The paper deals with the problem of packing a set of horizontal bars by taking into account some constraints on the distance between two consecutive bars on the same row. This problem is deeply connected with Discrete Tomography and it finds application in workforce scheduling. We study the complexity of the problem and show that, depending on the kind of constraints considered, the problem can be polynomial or NP-Complete. We analyze in details the case where a minimal distance between consecutive bars is required and propose a greedy algorithm which solves this problem in polynomial time.