A reply to Ponte et al (2016) Supply chain collaboration: Some comments on the nucleolus of the beer game

Purpose: The aim of the paper is to pick up the result of a previously published paper in order to deepen the discussion. We analyze the solution against the background of some well-known concepts and we introduce a newer one. In doing so we would like to inspire the further discussion of supply chain collaborationDesign/methodology/approach: Based on game theoretical knowledge we present and compare seven properties of fair profit sharing.Findings: We show that the nucleolus is a core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional fairness criteria.Originality/value: We discuss the very involved procedure of establishing lexicographic orders of excess vectors for games with many players.

Non-dominated Sorting Genetic Algorithms for a Multi-objective Resource Constraint Project Scheduling Problem

The resource constraint project scheduling problem (RCPSP) has attracted growing attention since the last decades. Precedence constraints are considered as well as resources with limited capacities. During the project, the same resource can be required by several in-process jobs and it is compulsory to ensure that the consumptions do not exceed the limited capacities. In this paper, several criteria are involved, namely makespan, total job tardiness, and workload balancing level. Our problem is firstly solved by the non-dominated sorting genetic algorithm-II (NSGAII) as well as the recently proposed NSGAIII. Giving emphasis to the selection procedure, we apply both the traditional Pareto dominance and the less documented Lorenz dominance into the niching mechanism of NSGAIII. Hence, we adopt and modify L-NSGAII to our problem and propose L-NSGAIII by integrating the notion of Lorenz dominance. Our methods are tested by 1350 randomly generated instances, considering problems with 30–150 jobs and different configurations of resources and due dates. Hypervolume and C-metric are considered to evaluate the results. The Lorenz dominance leads the population more toward the ideal point. As experiments show, it allows improving the original NSGA approach.