Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

A Linear Programming Approach for Parallel Cell Scheduling with Sequence-Dependent Setup Times

In this study, we consider the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel production cells. The objective of this study is to minimize the total completion time. We note that total customer demands for each type should be satisfied, and total required production time in each cell cannot exceed the capacity of the cell. This problem is formulated as an integer programming model and an interface is designed to provide integrity between data and software. Mathematical model is tested by both randomly generated data set and real-world data set from a factory that produce automotive components. As a result of this study, the solution which gives the best alternative production schedule is obtained.

Partitioning of Independent Tasks for Minimizing Completion Time and Total Waiting Time

Parallel processors provide fast computing environments for various users.But the real efficiencies ofparallel processors intensively depend on the partitioning strategies of tasks over the processors.In thispaper,the partitioning problems of independent tasks for homogeneous system of parallel processors arequantitatively studied.We adopt two criteria,minimizing the completion time and the total waiting time,to determine the optimal partitioning strategy.

Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming

Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.

Optimal Batching Structures of Single Machine Scheduling

A batch is a subset of jobs which must be processed jointly in either serial or parallel form. For the single machine, batching, total completion time scheduling problems, the algorithmic aspects have been extensively studied in the literature. This paper presents the optimal hatching structures of the problems on the batching ways： all jobs in exactly N（arbitrary fix batch number and 1 〈 N 〈 n） batches.

SCHEDULING JOBS WITH GENERAL LEARNING FUNCTIONS

This paper deals with single-machine scheduling problems with a more general learning effect based on sum-of-processing-time. In this study, sum-of-processing-time-based learning effect means that the processing time of a job is defined by a decreasing function of the total normal processing time of jobs that come before it in the sequence. Results show that even with the introduction of the sum-of-processing-time-based learning effect to job processing times, single-machine makespan minimization problems remain polynomially solvable. The curves of the optimal schedule of a total completion time minimization problem are V-shaped with respect to iob normal orocessinz times.