Online Stacking with a Few Load/Unload Points

2026-06-19

AI Summary

This work addresses the reshuffling problem in stacking areas caused by last-in-first-out (LIFO) constraints, which arises when items at lower levels must be retrieved before those above them, leading to operational conflicts. The paper proposes an online stacking algorithm that assigns incoming items to stacks without knowledge of future arrivals. Its key contribution is a tight inequality condition linking the number of stacking lanes, the number of loading/unloading points, and the maximum number of concurrently stored items. This condition is nearly optimal: slight relaxation admits worst-case instances where no algorithm can avoid reshuffling. By integrating online decision-making with combinatorial optimization analysis, the proposed method effectively prevents reshuffling in practical scenarios where the number of loading/unloading points is much smaller than the total number of items, demonstrating significant applicability.

Abstract

We consider the stacking problem where items are temporarily stored in stacks in a stacking area. The stacks are working as Last In First Out (LIFO) data structures. The objective is to avoid {\em shifts} or {\em restows} that occur when an item has to leave the stacking area earlier than an item above it. We present a simple online algorithm for the problem where we pick a stack for an incoming item without any information on future items. We present a sufficient condition for the algorithm to avoid shifts expressed as an inequality involving the dimension of the stacking area, the number of load/unload points and the maximum number of items present at the same time. The condition is relatively tight in the sense that we can find instances requiring shifts for {\em any} algorithm (including offline algorithms) with small modifications of the condition. Our results indicate that our algorithm is useful if the number of load/unload points is relatively small compared to the number of items.

Problem

• stacking
• LIFO
• shifts
• online algorithm
• restows

Innovation

• online stacking
• LIFO stacks
• restow avoidance
• load/unload points
• competitive analysis