Linhui Sun

Scheduling jobs with truncated exponential learning functions

In this paper we consider the single machine scheduling problem with truncated exponential learning functions. By the truncated exponential learning functions, we mean that the actual job processing time is a function which depends not only on the total normal processing times of the jobs already processed but also on a control parameter. The use of the truncated function is to model the phenomenon that the learning of a human activity is limited. We show that even with the introduction of the proposed model to job processing times, several single machine problems remain polynomially solvable. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without truncated exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms.

Single-machine scheduling to minimize total absolute differences in waiting times with deteriorating jobs

In this paper we consider a single-machine scheduling problem with simple linear deterioration. By simple linear deterioration, we mean that the processing time of a job is a simple linear function of its execution starting time and its deterioration rate. The objective is to find a schedule that minimizes total absolute differences in waiting times. We show that the optimal schedule is V-shaped: jobs are arranged in descending order of their deterioration rates if they are placed before the job with the smallest deterioration rate, but in ascending order of their deterioration rates if placed after it. We prove other several properties of an optimal schedule, and introduce two efficient heuristic algorithms that are tested against a lower bound. We also provide computational results to evaluate the performance of the heuristic algorithms.

A note on flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

The main results in a recent paper [M. Cheng, S. Sun, L. He, Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines, European Journal of Operational Research 183 (2007) 115-124] are incorrect because job processing times are variable due to deteriorating effect, which is not taken into account by the authors. In this note, we show first by counter-examples that the published results are incorrect, and then we provide corrected results.

Scheduling jobs with an exponential sum-of-actual-processing-time-based learning effect

In this paper we consider single-machine scheduling problems with an exponential sum-of-actual-processing-time-based learning effect. By the exponential sum-of-actual-processing-time-based learning effect, we mean that the processing time of a job is defined by an exponential function of the sum of the actual processing times of the already processed jobs. For the proposed learning model, we show that under certain conditions, the makespan minimization problem, the sum of the @qth (@q>0) powers of completion times minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem all remain polynomially solvable.