A Puzzle-Based Sequencing System for Logistics Items

Abstract

Background: The new demands of the current market including for space should be satisfied by designing modern material flow systems. Designing warehouses using effective material handling equipment significantly supports cost reduction and efficient space utilization. Sequencing of items is an important process that leads to enhanced logistics operations. Current approaches are not capable of fully fulfilling dynamic changes. Methods: In this paper, a puzzle-based sequencing system with a high density and highly efficient floor space utilization was successfully developed. Accordingly, two solving methods were investigated: game tree and pathfinding algorithms. A-star was chosen based on pathfinding algorithms in order to find the shortest solution of the puzzle in which the sequencing time was decreased. The pre-sorting strategy was proposed to overcome the unsolvable configuration issue that cannot be solved by the aforementioned methods. Moreover, the shape of the puzzle was considered. Results: Based on numerical calculations, we found that a square shape was better than a rectangle in terms of solution steps, and we confirmed the direct relationship between the aspect ratio and rectilinear distance, which directly affects the pre-sorting steps. Conclusion: Our results prove that the puzzle-based sequencing system should be highly preferred for effective floor space utilization compared to the current systems.

The Fifteen Puzzle—A New Approach through Hybridizing Three Heuristics Methods

“…Furthermore, this total overestimation is very small and it does not have a great impact on the results of BA* as Table 6 shows that 91% of the instances are 0 to 6 moves away from their optimal solutions and reaching the goal for each instance, a small number of states are generated. Because of that reason we calculate the heuristic function in the evaluation function (Equation ( 2) [1]) as shown in Equation (3) named as Hybridizing Heuristic (HH). To find the shortest path, the A* algorithm uses the evaluation function as it is shown in Equation ( 2) which is equal to 𝑔(𝑠) the depth cost from the start state to the current state plus the ℎ(𝑠) the heuristic that estimates the distance from current state to the goal state.…”

“…Thayer, Dionne, and Ruml [32] state to reduce the solving time, a near-optimal solution is a practical alternative. To reduce the number of generated nodes, we have incorporated aspects from the three heuristics to create a better one and the heuristic function in the evaluation function (Equation (2) [1]) is calculated as shown in Equation (3). As shown in Equation (3) three heuristics are combined to estimate the cost from a given state (node) to the goal state.…”

“…The Fifteen Puzzle is a standard sliding puzzle invented by Samuel Loyd in the 1870s [1], which consists of 15 tiles with one tile missing within a 4x4 grid. The fifteen tiles numbered from 1 to 15.…”