Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.

The Car Resequencing Problem with Pull-Off Tables

The car sequencing problem determines sequences of different car models launched down a mixed-model assembly line. To avoid work overloads of workforce, car sequencing restricts the maximum occurrence of labor-intensive options, e.g., a sunroof, by applying sequencing rules. We consider this problem in a resequencing context, where a given number of buffers (denoted as pull-off tables) is available for rearranging a stirred sequence. The problem is formalized and suited solution procedures are developed. A lower bound and a dominance rule are introduced which both reduce the running time of our graph approach. Finally, a real-world resequencing setting is investigated.