Optimally rescheduling jobs with a Last-In-First-Out buffer

Abstract

This paper considers single-machine scheduling problems in which a given solution, i.e., an ordered set of jobs, has to be improved as much as possible by re-sequencing the jobs. The need for rescheduling may arise in different contexts, e.g., due to changes in the job data or because of the local objective in a stage of a supply chain that is not aligned with the given sequence. A common production setting entails the movement of jobs (or parts) on a conveyor. This is reflected in our model by facilitating the re-sequencing of jobs via a buffer of limited capacity accessible by a LIFO policy. We consider the classical objective functions of total weighted completion time, maximum lateness and (weighted) number of late jobs and study their complexity. For three of these problems, we present strictly polynomial-time dynamic programming algorithms, while for the case of minimizing the weighted number of late jobs NP-hardness is proven and a pseudo-polynomial algorithm is given.

Algorithms for rescheduling jobs with a LIFO buffer to minimize the weighted number of late jobs

“…In this paper, we consider the following setting of a singlemachine problem which was introduced in Nicosia et al (2019) and treated in more detail in Nicosia et al (2021).…”

“…The main contributions of the preceding paper by Nicosia et al (2021) for the rescheduling problem were strictly polynomial algorithms based on dynamic programming for the minimization of the following classical objective functions:…”

“…For this objective, the rescheduling problem was shown to be NP-hard. In Nicosia et al (2021), only a pseudo-polynomial dynamic programming algorithm was given, as an extension of the respective algorithm for the unweighted case. However, the development and evaluation of actually applicable solution strategies was left open in this previous work.…”

“…Two survey papers treating rescheduling topics are presented by Ouelhadj and Petrovic (2009) and Vieira et al (2003). Additional pointers to the related literature can be found in Nicosia et al (2021).…”

“…4, we develop a new realization of a dynamic programming algorithm. While the previous dynamic program from Nicosia et al (2021) turns out to be hardly applicable even for moderate-sized test instances, our new algorithm employs dominance criteria and an efficient handling of lists of states, resulting in a competitive solution method.…”