A.N.T.s: Algorithm for Navigating Traffic System in Automated Warehouses
According to CNN Indonesia 2020, the demand for e-Commerce in Indonesia has nearly doubled during this pandemic. This surge in demand calls for a time-efficient method for warehouse order-picking. One approach to achieve that goal is by incorporating automation in their warehouse systems. Globally, the market of warehouse robotics is expected to reach 12.6 billion USD by 2027 (Data Bridge Market Research, 2020). In this research, the warehouse system studied would utilize AMR (Autonomous Mobile Robots) to lift and deliver movable shelf units to the packing station where workers are at. This research designed a heuristic algorithm called A.N.T.s (Algorithm for Navigating Traffic System) to conduct task assigning and pathfinding for AMR in the automated warehouse. The warehouse layout was drawn as a two-dimensional map in grids. When an order is placed, A.N.T.s would assign the task to a robot that would require the least amount of time to reach the target shelf. A.N.T.s then conducted pathfinding heuristically using Manhattan Distance. A.N.T.s would help the robot to navigate its way to the target shelf unit, lift the shelf and bring it to the designated packing station. A.N.T.s algorithm was tested in various warehouse layouts and with a varying number of AMRs. Comparison against the commonly used Djikstra’s algorithm was also conducted (Shaikh and Dhale, 2013). Results show that the proposed A.N.T.s algorithm could execute 100 orders in a 27x23 layout with five robots 9.96 times faster than Dijkstra with no collisions. The algorithm is also shown to be able to help assign tasks to robots and help them find short paths to navigate their ways to the shelf units and packing stations. A.N.T.s could navigate traffic to avoid deadlocks and collisions in the warehouse with the aid of lanes and directions.
糖果傳遞問題之研究與推廣
n個人圍成一圈,面向圓心,且逆時針編號1,2,……,n。一開始每人手中有一個糖果,由1號開始,逆時針分別給右邊的人一個、兩個、一個、兩個……糖果,手上沒有糖果的人必須退出。我們將此傳遞規則定義為T_1,2,同理T_(1,2⋯,p)。這個傳遞遊戲,最終會有兩種情形,第一種是由一人獨得所有糖果(成功狀態),第二種是數人間傳遞糖果且形成循環(循環狀態)。 研究後得知,在傳遞規則T_(1,2⋯,p) (p≥2)下,若p=〖p_1〗^(α_1 ) 〖p_2〗^(α_2 )⋯〖p_i〗^(α_i )⋯〖p_j〗^(α_j ) ( 為p的相異質因數),任意的n值(n≥p+1)均可唯一表示成n=(p)^t×(〖p_1〗^(s_1 ) 〖p_2〗^(s_2 )⋯〖p_i〗^(s_i )⋅m)+q (t,m∈N, p ∤〖p_1〗^(s_1 ) 〖p_2〗^(s_2 )⋯〖p_i〗^(s_i ), (m,p)=1, q=1,2,⋯,p),令S=(p^t (p-q)+(pq-1))/(p-1)+R⋅p^t,則當m=1時,最終為成功狀態,且獨得糖果者的初始編號為S;當m≥2時,最終為循環狀態,且由m人循環傳遞糖果,而此m人的初始編號是S, S+p^t 〖p_1〗^(s_1 ) 〖p_2〗^(s_2 )⋯〖p_i〗^(s_i ), ⋯⋯ , S+(m-1)⋅p^t 〖p_1〗^(s_1 ) 〖p_2〗^(s_2 )⋯〖p_i〗^(s_i )。上述公式中的R值,可透過我們研究出來的「R值迭代法」求得。更進一步,我們也找出達到成功狀態或循環狀態的最小傳遞數。