On Interactive Sequencing Situations with Exponential Cost Functions

This paper addresses interactive one-machine sequencing situations in which the costs of processing a job are given by an exponential function of its completion time. The main difference with the standard linear case is that the gain of switching two neighbors in a queue is time-dependent and depends on their exact position. We illustrate that finding an optimal order is complicated in general and we identify specific subclasses, which are tractable from an optimization perspective. More specifically, we show that in these subclasses, all neighbor switches in any path from the initial order to an optimal order lead to a non-negative gain. Moreover, we derive conditions on the time-dependent neighbor switching gains in a general interactive sequencing situation to guarantee convexity of the corresponding cooperative game. These conditions are satisfied within our specific subclasses of exponential interactive sequencing situations.