T.C.E. Cheng

A concise survey of scheduling with time-dependent processing times

Abstract We consider a class of machine scheduling problems in which the processing time of a task is dependent on its starting time in a schedule. On reviewing the literature on this topic, we provide a framework to illustrate how models for this class of problems have been generalized from the classical scheduling theory. A complexity boundary is presented for each model and related existing results are consolidated. We also introduce some enumerative solution algorithms and heuristics and analyze their performance. Finally, we suggest a few interesting areas for future research.

Some scheduling problems with deteriorating jobs and learning effects

Although scheduling with deteriorating jobs and learning effect has been widely investigated, scheduling research has seldom considered the two phenomena simultaneously. However, job deterioration and learning co-exist in many realistic scheduling situations. In this paper, we introduce a new scheduling model in which both job deterioration and learning exist simultaneously. The actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. For the single-machine case, we derive polynomial-time optimal solutions for the problems to minimize makespan and total completion time. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. For the case of an m-machine permutation flowshop, we present polynomial-time optimal solutions for some special cases of the problems to minimize makespan and total completion time.

A note on the complexity of the problem of two-agent scheduling on a single machine

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agents objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.

A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations

Scheduling with learning effects has received a lot of research attention lately. By learning effect, we mean that job processing times can be shortened through the repeated processing of similar tasks. On the other hand, different entities (agents) interact to perform their respective tasks, negotiating among one another for the usage of common resources over time. However, research in the multi-agent setting is relatively limited. Meanwhile, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of jobs increases or a job with a long processing time exists. Motivated by these observations, we consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and three simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.

Scheduling problems with deteriorating jobs and learning effects including proportional setup times

Recently, interest in scheduling with deteriorating jobs and learning effects has kept growing. However, research in this area has seldom considered setup times. We introduce a new scheduling model in which job deterioration and learning, and setup times are considered simultaneously. In the proposed model, the actual processing time of a job is defined as a function of the setup and processing times of the jobs already processed and the jobs own scheduled position in a sequence. In addition, the setup times are assumed to be proportional to the actual processing times of the already scheduled jobs. We derive polynomial-time optimal solutions for some single-machine problems with or without the presence of certain conditions.

The complexity of scheduling starting time dependent tasks with release times

Abstract We consider a family of problems of scheduling a set of starting time dependent tasks with release times and linearly increasing/decreasing processing rates on a single machine to minimize the makespan. We first present an equivalence relationship between several pairs of problems. Based on this relationship, we show that the makespan problem with arbitrary release times and identical increasing processing rates is strongly NP-complete and the corresponding case with only one non-zero release time is at least NP-complete in the ordinary sense. On the other hand, the makespan problem with arbitrary release times and identical decreasing processing rates is solvable in O(n6 log n) time by a dynamic programming algorithm. Using a different approach, we also show that, when the normal processing times are identical, the makespan problem with arbitrary release times and increasing/decreasing processing rates is strongly NP-complete and the corresponding case with only one non-zero release time is at least NP-complete in the ordinary sense.

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

Scheduling with learning effects has attracted growing attention of the scheduling research community. A recent survey classifies the learning models in scheduling into two types, namely position-based learning and sum-of-processing-times-based learning. However, the actual processing time of a given job drops to zero precipitously as the number of jobs increases in the first model and when the normal job processing times are large in the second model. Motivated by this observation, we propose a new learning model where the actual job processing time is a function of the sum of the logarithm of the processing times of the jobs already processed. The use of the logarithm function is to model the phenomenon that learning as a human activity is subject to the law of diminishing return. Under the proposed learning model, we show that the scheduling problems to minimize the makespan and total completion time can be solved in polynomial time. We further show that the problems to minimize the maximum lateness, maximum tardiness, weighted sum of completion times and total tardiness have polynomial-time solutions under some agreeable conditions on the problem parameters.

Two-agent scheduling with position-based deteriorating jobs and learning effects

Scheduling with deteriorating jobs and learning effects has been widely studied. However, multi-agent scheduling with simultaneous considerations of deteriorating jobs and learning effects has hardly been considered until now. In view of this, we consider a two-agent single-machine scheduling problem involving deteriorating jobs and learning effects simultaneously. In the proposed model, given a schedule, we assume that the actual processing time of a job of the first agent is a function of position-based learning while the actual processing time of a job of the second agent is a function of position-based deterioration. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and several simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.

Unrelated parallel-machine scheduling with deteriorating maintenance activities

We study the problem of unrelated parallel-machine scheduling with deteriorating maintenance activities. Each machine has at most one maintenance activity, which can be performed at any time throughout the planning horizon. The length of the maintenance activity increases linearly with its starting time. The objective is to minimize the total completion time or the total machine load. We show that both versions of the problem can be optimally solved in polynomial time.

A Self-guided Genetic Algorithm for permutation flowshop scheduling problems

In this paper we develop a Self-guided Genetic Algorithm (Self-guided GA), which belongs to the category of Estimation of Distribution Algorithms (EDAs). Most EDAs explicitly use the probabilistic model to sample new solutions without using traditional genetic operators. EDAs make good use of the global statistical information collected from previous searches but they do not efficiently use the location information about individual solutions. It is recently realized that global statistical information and location information should complement each other during the evolution process. In view of this, we design the Self-guided GA based on a novel strategy to combine these two kinds of information. The Self-guided GA does not sample new solutions from the probabilistic model. Instead, it estimates the quality of a candidate offspring based on the probabilistic model used in its crossover and mutation operations. In such a way, the mutation and crossover operations are able to generate fitter solutions, thus improving the performance of the algorithm. We tested the proposed algorithm by applying it to deal with the NP-complete flowshop scheduling problem to minimize the makespan. The experimental results show that the Self-guided GA is very promising. We also demonstrate that the Self-guided GA can be easily extended to treat other intractable combinatorial problems.