Abstract
In this paper, we address a layout design problem, PTN[2], for determining an appropriate 2-class-based dedicated storage layout in a class of unit load storage systems. Our strong conjecture is that PTNI2] is NP-hard. Restricting PTN[2], we provide three solvable cases of PTN[2] in which an optimal solution to the solvable cases is one of the partitions based on the PAI(product activity index)-nonincreasing ordering. However, we show with a counterexample that a solution based on the PAI-non increasing ordering does not always give an optimal solution to PTN[2]. Utilizing the derived properties, we construct an effective heuristic algorithm for solving PTN[2] based on a PAI-non increasing ordering with performance ratio bound. Our algorithm with O($n^2$) is effective in the sense that it guarantees a better class-based storage layout than a randomized storage layout in terms of the expected single command travel time.