late work, or minimize the total late work with a constraint on the total resource consumption cost. Under any objective, we prove the NP-hardness of the case with more than or equal to two different due dates, and the polynomiality of the case with a common due date.

In this paper, we consider three preemptive Pareto-scheduling problems with two competing agents on a single machine. In each problem, the objective function of agent A is the total completion time, the maximum lateness, or the total late work while the objective function of agent B is the total late work. For each problem, we provide a polynomial-time algorithm to characterize the trade-off curve of all Pareto-optimal points.

Scheduling is considered as a key task in many industries, such as project based scheduling, crew scheduling, flight scheduling, machine scheduling, etc. In the machine scheduling area, the job shop scheduling problems are considered to be important and highly complex, in which they are characterized as NP-hard. The job shop scheduling problems with late work criterion and non-preemptive jobs are addressed in this paper. Late work criterion is a fairly new objective function. It is a qualitative measure and concerns with late parts of the jobs, unlike classical objective functions that are quantitative measures. In this work, simulated annealing was presented to solve the scheduling problem. In addition, operation based representation was used to encode the solution, and a neighbourhood search structure was employed to search for the new solutions. The case studies are Lawrence instances that were taken from the Operations Research Library. Computational results of this probabilistic meta-heuristic algorithm were compared with a conventional genetic algorithm, and a conclusion was made based on the algorithm and problem.

Open shop scheduling problems with late work criteria

This paper studies a two-agent single-machine scheduling problem with sum-of-processing-times-based learning consideration. The goal is to find an optimal schedule to minimize the total late work of the first agent subject to the restriction that the maximum lateness of the second agent has an upper bound. For this problem, a branch-and-bound algorithm along with several dominances and a lower bound is developed to find the optimal solution, and a tabu algorithm with several improvements is proposed to find the near-optimal solution. Computational experiments are provided to further measure the performance of the proposed algorithms.

This paper addresses a two-agent scheduling problem where the objective is to minimize the total late work of the first agent, with the restriction that the maximum lateness of the second agent cannot exceed a given value. Two pseudo-polynomial dynamic programming algorithms are presented to find the optimal solutions for small-scale problem instances. For medium- to large-scale problem instances, a branch-and-bound algorithm incorporating the implementation of a lower bounding procedure, some dominance rules and a Tabu Search-based solution initialization, is developed to yield the optimal solution. Computational experiments are designed to examine the efficiency of the proposed algorithms and the impacts of all the relative parameters.

Single machine scheduling problems with resource dependent release times

Single machine scheduling with assignable due dates to minimize maximum and total late work

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.

In the paper, we consider the problem of scheduling jobs on parallel identical machines with the late work criterion and a common due date, both offline and online cases. Since the late work criterion has not been studied in the online mode so far, the analysis of the online problem is preceded by the analysis of the offline problem, whose complexity status has not been formally stated in the literature yet. Namely, for the offline mode, we prove that the two-machine problem is binary NP-hard, and the general case is unary NP-hard. In the online mode we assume that jobs arrive in the system one by one, i.e., we consider the online over list model. We give an algorithm with a competitive ratio being a function of the number of machines, and we prove the optimality of this approach for two identical machines.

Single machine scheduling problems with deteriorating jobs