Step out–Step in sequencing games

Abstract

In this paper a new class of relaxed sequencing games is introduced: the class of Step out -Step in sequencing games. In this relaxation any player within a coalition is allowed to step out from his position in the processing order and to step in at any position later in the processing order. Providing an upper bound on the values of the coalitions we show that every Step out -Step in sequencing game has a non-empty core. This upper bound is a sufficient condition for a sequencing game to have a non-empty core. Moreover, this paper provides a polynomial time algorithm to determine the coalitional values of Step out -Step in sequencing games.

A short proof of convexity of step-out–step-in sequencing games

“…Musegaas et al [3] consider the following greedy algorithm for computing v(S) (in fact, they consider a variation of this which is more complicated to describe, but which is equivalent; see Lemma 2). Start with the order σ ′ = σ 0 , and consider each player i ∈ S in turn, from latest to earliest according to σ 0 .…”

“…How one interprets the notion of "no worse off" gives rise to many different variants of sequencing games. Musegaas, Brom, and Quant [3] introduced the Step out-Step in (SoSi) sequencing game where coalition members cannot move ahead of non-coalition members. They provide a greedy algorithm for computing the optimal cost savings for a coalition in their original paper [3].…”

“…Musegaas, Brom, and Quant [3] introduced the Step out-Step in (SoSi) sequencing game where coalition members cannot move ahead of non-coalition members. They provide a greedy algorithm for computing the optimal cost savings for a coalition in their original paper [3]. In a follow-up work, they prove that the SoSi game is convex [4].…”

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.…”

Sequencing Situations and Games With Non-Linear Cost Functions

“…This line of approach follows the direction of research in which assumptions of the standard sequencing model are relaxed or modified. For example, Slikker (2006) relaxed the assumption of cooperation between players, Lohmann, Borm, and Slikker (2014) modified the definition of the time a job spends in the system, and Musegaas, Borm, and Quant (2015) relaxed the set of admissible rearrangements. On the other hand, a lot of research is done in the direction of adding components to the model.…”