Abstract
Stacking goods or items is one of the most common operations in everyday life. It happens abundantly in not only transportation applications such as container ports, container ships, warehouses, factories, sorting centers, freight terminals, etc., but also computing systems, supermarkets, and so on. We investigate the problem of stacking a sequence of items into a set of capacitated stacks, subject to stacking constraints. In every stack, items are accessed in the last-in-first-out order. So at retrieval time, getting any lower item requires reshuffling all upper items that are blocking the way (called blocking items). These reshuffles are redundant and expensive. The challenge is to prevent reshuffles from happening. For this purpose, we aim at assigning items to stacks to minimize the number of blocking items with respect to the retrieval order. We provide some mathematical analyses on the feasibility of this problem and lower bounds. Besides, we provide a mathematical model and a two-step heuristic framework. We illustrate the applications of these models and heuristic framework in the real cargo handling process in an Asian port. Experimental results on real scenarios show that the proposed model can eliminate almost all reshuffles, and thus decrease the number of stacking violations from 62.6 % to 0.9 %. We also provide an empirical analysis of variants of the heuristic framework.
Highlights
The problem of stacking goods/items arises in many applications such as container terminals, warehouses, factories, supermarkets, computer memory, and so on
PROBLEM DESCRIPTION The problem investigated in this paper is named as Stack Loading Problem (SLP)
The SLP model was run on these instances with CPLEX 12.9.0 configured with a time limit of 5 seconds
Summary
The problem of stacking goods/items (we call it the Stack Loading Problem, abbreviated as SLP) arises in many applications such as container terminals, warehouses, factories, supermarkets, computer memory, and so on. This paper attempts to minimize reshuffles in stacks by minimizing the number of blocking items while making sure that no item violates hard stacking constraints It has the following contributions: (1) Lemmas on the feasibility of the problem and lower bounds, (2) A mathematical model which allows the problem to be solved to optimality, (3) Applications of the proposed model on a real-world problem in an Asian port, showing a significant improvement in stacking efficiency, (4) A two-step heuristic framework with several variants, (5) An empirical analysis of these variants. Delgado et al [10] proposed an integer and a constraint programming models to optimize a weighted sum of four objectives, including the number of blocking items They assumed that the arrival order of items is not imposed.
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