Choosing the Job Sequence and Processing Times to Minimize Total Processing Plus Flow Cost on a Single Machine

Abstract

This paper treats the problem of minimizing the total weighted flow cost plus job-processing cost in a single machine sequencing problem for jobs having processing costs which are linear functions of processing times. The optimal job sequence and processing times are obtainable from the solution of an associated problem of optimal row and column selection in a symmetric matrix. Some sufficient conditions for expediting certain jobs are proved. In order to handle cases in which these conditions fail to complete the solution to the problem a heuristic algorithm with a provable performance bound is developed. The heuristic solutions are compared with optimal solutions obtained by branch and bound in numerous randomly generated problems and are found to be optimal in most cases.

Resource Management in Machine Scheduling Problems: A Survey

“…These models, however, do not reflect precisely many real life production systems in which problems parameters are variables dependent on some additional resources. In early 80's these classical models were extended by Janiak [41] and independently by Vickson [77], [78] to models with resource dependent processing times. Similarly, in 1989 Janiak introduced the problems with resource dependent release dates [31].…”

A new bounding mechanism for the CNC machine scheduling problems with controllable processing times

“…Karabati and Kouvelis [6] solve the simultaneous scheduling and optimal processing times selection problem in a flow line operated under a cyclic scheduling policy. Vickson presents simple methods for solving two single machine sequencing problems when job processing times are themselves decision variables having their own linearly varying costs [13].…”

Approximation schemes for job shop scheduling problems with controllable processing times

“…A scheduling problem in which the processing times of the jobs can be reduced at some expense is called a scheduling problem with controllable processing times. Scheduling problems with controllable processing times have gained importance in scheduling research since the pioneering works of Vickson [23,24]. For a survey of this area until 1990, the reader is referred to [17].…”