Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs

In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this paper we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (hard capacities), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution (soft capacities). We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item lot sizing inventory pr...

• Type: Journal
• Year: 2008
• Where: TALG
• Authors: Guy Even, Retsef Levi, Dror Rawitz, Baruch Schieber, Shimon Shahar, Maxim Sviridenko
• Keywords: Hard Capacities, Rectangle, Rectangle Stabbing Problem, TALG 2008