JP2004359452A - Location arrangement method for flatly placing warehouse and flatly placing warehouse - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To convert an arrangement plan of location of a flatly placing warehouse into a calculable problem to obtain semi-optimum solution within practical time. <P>SOLUTION: The arrangement plan of location is divided into three problems including No. 1: search for location to be emptied, No. 2: search for conveying an article in the location to be emptied into which location, No. 3: scheduling for assigning which conveyance work to which carrier to obtain the optimum solution per problem. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

ｋはフォークリフトを示す添字で、（１）は作業時間が最大のフォークリフトでも指定された時間内に作業を完了することを意味する。
ｘ∈Ｓ
Ｓ： 搬送スケジュールの集合
ｘ： 搬送スケジュール
Ｅ（ｘ）： 空のロケーションの数
Ｔｋ（ｘ）： フォークリフトｋの作業時間
Ｔｒｅｑｕｅｓｔ： 要求作業時間
【００２５】
＜入力情報＞
（１） 各ロケーションの情報： 位置，形状，在庫パレット数・品目・製造日，最大容量
（２） 要求作業時間
（３） フォークリフトの台数
＜出力情報＞
各フォークリフトの搬送スケジュール： 「ロケーションｉからｊへの１パレットの搬送」を単位タスクとして、各フォークリフト毎にタスクを実行する順序を示したもの。フォークリフト毎の搬送スケジュールの全フォークリフトに対する総和を考えると、搬送スケジュールｘとなる。
【００２６】
＜変数の定義等＞
Ｌ： ロケーションの集合
ｉ： 原則としてロケーションを表す添字
Ｑｉ： ロケーションｉのパレット数
Ｋｉ： ロケーションｉに置かれている品目
Ｃｉ： ロケーションｉの容量
ｗ_ｉｊ： ロケーションｉ−ｊ間の移動コスト
Ｒ_ｉｊ： ロケーションｉ−ｊ間の搬送回数
Ｆ： フォークリフトの集合
Ｎｋ： フォークリフトｋの現在いるロケーション
Ｓｋ： フォークリフトｋのスケジュール
【００２７】
整理計画を３つの段階に分解する。
＃１ 空にするロケーションの決定
＃２ パレットの搬送先の決定
＃３ スケジュールリング
図３〜図５に示すとおり、＃２は＃３を、＃１は＃２と＃３を内包しているが、各々の階層では独立したアルゴリズムで解を求めることができる。＃１，２ではシミュレーテッドアニーリング（以下ＳＡ）を、＃３では巡回路生成に関する近似アルゴリズム（グリーディ法やラージアークアルゴリズム）を用いる。これらを共通の枠組みとした上で、作業開始前のオフラインでの計画と、実際の整理作業と平行したオンラインの再計画とを行う。オフラインでは＃１−＃３を、オンラインでは＃３を実行する。
【００２８】
ロケーション整理での最適化問題は（１）式で与えられ、（１）式をそのまま評価関数として使うこともできるが、制約条件により探索過程で解が推移する空間が制限され、探索効率が悪化することが考えられる。そこで実施例では、次式を評価関数として用いる。

ここで、αは定数、（３）式での最大値はｋに関して求め、（４）式のＰ^ｋｉｊ（ｘ）は、スケジュールｘにおいてフォークリフトｋがロケーションｉ−ｊ間を移動する回数で、（４）式のｉ，ｊはロケーションの集合Ｌの範囲で検討する。ペナルティ関数Ψ（ｘ）は得られた作業時間が要求を満たす際は１より小さい正の値、充たさない場合は負の値となる。
【００２９】
初期解は以下のようにして生成する。このアルゴリズム１によって、ロケーションｉからｊへの搬送回数Ｒ_ｉｊが得られる。
アルゴリズム１ （初期解の生成法）
ステップ１ 全ての品目ｍに対し、再配置により空きにすることができるロケーションの数ΔＥ_ｍを求める。
ステップ２ ロケーションｉが同じ品目がおかれているロケーションの中で、パレット数が少ない順にΔＥ_ｍ番目までであれば、Ｍｉをｔｒｕｅとし、そうでなければｆａｌｓｅとする。ステップ２は全ロケーションに対して行う。
ステップ３ Ｍｉがｔｒｕｅのロケーションを、パレット数の少ない順にリストして、順列Πとする。
ステップ４ Ｒｉｊ←０（^∀ｉ∈Ｌ，^∀ｊ∈Ｌ） ｔ←１とする。
ステップ５ 順列Πのｔ番目の要素をａに代入
ステップ６ （Ｋａ＝Ｋｊ∩Ｃｊ−Ｑｊ−Σ_{ｉ ∈ Ｌ}Ｒｉｊ）＞０を満たすｊ（∈Ｌ）をランダムに選び、Ｒａｊ←Ｒａｊ＋１とする。これをＱａ回繰り返す。
ステップ７ 後述のアルゴリズム３を実行。得られた解が要求作業時間を満たせばｔ←ｔ＋１としステップ５へ、満たさない場合はＲａｊ←０（^∀ｊ∈Ｌ）として終了。
【００３０】
＃１，＃２での探索アルゴリズムとして、図８に示すシミュレーテッドアニーリングを用いる。シミュレーテッドアニーリングは選んだ近傍解が現在より改善されれば採択し、改悪されても改悪量をｄとしてｅｘｐ（−ｄ／ｔｉ）の確率で採択する。ｔｉは温度関数で、ｔｉが探索回数ｉに対し正値で単調減少するため、探索の初期段階では大域的な探索をし、探索が進むにつれ解が改善される方向に探索範囲を絞り、準最適解に収束することができる。
【００３１】
先ず初めの段階として。空けるロケーションを探索する。これは図３の＃１（図４、図５のＬａｙｅｒ１）に対応する。この階層でのフローチャートを図５に示す。ここでは、図７に示す３つの近傍探索法を用いる。
【００３２】
Ａｄｄ： 任意のパレット受け入れロケーションから、ランダムにａ（∈Ｌ）を選び、空にするロケーションのリストに追加し、Ｋａ＝Ｋｊ∩Ｃｊ−Ｑｊ−Σ_{ｉ ∈ Ｌ}Ｒｉｊ＞０を満たすｊ（∈Ｌ）をランダムに選び、Ｒａｊ←Ｒａｊ＋１とする。
Ｄｅｌｅｔｅ： 空にするロケーションのリストから、ランダムにｂ（∈Ｌ）を選び、リストから削除。Ｒｂｊ←０（^∀ｊ∈Ｌ）とする。
Ｅｘｃｈａｎｇｅ： Ｄｅｌｅｔｅを実行後、Ａｄｄを実行する。
【００３３】
ここで注意すべき点は、入れ替え（Ｅｘｃｈａｎｇｅ）という操作である。この操作は追加と削除の組み合わせであるが、連続に行った後で解の評価を行うところに意味がある。入れ替えでは（２）式におけるＥ（ｘ）の値を固定したまま解を推移させることが可能で、作業時間の短縮のみに焦点を絞ることができる。また図５に示すように、得られたスケジュールが要求作業時間を満たすときは追加し、越える場合は削除または入れ替えを適当な確率、例えば等確率で選ぶ。このように取り得る近傍探索法を限定することにより、空きにするロケーションの探索効率の改善を図る。
【００３４】
空けるロケーションを決定した後、次にどこにパレットを搬送させるかを決定する（図３の＃２、図４，図５のＬａｙｅｒ２に対応）。この階層でのアルゴリズムのフローチャートを図６に示す。ここでは、次に示す近傍探索法を用いる。
Ｓｈｉｆｔ： （Ｋｉ＝Ｋｊ＝Ｋｋ∩Ｒｉｊ＞０） ∩ （Ｃｋ−Ｑｋ−Σ_{ｌ ∈ Ｌ}Ｒｌｋ＞０）を満たす、ｉ，ｊ，ｋ（∈Ｌ，ｉ≠ｊ，ｊ≠ｋ，ｋ≠ｉ）をランダムに選び、Ｒｉｊ←Ｒｉｊ−１，Ｒｉｋ←Ｒｉｋ＋１とする。
【００３５】
図６のアルゴリズムでは、搬送先のロケーションをシフト動作により変化させて搬送先の組み合わせの新たな候補を発生させ、この候補毎に＃３のスケジューリング問題の近似解を求めて、搬送先の組み合わせの候補を評価し、シミュレーテッドアニーリングにより所定の回数搬送先の候補の探索を繰り返して、搬送先の組み合わせの準最適解を求める。
【００３６】
決定されたパレットの配置を実現させるべく、実際にフォークリフトに搬送作業をその作業順と共に割り当てる（図３の＃３、図４のＬａｙｅｒ３，図５の搬送スケジューリングに対応）。ここでのスケジューリング問題は一般に巡回セールスマン問題（以下ＴＳＰ）と呼ばれるものの一種で、ＴＳＰの解法には、ラージアークアルゴリズムなどがある。しかし、これらのアルゴリズムの計算時間は、いずれも搬送するパレット数の３乗のオーダーで増加するため、本問題のように大規模で、しかも全体のアルゴリズム（＃１〜＃３）の最下層で繰り返し計算を行う（図３〜図５、図６参照）には不向きである。従って実施例では、以下のようなアルゴリズム（グリーディ法）を用いる。
【００３７】
アルゴリズム２ （グリーディ法： ＴＳＰの近似解法）
変数の定義 フォークリフトｋの作業見積もり時間をＴｋ，ロケーションｉにおける優先フォークリフトを示すインデックスをＩｉとする。
ステップ１ ^∀ｋ∈Ｆに関して、Ｔｋ←０，Ｎｋにフォークリフトｋの最寄りロケーションをセットする。また^∀ｉ∈Ｌに関して、Ｉｉ←φとする。
ステップ２ ａｒｇｍｉｎ_ｋＴｋとなるｋを選ぶ。これは引数ｋに対してＴｋが最小となるｋを選ぶことで、ａｒｇｍｉｎ_ｘＹｘは引数Ｙｘが最小となるｘを選ぶことである。そのｋに対し、
（^∃ｊ∈Ｌ，Ｒｉｊ＞０） ∩ （Ｉｉ＝ｋ ∪ Ｉｉ＝φ） の条件下でａ←ａｒｇｍｉｎ_ｉｗＮ_ｋｉとする。そのようなロケーションがない場合はステップ４へ移行する。
ステップ３ Ｒａｊ＞０の条件下でｂ←ａｒｇｍｉｎ_ｊｗ_ａｊとする。ロケーションＮｋからａまでの「移動」と、ロケーションａからｂまでの「搬送」をスケジュールＳｋに加える。Ｔｋ←Ｔｋ＋ｗ_Ｎｋａ＋ｗ_ａｂ，Ｎｋ←ｂ，Ｉａ←ｋ，Ｒａｂ←Ｒａｂ−１とする。
Ｒｉｊ＝０（^∀ｉ∈Ｌ，^∀ｊ∈Ｌ）ならば終了、そうでなければステップ２へ。
ステップ４ ^∃ｊ∈Ｌ，Ｒｉｊ＞０の条件下でａ←ａｒｇｍｉｎ_ｉｗ_Ｎｋｉとし、ステップ３へ戻る。
【００３８】
このアルゴリズムでは、ロケーションｉにおける優先フォークリフトを示すインデックスＩｉを設け、１つの搬送元ロケーションに複数のフォークリフトが集中することを防いでいる。
【００３９】
以上が、オフラインでの整理計画法であるが、実施例では実作業の開始後にも、作業の進行状況を情報として取り入れ、逐次再計画を行う。用いる情報は、
（ｉ） その時点でのパレット配置、
（ｉｉ） フォークリフトの位置、
（ｉｉｉ） 残りの搬送スケジュール、
の３つである。再計画対象はスケジューリングの部分のみとし、これは再計画に要する時間を極力短縮するためである。なお再計画に数分必要であると、その間作業を止めるか、数分前のパレットやフォークリフトの配置を元にスケジューリングをやり直すことになる。再計画のアルゴリズム（アルゴリズム３）はアルゴリズム２とほぼ同様であるが、ステップ１のみ以下のように異なる。図９に、３台のフォークリフトに対する６パレットの搬送タスクに関し、スケジューリングを再度行う例を示す。
【００４０】
アルゴリズム３ （オンラインでの再計画法）
ステップ１ ^∀ｋ∈Ｆに関して、フォークリフトｋがロケーションｉからｊまで搬送中ならばＴｋ←ｗ_ｉｊ，Ｎｋ←ｊとする。搬送中でなければＴｋ←０，Ｎｋには最寄りのロケーションをセットする。未実行の搬送スケジュール（移動のみのものを含まない）をロケーションｉ−ｊ間毎に数え上げＲ_ｉｊに代入。また、Ｓｋ←φ，（^∀ｋ∈Ｆ），Ｉｉ←φ，（^∀ｉ∈Ｌ）とする。
ステップ２−４ アルゴリズム２に同じ。
【００４１】
実施例の有効性を検証すべくシミュレーション実験を行った。図１にシミュレーションで使用する倉庫のレイアウトを示す。ロケーション数は１１６，品目数は５０，フォークリフト台数は８とした。パレットは２段積みでロケーション奥から詰めて置いていく。１つのロケーションには奥行き２０，横２列，垂直２段で最大８０パレット置くことができる。各ロケーションの在庫パレット数、及びその品目はランダムで５０パターン生成する。また、フォークリフトの速度は一定で３．０ｍ／ｓとする。
【００４２】
シミュレーテッドアニーリングにおける温度関数ｔｉは以下の式を用いる。
ｔｉ＝ζ^ｉ−１ｔ１ （５）
＃１の空きにするロケーションの探索ではζ＝０．９０，ｔ１＝１．０とし，＃２の搬送先の探索ではζ＝０．９５，ｔ１＝１００とした。終了条件は＃１では２４０回，＃２では１０００回の探索を終えた時点とした。また式（３）においてα＝０．５４ｍｉｎ^−１とした。オンラインでの再計画は作業時間にして１．０ｍｉｎごとに行った。計画にはＰｅｎｔｉｕｍ４（Ｐｅｎｔｉｕｍはインテル社の登録商標） １．５ＧＨｚのＣＰＵを搭載した計算機を用いた。オフラインでの計画には約１８０ＣＰＵｓｅｃ，オンラインでの再計画には０．０１ＣＰＵｓｅｃ以下の計算時間を要した。
【００４３】
まずオンラインでの逐次再計画の有効性について検証する。表１に逐次再計画を行ったものと、行わなかったものの３つの異なる要求作業時間に対する、各５０試行平均のデータを示す。ここで、空きロケーション数とは要求作業時間内に空けられたロケーションの数，超過時間とは要求作業時間に対し、計画した作業を全て遂行するのに要した時間の超過分、作業終了時間差とはフォークリフト間のの作業終了時刻の最大差を指している。
【００４４】
【表１】

【００４５】
表１より、逐次再計画を行ったものは全時間平均で４．７％多くのロケーションを空けている。特筆すべきところは、作業終了時間差が、逐次再計画を行うと逐次再計画を行わない場合の、４０〜２０％に抑えられている点である。このことより、逐次再計画によって作業が進行状況に合わせて割り当てられ、各フォークリフト間の作業時間格差を減少させていることが分かる。このことで、結果的に作業時間を短縮させ、要求作業時間内により多くのロケーションを空けることができた。
【００４６】
【実施例の効率評価】
図１０〜図１２に、図２の従来例との比較で実施例の効率を示す。図２の従来例では、パレット数の少ないものから空きにするロケーションとし、空きにする各ロケーションについて１台ずつフォークリフトを配置し、作業時間内に手空きになったフォークリフトがあると、次にパレット数の少ないロケーションを空きにする作業を開始する。
【００４７】
図１０は、１０分、２０分、３０分の要求作業時間内に空きにできたロケーションの数の比較で、各要求作業時間に対して、パレット配置のテストパターンを２０種用意して行った。実施例ではどの作業時間でも効率が高く、平均で１４％多くのロケーションを空きにしている。
【００４８】
図１１は、パレット数や品目数に対する空きにできたロケーション数の依存性を示し、要求作業時間は２０分とした。パレット数が同じで品目数が少なくなると、どのロケーションからどのロケーションにパレットを搬送するかの作業のバリエーションが増し、実施例と従来例との効率の差が増している。一方パレット数や品目数が増すと、遠距離搬送が通常になり、スケジューリングの差が出ないなどにより、効率の差は小さくなる。
【００４９】
図１２は、要求作業時間を２０分にした際の、フォークリフトの台数と、空きにできたロケーションの数とを示す。どの台数でも、実施例は従来例よりも高い作業効率を示す。
【００５０】
図１３に、実施例の平置き倉庫の制御部１０の構成を示す。１２は操作パネルで、整理計画の立案や実行などの指示を受け、在庫ファイル１３は各ロケーションの在庫パレット数と品目とを記憶しており、フォークリフト管理部１４は複数のフォークリフト１６に搬送指令を割り付け、搬送結果を管理する。通信部１５からフォークリフト１６へ搬送指令を送信する。またフォークリフト１６は搬送作業を完了すると、その場で完了した旨を通信により報告するので、フォークリフト１６の現在位置と作業の進捗状況とが判明する。フォークリフト１６は有人でも無人でも良い。
【００５１】
整理計画の立案時には、その旨をマニュアルなどで操作パネル１２から入力し、フォークリフト管理部１４で記憶している稼働中のフォークリフトの台数、あるいは操作パネル１２からマニュアルで入力した台数を作業台数とする。また作業時間は操作パネル１２からマニュアルで入力する。
【００５２】
空きロケーション探索部１８は、図４〜図５の手法で、＃１の空きにするロケーションを探索する。パレット搬送先探索部２０は、図４〜図７の手法で、＃２のパレットの搬送先のロケーションを探索する。ここで＃１や＃２の探索は、複数回行って最適化し、途中での候補の評価にはシミュレーテッドアニーリング部２８を用い、採用確率は図８に示すものなどを用い評価部３０で実行する。
【００５３】
スケジューリング処理部２２は、グリーディ処理部２３あるいはラージアークアルゴリズム処理部２４などを用いて、＃３のフォークリフトへの搬送スケジュールを作成する。スケジューリングの手法は、制御部１０の計算能力に応じて追加や変更をして行けばよい。オンライン再計画部２６は、フォークリフト１６が整理作業を開始した後に、適宜の間隔で＃３のフォークリフトの搬送スケジュールを再作成する。
【図面の簡単な説明】
【図１】ロケーションの整理対象の平置き倉庫の斜視図
【図２】従来例での作業計画の作成アルゴリズムを示すフローチャート
【図３】実施例での、ロケーション整理に関する問題の分割を示す図
【図４】実施例での、ロケーション整理計画の全体的作成アルゴリズムを示す図
【図５】実施例での空きロケーションの探索アルゴリズムを示す図
【図６】実施例での、搬送先の探索アルゴリズムを示すフローチャート
【図７】実施例での、空きにするロケーションの探索手法を示す図
【図８】実施例での、シミュレーテッドアニーリングでの新たな計画の採用確率を、探索回数並びに改悪量の関数として示す図
【図９】実施例での、ロケーション整理の実行中の、オンライン逐次再計画を模式的に説明する図
【図１０】要求作業時間に対する空きローケーション数を、従来例と実施例とで示す図
【図１１】パレット数と品目数に対する空きローケーション数を、従来例と実施例とで示す図
【図１２】フォークリフト数に対する空きローケーション数を、従来例と実施例とで示す図
【図１３】実施例の平置き倉庫でのロケーション整理制御部のブロック図
【符号の説明】
２ 平置き倉庫
４ 通路
６ ロケーション
８ 空きスペース
１０ 制御部
１２ 操作パネル
１３ 在庫ファイル
１４ フォークリフト管理部
１５ 通信部
１６ フォークリフト
１８ 空きロケーション探索部
２０ パレット搬送先探索部
２２ スケジューリング処理部
２３ グリーディ処理部
２４ ラージアークアルゴリズム処理部
２６ オンライン再計画部
２８ シミュレーテッドアニーリング部
３０ 評価部[0001]
Field of application of the invention
BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flat storage warehouse, and more particularly to an arrangement of locations where pallets are rearranged to create empty locations.
[0002]
[Prior art]
[0003]
[Patent Document 1] JP-A-6-239420
Patent Literature 1 discloses arrangement of locations of flat storage warehouses. As the variety and quantity production becomes more important, there is an increasing need to arrange the locations in flat warehouses so that the next delivery can be carried out smoothly.
[0004]
The arrangement plan of the location of the flat warehouse is divided into two: (i) a pallet rearrangement plan, and (ii) a pallet transport plan by a plurality of forklifts. In the rearrangement plan (i), the pallet arrangement is optimized with respect to the current pallet arrangement in preparation for the next entry / exit. In the transfer plan of (ii), in order to realize the arrangement determined in the rearrangement plan of (i), the work and its order are assigned to a plurality of forklifts. Incidentally, FIG. 1 shows an example of the flat storage warehouse 2, wherein 4 is a passage of a forklift, 6 is an individual location, and 8 is an empty space in the location. In the flat warehouse 2, it is preferable to arrange the same type of articles at the same location 6, and it is not preferable to arrange different types of articles at the same location. Also, considering that there is a difference in the production date for each product type, products of the same product type with the same or close production dates are collected in the same location.
[0005]
Due to these restrictions, an extremely large number of patterns can be considered for the pallet arrangement, and the pallet arrangement pattern increases exponentially according to the number of varieties, and becomes enormous. The transfer plan (ii) is a kind of the traveling salesman problem, and is basically an NP-hard problem. For such a large-scale optimization problem, it is extremely difficult to find a sub-optimal solution in a practical time (within 10 minutes as a guide).
[0006]
In a flat warehouse, there is interference between forklifts because multiple forklifts share a work space. For this reason, even if suboptimal solutions for the pallet rearrangement plan and the transport plan for the flat warehouse are determined, it is practically impossible to consider interference between forklifts in these optimal solutions. In the case of a manned forklift, the work efficiency varies from driver to driver, and it is difficult to incorporate this into the transport plan.
[0007]
FIG. 2 shows a currently used flat warehouse arrangement algorithm, in which a list is created as a candidate for a location to be vacated from a location having a small number of pallets. Next, from the top of the list (locations with a small number of pallets), transfer operations are assigned to forklifts. If a predetermined condition is satisfied, the location is determined to be from a nearby location. Then, one forklift is assigned to one location. In this method, the location to be emptied is determined based on an empirical standard that the number of pallets is small, and optimizing the transport plan, in other words, tackling the traveling salesman problem is abandoned.
[0008]
[Problems of the Invention]
An object of the present invention is to make it possible to efficiently arrange the locations of flat storage warehouses (claims 1 to 3).
An additional object of the second aspect of the present invention is to further efficiently arrange locations.
[0009]
Configuration of the Invention
The method for arranging the locations of flat storage warehouses according to the present invention is a method for rearranging articles in flat storage warehouses by carts to organize empty warehouses to create empty locations. A step of searching for a location to be vacated, a step of searching for a location to transport articles in the vacant location to, and a scheduling step to plan which transport work is to be allocated to which trolley, using the organizing work time as input information. The following three steps are performed (claim 1).
[0010]
Preferably, during the execution of the location rearrangement, the scheduling step is performed again for the remaining transport operations in the location rearrangement, and the allocation of the transport operations to the carts is re-planned (claim 2).
[0011]
In addition, the flat storage warehouse of the present invention searches for a location to be vacant using the current state of the location, the number of carts to be put in, and the work time for rearranging as input information, and searches for a location to transport the goods in the vacant location. And a control unit for planning which transport work is to be allocated to which truck (claim 3).
[0012]
Particularly preferably, in the search for a location to be vacant, for each candidate for a location to be vacant, a search for a transport destination to which the article in the vacant location is to be transported is repeated a plurality of times, and a candidate for a location to be vacant is obtained. Evaluate the efficiency of In the search for a destination to which an article in an empty location is to be transported to which location, a plan is to be assigned to which truck and which transport work is to be assigned to each destination candidate, and the efficiency of the destination candidate is evaluated. .
[0013]
Preferably, a plurality of candidates are evaluated in the search for a candidate for a location to be vacated, and a plurality of candidates for a destination are evaluated for each candidate for a location to be vacated in the search for a destination. In this evaluation, it is preferable to use a simulated annealing or a genetic algorithm, etc., so as not to fall into the local optimal solution, and even under a lower efficiency candidate than the previous candidate, under a predetermined condition, for example, a predetermined probability, Try to adopt new candidates. Preferably, simulated annealing is used, candidates with higher efficiency than previous ones are employed, candidates with lower efficiency than previous ones are employed with a predetermined probability, and this probability is increased by the number of executed searches. The smaller the efficiency is, the smaller the efficiency is, so that the sub-optimal solution is reached at the end of the search.
[0014]
The assignment plan (transportation plan) of the transport operation to the cart becomes a traveling salesman problem for a plurality of salesmen, and is a problem that is difficult to NP. This problem is considered as a problem of a bipartite graph in which the location of the transfer source is one set and the location of the transfer destination is the other set, and a problem of finding a long path between the bipartite graphs (large arc algorithm). You can solve it. However, in the embodiment, a calculation method (a greedy method described later) having a smaller calculation amount is used.
[0015]
Function and Effect of the Invention
In the present invention, the location consolidation plan
# 1 Search for vacant locations,
# 2 Searching for the location to transport the goods in the empty location,
# 3 Scheduling of which transport work to assign to which bogie,
And derive a sub-optimal solution for each problem. For this reason, the arrangement plan of the location of the flat warehouse can be converted into a computable problem and a sub-optimal solution can be obtained (claims 1 to 3).
[0016]
In the conventional rearranging plan, an algorithm that uses only the current state of the location as input information, such as emptying a location with a small number of pallets and allocating a truck to each empty location (FIG. 2), is used. In addition to the algorithm shown in Fig. 2, an algorithm may be added, such as a location with a large number of pallets to transfer destinations. However, this also only takes into account the current state of the location, and takes into account the number of forklifts and other trucks to be loaded and the working time. It is similar in that it does not. In these algorithms, work is started from a location with a small number of pallets that can be vacated in a short time, and if the work time runs out, the work is stopped midway.
[0017]
In order to store the pallets at full capacity, priority is given to locations with a large number of pallets, but no consideration is given to shortening the traveling path length of the bogie. On the other hand, taking into account the work time and the number of works, the problems are: # 1 search for a location to be vacant, # 2 search to which location to transport articles in a vacant location, # 3 which transport work to which truck. When the scheduling is divided into three, the total of the traveling route lengths of the bogies is minimized for the same amount of transport work by the scheduling of # 3, the optimal transport destination is selected in # 2, and given in # 1. It is possible to optimize which location is vacant with respect to the obtained work time and the number of works (claims 1 to 3).
[0018]
Further, when the scheduling of # 3 is performed again during the execution of the organizing work, for example, about 5% more empty locations could be created as compared with the case where the scheduling is not performed again. Although the optimization of scheduling is a problem that is difficult to make NP and a problem that is difficult to predict such as interference between bogies, the above-mentioned difficulties can be avoided by performing rescheduling during the execution of the sorting work. 2).
[0019]
The efficiency of the present invention (here, the number of locations that can be vacated with the same work time and the same number of work) depends on the number of items, the number of pallets to be conveyed, and the like. We were able to create as many empty locations. In addition, the calculation time required to create a location arrangement plan is an order of less than one hour in CPU time (for example, about 10 minutes), and when work time is likely to be spared, during lunch breaks, and before starting work in the morning. It is within the range that it is possible to make a reorganization plan at the time, spare time after the work in the evening, etc. Therefore, according to the present invention, the location of the flat warehouse can be arranged not only at the time of scheduling in advance but also flexibly.
[0020]
【Example】
In the embodiment, two models are prepared: a model used in the planning stage = a planning model and an execution model that defines a simulation environment. In the embodiment, FIGS. 3 to 9 show a method of creating a rearranging plan, FIGS. 10 to 12 show evaluation results thereof, and FIG. 13 shows a control unit for drafting and executing the rearranging plan. The specifications of the two models are shown below.
[0021]
<Preconditions>
The work time is represented by the sum of the moving costs between locations. The moving cost was obtained by dividing the average of the shortest path lengths between the locations by the average moving speed of the forklift, which was obtained in 1000 simulations (with the execution model) in which the arrangement of the luggage was randomly changed in advance. . This is a model that ignores the time required to transfer pallets.
<Element to be modeled>
(1) Information on each location: number of pallets, item, date of manufacture, maximum capacity
(2) Transfer cost between locations
There are cases where the item is used simply for the meaning of the product type and for the meaning of the combination of the product type and the production date.
[0022]
[Execution model]
<Preconditions>
(1) The forklift shall move at a constant speed.
(2) The time required for the operation of scooping and lowering the pallet is set to 0 and ignored.
(3) Forklifts follow traffic rules, avoid collisions, and move between locations on the shortest route.
[0023]
<Element to be modeled>
(1) Information on each location: position / shape, number of pallets / item / production date, maximum capacity
(2) Interference between forklifts or between a forklift and a pallet
(3) Traffic rules for avoiding collisions (traffic classification, standby)
In the execution model, as compared to the plan model, the forklift moves on a two-dimensional plane, and there is a geometric distance and interference between the forklifts and between the forklift and the pallet. In order to avoid collisions and prevent deadlock between forklifts, set appropriate traffic rules, set speed limits, priority driving order and standby order, etc.When other forklifts are working at the target location, It imposes restrictions such as waiting at the near position.
[0024]
The definitions of input information, output information, and variables used are shown below.

k is a suffix indicating a forklift, and (1) means that the work is completed within the designated time even with the forklift having the longest working time.
x∈S
S: Set of transfer schedule
x: Transport schedule
E (x): number of empty locations
Tk (x): Working time of forklift k
Trequest: Required work time
[0025]
<Input information>
(1) Information on each location: location, shape, number of pallets in stock, item, date of manufacture, maximum capacity
(2) Required work time
(3) Number of forklifts
<Output information>
Transport schedule of each forklift: An order in which tasks are executed for each forklift, with “transport of one pallet from location i to j” as a unit task. Considering the total sum of the transfer schedule for each forklift for all forklifts, the transfer schedule is x.
[0026]
<Definition of variables>
L: Set of locations
i: Subscript representing location in principle
Qi: Number of pallets at location i
Ki: Item located at location i
Ci: Capacity of location i
w_ij: Travel cost between locations ij
R_ij: Number of transfers between locations ij
F: Forklift assembly
Nk: Current location of forklift k
Sk: Schedule of forklift k
[0027]
Break down the consolidation plan into three stages.
# 1 Decide which location to empty
# 2 Determination of pallet destination
# 3 Scheduling
As shown in FIGS. 3 to 5, # 2 includes # 3, and # 1 includes # 2 and # 3, but a solution can be obtained by an independent algorithm in each layer. In # 1 and # 2, simulated annealing (hereinafter referred to as SA) is used, and in # 3, an approximation algorithm (greedy method or large arc algorithm) related to traveling circuit generation is used. With these as a common framework, we perform offline planning before starting work and online replanning in parallel with actual organization work. # 1- # 3 is executed offline, and # 3 is executed online.
[0028]
The optimization problem in location reduction is given by equation (1), and equation (1) can be used as it is as an evaluation function. However, the space in which the solution transitions in the search process is limited by the constraints, and search efficiency deteriorates It is possible to do. Therefore, in the embodiment, the following expression is used as an evaluation function.

Here, α is a constant, the maximum value in equation (3) is obtained with respect to k, and P in equation (4) is obtained.^kij (x) is the number of times the forklift k moves between the locations ij in the schedule x, and i and j in the expression (4) are considered within the range L of the locations. The penalty function Ψ (x) has a positive value smaller than 1 when the obtained operation time satisfies the request, and has a negative value otherwise.
[0029]
The initial solution is generated as follows. According to this algorithm 1, the number of transfers R from the location i to the j is R_ijIs obtained.
Algorithm 1 (Method of generating initial solution)
Step 1 Number ΔE of locations that can be made empty by relocation for all items m_mAsk for.
Step 2 Among locations where the same item is placed in the location i, ΔE_mIf it is up to the first, Mi is set to true; otherwise, it is set to false. Step 2 is performed for all locations.
Step 3 The locations where Mi is true are listed in ascending order of the number of pallets, and are set as a permutation Π.
Step 4 Rij ← 0 (^∀i∈L,^∀j∈L) Let t ← 1.
Step 5 Substitute the tth element of permutation Π for a
Step 6 (Ka = Kj∩Cj-Qj-Σ_{i ∈ L}J (） L) that satisfies Rij)> 0 is randomly selected, and Raj ← Raj + 1. This is repeated Qa times.
Step 7 Execute algorithm 3 described later. If the obtained solution satisfies the required operation time, it is assumed that t ← t + 1.^∀j∈L).
[0030]
Simulated annealing shown in FIG. 8 is used as a search algorithm in # 1 and # 2. The simulated annealing is adopted if the selected neighborhood solution is improved from the present, and even if it is deteriorated, the simulated annealing is adopted with the probability of exp (−d / ti) where d is the amount of deterioration. Since ti is a temperature function and ti monotonically decreases as a positive value with respect to the number of searches i, a global search is performed in the initial stage of the search, and the search range is narrowed in a direction in which the solution is improved as the search progresses. It can converge to the optimal solution.
[0031]
First as a first step. Search for an empty location. This corresponds to # 1 in FIG. 3 (Layer 1 in FIGS. 4 and 5). FIG. 5 shows a flowchart at this level. Here, three neighborhood search methods shown in FIG. 7 are used.
[0032]
Add: a (ａL) is randomly selected from any pallet receiving location and added to the list of empty locations, and Ka = Kj 、 Cj-Qj-Σ_{i ∈ L}J (∈L) that satisfies Rij> 0 is selected at random, and Raj ← Raj + 1.
Delete: From the list of locations to be emptied, randomly select b (@L) and delete from the list. Rbj ← 0 (^∀j∈L).
Exchange: After executing Delete, execute Add.
[0033]
A point to be noted here is an operation of “exchange”. Although this operation is a combination of addition and deletion, it is significant to evaluate the solution after performing the operation continuously. In the replacement, it is possible to change the solution while fixing the value of E (x) in the equation (2), and it is possible to focus only on shortening the working time. Also, as shown in FIG. 5, when the obtained schedule satisfies the required work time, the schedule is added, and if it exceeds, the deletion or replacement is selected with an appropriate probability, for example, with equal probability. By limiting the neighborhood search method that can be taken in this way, the search efficiency of a vacant location is improved.
[0034]
After determining the empty location, it is determined where the pallet is to be transported next (corresponding to # 2 in FIG. 3, and Layer 2 in FIGS. 4 and 5). FIG. 6 shows a flowchart of the algorithm in this hierarchy. Here, the following neighborhood search method is used.
Shift: (Ki = Kj = Kk∩Rij> 0) ∩ (Ck−Qk−Σ)_{l ∈ L}Rlk> 0), i, j, k (， L, i ≠ j, j ≠ k, k ≠ i) are randomly selected, and Rij ← Rij−1 and Rik ← Rik + 1.
[0035]
In the algorithm of FIG. 6, the location of the destination is changed by the shift operation to generate a new candidate of the destination combination, an approximate solution of the scheduling problem of # 3 is obtained for each candidate, and the destination combination is determined. The candidates are evaluated, and the search for the destination candidate is repeated a predetermined number of times by simulated annealing to obtain a sub-optimal solution of the combination of destinations.
[0036]
In order to realize the determined pallet arrangement, the transfer work is actually assigned to the forklift together with the work order (corresponding to # 3 in FIG. 3, Layer 3 in FIG. 4, and transfer scheduling in FIG. 5). The scheduling problem here is a kind of what is generally called a traveling salesman problem (TSP), and the TSP solution includes a large arc algorithm and the like. However, since the calculation time of each of these algorithms increases in the order of the cube of the number of pallets to be conveyed, the calculation time is large and the lowest layer of the entire algorithm (# 1 to # 3) as in this problem. It is not suitable for performing repeated calculations (see FIGS. 3 to 5 and 6). Therefore, in the embodiment, the following algorithm (greedy method) is used.
[0037]
Algorithm 2 (greedy method: TSP approximation)
Definition of Variables The estimated work time of the forklift k is Tk, and the index indicating the priority forklift at the location i is Ii.
Step 1^∀For k∈F, the nearest location of the forklift k is set to Tk ← 0, Nk. Also^∀For i∈L, let Ii ← φ.
Step 2 argmin_kChoose k that will be Tk. This is done by choosing k that minimizes Tk for argument k, argmin_xYx is to select x that minimizes the argument Yx. For that k,
(^∃j∈L, Rij> 0) a ← argmin under the condition of (Ii = k で Ii = φ)_iwN_ki. If there is no such location, go to step 4.
Step 3 b ← argmin under the condition of Raj> 0_jw_ajAnd “Move” from the location Nk to a and “transport” from the location a to b are added to the schedule Sk. Tk ← Tk + w_Nka+ W_ab, Nk ← b, Ia ← k, Rab ← Rab−1.
Rij = 0 (^∀i∈L,^∀If j∈L), end; otherwise, go to step 2.
Step 4^∃a ← argmin under the condition of j∈L, Rij> 0_iw_NkiAnd returns to step 3.
[0038]
In this algorithm, an index Ii indicating a priority forklift at a location i is provided to prevent a plurality of forklifts from concentrating on one transport source location.
[0039]
The above is the off-line reorganization planning method. In the embodiment, even after the start of the actual work, the progress of the work is taken in as information and the re-planning is performed sequentially. The information used is
(I) pallet arrangement at that time,
(Ii) forklift position,
(Iii) remaining transport schedule,
The three. The rescheduling target is only the scheduling part, in order to minimize the time required for rescheduling. If re-planning requires several minutes, the work may be stopped during that time or the scheduling may be re-executed based on the arrangement of pallets and forklifts several minutes ago. The re-planning algorithm (algorithm 3) is almost the same as algorithm 2, except for step 1 as follows. FIG. 9 shows an example in which scheduling is performed again for the task of transporting six pallets to three forklifts.
[0040]
Algorithm 3 (Online replanning)
Step 1^∀For k∈F, if the forklift k is transporting from location i to j, then Tk ← w_ij, Nk ← j. If not, the nearest location is set to Tk ← 0, Nk. Unexecuted transfer schedules (not including only transfer schedules) are counted for each location ij._ijAssigned to Also, Sk ← φ, (^∀k∈F), Ii ← φ, (^∀i∈L).
Step 2-4 Same as algorithm 2.
[0041]
A simulation experiment was performed to verify the effectiveness of the example. FIG. 1 shows a layout of a warehouse used in the simulation. The number of locations was 116, the number of items was 50, and the number of forklifts was 8. Pallets are packed in two-tiered stacks from the back of the location. One location can hold up to 80 pallets with a depth of 20, horizontal 2 rows and vertical 2 tiers. The number of pallets in stock at each location and its items are randomly generated in 50 patterns. The speed of the forklift is constant at 3.0 m / s.
[0042]
The temperature function ti in the simulated annealing uses the following equation.
ti = ζ^i-1t1 (5)
In the search for the empty location of # 1, ζ = 0.90 and t1 = 1.0, and in the search for the transport destination of # 2, ζ = 0.95, t1 = 100. The ending condition is the time when the search has been completed 240 times in # 1 and 1000 times in # 2. In equation (3), α = 0.54 min^-1And Online re-planning was performed every 1.0 min of working time. A computer equipped with a Pentium 4 (Pentium is a registered trademark of Intel Corporation) 1.5 GHz CPU was used for the plan. It took about 180 CPUsec for offline planning and 0.01 CPUsec or less for online replanning.
[0043]
First, the effectiveness of online re-planning is verified. Table 1 shows the data for the average of 50 trials for three different required working times, one with and one without sequential rescheduling. Here, the number of vacant locations is the number of locations vacated within the requested work time, and the excess time is the excess of the time required to perform all the planned work with respect to the requested work time, the difference between the work end time and Indicates the maximum difference in work end time between forklifts.
[0044]
[Table 1]

[0045]
As shown in Table 1, 4.7% more locations are open on the average for the entire time when the re-planning is performed. It should be noted that the work end time difference is suppressed to 40 to 20% of the case where the sequential replanning is not performed when the sequential replanning is performed. From this, it can be seen that the work is allocated according to the progress by the sequential re-planning, and the work time difference between the forklifts is reduced. As a result, the working time was shortened, and more locations could be opened within the required working time.
[0046]
[Efficiency evaluation of embodiment]
10 to 12 show the efficiency of the embodiment in comparison with the conventional example of FIG. In the conventional example shown in FIG. 2, the locations where the number of pallets is small are set as empty locations, and forklifts are arranged one for each location to be empty. Start working to free up a few locations.
[0047]
FIG. 10 is a comparison of the number of locations that can be vacated within the required work time of 10 minutes, 20 minutes, and 30 minutes. For each required work time, 20 types of pallet layout test patterns are prepared. . In the embodiment, the efficiency is high at any work time, and an average of 14% of the locations are vacant.
[0048]
FIG. 11 shows the dependence of the number of vacant locations on the number of pallets and the number of items, and the required operation time is 20 minutes. When the number of items is reduced while the number of pallets is the same, the variation in the operation of transferring pallets from which location to which location increases, and the difference in efficiency between the embodiment and the conventional example increases. On the other hand, when the number of pallets or the number of items increases, long-distance transport becomes normal, and the difference in efficiency becomes smaller because there is no difference in scheduling.
[0049]
FIG. 12 shows the number of forklifts and the number of vacant locations when the required work time is set to 20 minutes. In any number, the embodiment shows higher working efficiency than the conventional example.
[0050]
FIG. 13 illustrates a configuration of the control unit 10 of the flat storage according to the embodiment. Reference numeral 12 denotes an operation panel, which receives instructions for drafting and executing a rearranging plan, a stock file 13 storing the number of stock pallets and items at each location, and a forklift management unit 14 issuing a transfer command to a plurality of forklifts 16. Manage allocation and transport results. A communication command is transmitted from the communication unit 15 to the forklift 16. Further, when the forklift 16 completes the transfer operation, the completion is reported on the spot by communication, so that the current position of the forklift 16 and the progress of the operation are known. Forklift 16 may be manned or unmanned.
[0051]
At the time of drafting the rearrangement plan, the fact is input from the operation panel 12 by manual or the like, and the number of operating forklifts stored in the forklift management unit 14 or the number manually input from the operation panel 12 is set as the number of work. . The work time is manually input from the operation panel 12.
[0052]
The vacant location search unit 18 searches for a vacant location of # 1 by using the method shown in FIGS. The pallet transfer destination search unit 20 searches for a pallet # 2 transfer destination location by the method shown in FIGS. Here, the search for # 1 and # 2 is performed a plurality of times for optimization, and the simulated annealing unit 28 is used to evaluate candidates in the middle, and the adoption probability is executed by the evaluation unit 30 using the one shown in FIG. I do.
[0053]
The scheduling processing unit 22 creates a transfer schedule to the # 3 forklift using the greedy processing unit 23 or the large arc algorithm processing unit 24 or the like. What is necessary is just to add or change the scheduling method according to the calculation capability of the control part 10. The online replanning unit 26 re-creates the transportation schedule of the forklift # 3 at appropriate intervals after the forklift 16 starts the rearranging work.
[Brief description of the drawings]
FIG. 1 is a perspective view of a flat storage warehouse whose locations are to be rearranged.
FIG. 2 is a flowchart showing an algorithm for creating a work plan in a conventional example.
FIG. 3 is a diagram showing division of a problem related to location arrangement in the embodiment.
FIG. 4 is a diagram showing an overall algorithm for creating a location consolidation plan in the embodiment.
FIG. 5 is a diagram showing a search algorithm for a free location in the embodiment.
FIG. 6 is a flowchart illustrating a search algorithm of a transfer destination in the embodiment.
FIG. 7 is a diagram showing a method for searching for a location to be vacant in the embodiment.
FIG. 8 is a diagram showing the adoption probability of a new plan in the simulated annealing as a function of the number of searches and the amount of deterioration in the embodiment.
FIG. 9 is a diagram schematically illustrating on-line sequential replanning during execution of location consolidation in the embodiment.
FIG. 10 is a diagram showing the number of free locations with respect to a requested work time in a conventional example and an embodiment.
FIG. 11 is a diagram showing the number of empty locations with respect to the number of pallets and the number of items in a conventional example and an embodiment.
FIG. 12 is a diagram showing the number of empty locations with respect to the number of forklifts in a conventional example and an example.
FIG. 13 is a block diagram of a location arrangement control unit in a flat storage warehouse according to the embodiment;
[Explanation of symbols]
2 flat storage
4 passage
6 locations
8 free space
10 control unit
12 Operation panel
13 Inventory file
14 Forklift management department
15 Communication unit
16 Forklift
18 Empty Location Search Unit
20 Pallet transport destination search section
22 Scheduling processing unit
23 Greedy processing unit
24 Large Arc Algorithm Processing Unit
26 Online Replanning Department
28 Simulated annealing part
30 Evaluation Department

Claims (3)

In the method of rearranging goods in a flat storage warehouse with a trolley, to organize the warehouse and create an empty location,
Using the current location information, the number of carts to be loaded, the number of carts to be put in, and the sorting work time as input information, a step of searching for a location to be vacated, a step of searching to which location articles to be transported in the vacant location, and which transport to which cart. A method of organizing locations of a flat warehouse, wherein three steps of a scheduling step for planning whether to allocate work are performed. 2. The flat-warehouse according to claim 1, wherein, during the execution of the location consolidation, the scheduling step is performed again for the remaining conveyance work in the location consolidation, and the allocation of the conveyance work to the cart is re-planned. Location organization method. In a flat warehouse where many goods are laid flat at multiple locations and loaded and unloaded with a trolley,
Using the current location information, the number of carts to be loaded, and the work time for rearranging as input information, search for a location to be vacant, search for which location to transport the goods in the vacant location, and which transport task to which trolley. A flat-warehouse equipped with a control unit for planning whether to allocate.

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