Family sequencing and cooperation

Abstract

This paper analyzes a single-machine scheduling problem with family setup times both from an optimization and a cost allocation perspective. In a so-called family sequencing situation jobs are processed on a single machine, there is an initial processing order on the jobs, and every job within a family has an identical cost function that depends linearly on its completion time. Moreover, a job does not require a setup when preceded by another job from the same family while a family specific setup time is required when a job follows a member of some other family.Explicitly taking into account admissibility restrictions due to the presence of the initial order, we show that for any subgroup of jobs there is an optimal order, such that all jobs of the same family are processed consecutively. To analyze the allocation problem of the maximal cost savings of the whole group of jobs, we define and analyze a so-called corresponding cooperative family sequencing game which explicitly takes into account the maximal cost savings for any coalition of jobs. Using nonstandard techniques we prove that each family sequencing game has a non-empty core by showing that a particular marginal vector belongs to the core. Finally, we specifically analyze the case in which the initial order is family ordered.

Cooperation and Competition in Linear Production and Sequencing Processes

“…The first so-called sequencing game was developed by Curiel et al (1989b) for the deterministic one-machine sequencing problem. The work on sequencing games has been extended in several ways (see also Curiel et al (2002) for a survey), including, but not limited to sequencing games with ready times (Hamers et al, 1995), due dates (Borm et al, 2002), setup times (Grundel et al, 2013), precedence relations (Hamers et al, 2005), and externalities (Yang et al, 2019).…”

On interactive sequencing situations with exponential cost functions

“…We mention Hamers, Borm, and Tijs (1995) by imposing ready times, Borm, Fiestras-Janeiro, Hamers, Sánchez, and Voorneveld (2002) by imposing due dates, Rustogi and Strusevich (2012) by studying positional effects, Lohmann, Borm, and Slikker (2014) by analyzing just-in-time arrivals and Musegaas, Borm, and Quant (2015) by considering step out-step in sequencing games. Moreover, Grundel, Çiftçi, Borm, and Hamers (2013), Gerichhausen and Hamers (2009) and Çiftçi, Borm, Hamers, and Slikker (2013) studied the grouping of players in families or batches. Finally, we mention Klijn and Sánchez (2006), who studied uncertainty sequencing games.…”

Shapley Value for Parallel Machine Sequencing Situation without Initial Order

“…Hamers et al [10], Borm et al [11], and Hamers et al [12] imposed ready times, due dates, and chains precedence constraints, respectively, on the jobs. Grundel et al [13] analyzed the single machine sequencing situation with family setup times, where the jobs within a family have an identical cost function.…”