Optimal servicing strategy design problems for stationary objects in a one-dimensional working zone of a processor

We introduce a model of one-stage service for a group of stationary objects located along a one-dimensional working zone of a moving processor. For the servicing, the processor sequentially performs two passes between boundary points of the working zone: the direct pass, servicing some of the objects, and the reverse pass, servicing all remaining objects of a group. With each object, we associate an individual penalty function that increases monotonely with the time of finishing its servicing. We formulate design problems for optimal servicing strategies, give algorithms of their solutions, and study the issues of computational complexity.