Abstract
In this paper, we present complexity results for storage loading problems where the storage area is organized in fixed stacks with a limited common height. Such problems appear in several practical applications, e.g., in the context of container terminals, container ships or warehouses. Incoming items arriving at a storage area have to be assigned to stacks so that certain constraints are respected (e.g., not every item may be stacked on top of every other item). We study structural properties of the general model and special cases where at most two or three items can be stored in each stack. Besides providing polynomial time algorithms for some of these problems, we establish the boundary to NP-hardness.
Highlights
Storage loading problems arise in several practical applications, e.g., in the context of container terminals, container ships, warehouses or steel yards
In the following we prove that already the special case of transitive stacking constraints sij is NP-complete by showing that the reduction from X3C holds if the graph G = (V, A) is transitive
We show that the problem without stacking constraints is polynomially solvable if the objective is to minimize the transportation costs TC(x, y), the number of items stacked above the ground level #SI>1, or a weighted sum of them
Summary
Storage loading problems arise in several practical applications, e.g., in the context of container terminals, container ships, warehouses or steel yards In such problems incoming items arrive at a storage area by trains, vessels or trucks and have to be assigned to stacks respecting certain constraints. We study problems where items have to be loaded into a twodimensional storage area consisting of stacks where each stack has its own fixed position. The main goal of a storage loading problem is to assign each incoming item to a feasible position in a stack such that a given objective function is optimized. Several aspects of such problems are of interest for practitioners.
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