Scheduling with tool changes to minimize total completion time: Basic results and SPT performance

Abstract

We consider a single machine sequencing problem subject to tool wear, where the objective is to minimize the total completion time. We briefly describe the problem and discuss its properties, complexity and solution. Mainly, however, we focus on the performance of the SPT list-scheduling heuristic. We provide theoretical worst-case bounds on SPT performance and also demonstrate its empirical behavior.

Scheduling preventive maintenance on a single CNC machine

“…This property is also similar for the problems in Qi et al (1999) and Akturk et al (2004). Proof: The left inequality above is a feasibility condition for the problem.…”

“…The total completion time problem with fixed processing times and unavailability constraints such that a machine can operate at most T40 hours between two PM visits was shown to be NP-hard by Qi et al (1999) and Akturk et al (2004). In this study, we have controllable processing times and employ a nonlinear PM index function for PM scheduling decisions, therefore we deal with a more difficult problem.…”

“…Increasing both p i and M(p i ) increases the total completion time. Therefore, we should not allow et al (1999) and Akturk et al (2004) proved some optimality properties for the total completion time problem with a maintenance or tool change constraint on a single machine. These two studies assume that maintenance or tool change should take place on a machine without exceeding a predefined operation time T. Our problem is different than these two problems in the sense that they assume that a job contributes to the PM need or tool need of a machine in proportion to its processing time, whereas we assume, in contrast to the current studies, that smaller processing time values (or higher cutting speeds and/or feed rates) may lead to a higher maintenance requirement since more force will be exerted on the CNC machine.…”

“…Qi et al (1999) study the total completion time of jobs 6798 S. Gurel and M. Selim Akturk on a single machine with multiple maintenance intervals of variable duration, and prove that this problem is NP-hard in a strong sense. Akturk et al (2004) and Qi (2007) establish the theoretical worst case performance of the SPT rule for this particular problem. Kutanoglu (2003, 2005) also consider the preventive maintenance planning and production scheduling decisions simultaneously to minimize the total weighted tardiness and total expected weighted completion time, respectively.…”

“…This property is common for the total completion time problems in Qi et al (1999) and Akturk et al (2004). Proof: Assume that the opposite holds, i.e.…”