自動車専用船における配置割当て問題に関する研究

自動車専用船における配置割当て問題に関する研究自動車専用船における配置割当て問題に関する研究海運ロジスティクス専攻学籍番号0555015 若林　篤

発表内容 • 研究背景 • 自動車専用船における配置割当て問題について • 数値実験 • 考察,まとめ • 今後の課題

研究背景～自動車産業の動向と自動車専用船の動向研究背景～自動車産業の動向と自動車専用船の動向 • 自動車専用船は昔は単純なピストン輸送。 • 現在は自動車生産工場が海外に複数存在。 • 自動車専用船では1隻で4000～6000台数の積載可能。 • 複数積み込み港・下ろし港が存在する。 • 複数の積み込み・下ろし港で自動車をスムーズに積み込み・下ろしを行うには配置割当てが重要。 • 自動車の配置割当てを決定することは，とても困難。

研究背景～日本メーカ，海外生産へシフト • 出所：JAMA(社団法人　日本自動車工業会)http://www.jama.or.jp/industry/industry/industry_4.html

先行研究について • わが国での，自動車船による配置割当てについて行って　　　いる研究は2003年，OR学会で斉藤らが発表した1件。 (フェリー船などによる自動車配置割当て問題は存在している) • 自動車の積み込み・下ろし,入替え時間の最小化を目的としたローカルサーチを用いた近似解法 • 自動車の配置場所によって,船体の傾きが変化し安全に輸送活動を行う為には,船にかかるモーメントを考慮する必要があるが考慮されていないと思われる。

研究の目的 安全に輸送活動を行うためにモーメントを考慮した，自動車専用船における配置割当ての支援を行うことが目的。　数理計画法は，問題規模が大きくなるほど求解時間がかかる。定式化を行っただけでは,不十分である。自動車専用船における配置割当て問題の定式化を行いモデリング言語によるプログラムの実装を行う。しかし… 数値実験を行うことにより，どのパラメータが，求解を困難にしているのかを明らかにする。

複数下ろし 自動車専用船について～航路について複数積み込み出所：川崎汽船ｈttp://www.kline.co.jp/plaza/letter06.html

自動車専用船について～配置区画について • 配置区画について • 12デッキあり全部で41区画分けられている。出所：川崎汽船 http://www.kline.co.jp/plaza/letter06.html

自動車専用船について～高さについて • 各階の高さは可変式のも出現している。 • 配置場所の階ごとの高さよりも背高がある品種は,その区画に配置することができない • 各階ごとの高さは160～220cm或いは440cmまである。 • 3900台数積み込み可能品種の背高＞各階高 3F 2F 1F 出所：イースタンカーライナー http://www.ecl.co.jp/top.html

(横メタセンター)＝0としている。 • これは,配置場所が大きな駐車場のような構造となっているので,左右均等に配置する。 • (縦メタセンター)。 • これは,前後方向の重心の距離重心G • の許容範囲を計算（どれだけ重心Gから離れても良いか）自動車専用船について～船の自重とモーメントについて

DELPHINUS LEADER 主　要　目全　長 199.44m 全　幅 32.20m 深　さ 34.34m 最大喫水 10.06m 総トン数 57,391G/T 積載台数（乗用車換算） 6000台主機出力 19,300ps 航海速力 19.30knot 自動車専用船について～船の自重とモーメントについて自動車専用船が,安全に輸送活動を行うためには,配置場所によって船体が傾いても良い上限値を計算 • 船の自重の概略値を計算。 • 全長を180m，全幅を32m，喫水を10m。 • 簡略のためとして57600㎥となる。 • 水の重量１kgをかけることによって船の自重は概略57600tを得る。

自動車専用船について～モーメントの計算について自動車専用船について～モーメントの計算について • バラスト水槽に，海水を注入することによって，　　　　　許容範囲上限を算出する。出所：日本船主協会 http://www.jsanet.or.jp/environment/index.html

自動車専用船について～まとめ • 車の台数 • 航路は先のスライドなど使用 • 船の自重 • モーメントの上限は先の計算方法で算出 • 需要の発生地や集中地 • 品種の重さや高さを擬似データで作成 • 船の配置場所の区画は40(上記のスライドから) • 船の区画ごとに配置できる量や，高さ制限を擬似データで作成上記のデータや情報を使用して,定式化を行った

自動車専用船における配置割当て問題の定式化について自動車専用船における配置割当て問題の定式化について • 2種類の定式化を行った。 • 非線形関数による定式化 • 非線形関数による定式化は積み込み・下ろし,入替え時間を同時に考慮した配置割当て。 • 複数の港に対し,複数の品種は,どこに配置されるか分からない(変数)。 • そして,次の港以降で新たに積み込まれる品種の配置場所分からない(変数)によっては入替えが発生する。 • 変数×変数 • 非線形関数による定式化は，求解時間が非常にかかる。

自動車専用船における配置割当て問題の定式化について自動車専用船における配置割当て問題の定式化について非線形関数を避けるために線形関数による二段階方法による定式化を行う。第一段階では,積み込み・下ろし時間を最小化した配置割当てを行う。第二段階では,一段階目の配置割当ての結果を使って, 積み込み・下ろし時間,入替え時間を最小化した配置割当てを行う。

積み込み台数 積み下ろし台数各港で,配置区画によって積み込み・下ろし時間が異なる第一段階では積み込み・下ろし時間の最小化目的関数

1,2,3という順に港によっていく 1 ShipInv1 階が高いほど出入口に近い ShipInv2 ShipInv3 ShipInv4 ShipInv5 ShipInv6 ShipInv7 ShipInv8 ShipInv9 ShipInv10 ShipInv11 ShipInv12 入替回数の合計6回。 ShipInv13 ShipInv14 ShipInv15 ShipInv16 配置割当てについて船の区画の一部 2 3 10F ShipInv1 ShipInv1 最初の港1での積み込みを青で表現最初は,何にもないので積み込み ShipInv2 ShipInv2 ShipInv3 ShipInv3 次の港2で,新しい配置場所に割り当てられた自動車を赤で表現 ShipInv4 ShipInv4 9F ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv7 ShipInv7 次の港3では積み下ろしがある配置場所を黄色とする。 ShipInv8 ShipInv8 8F ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv12 ShipInv12 7F ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv16 ShipInv16

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10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第一段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 新しい区画場所に配置された。 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第一段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 積み下ろしが発生する区画 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 積み込み時間積み下ろし時間を最小化した配置結果出入口に一番近い区画に配置している 9F 8F 7F 6F 5F 4F 3F 2F 1F 第一段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 Shipnv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 第一段階で配置割当てを決定してしまうと入替え時間を考慮してないので ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 合計503回の入替え ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

第二段階の定式化 • 上記の第一段階の積みこみ・下ろし時間最小化の配置結果を使用する。 • 積み替え時間を考慮した,定式化ができる。 • 第二段階の定式化は第一段階の定式化を拡張。 • 制約式の追加を行う。

入替え発生 第二段階での配置区画について第一段階では,配置したい区画までに通過するときに，通過区画に自動車があるか分からない。出入口これを第一段階で得た配置結果を0-1定数によって与える。出入口 1 0 0 1 1 0 1 0

0-1定数で配置情報 入替えにかかる時間入替え時間 • 新たに制約式を追加出入口 1 0 0 1 1 0 1 0

積み込み量 積み込み量積み下ろし量積み下ろし量積み込み時における入替えにかかる時間積み下ろし時における入替えにかかる時間第二段階の定式化～目的関数拡張第一段階 • 目的関数も以下に拡張第二段階

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第二段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第二段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 第一段階では出入口に近いとこに配置してたが, 今回は入替えも考慮されているので配置されていない。 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第二段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 新しい区画場所に配置された。 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 第二段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 積み下ろしが発生する区画 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

10F 9F 8F 7F 積み込み時間積み下ろし時間の最小化ではずっと使用していた区画が入替えを考慮すると使用されなくなった 6F 5F 4F 3F 2F 1F 第二段階の結果例 1 2 3 4 5 6 7 8 9 10 11 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv1 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv2 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv3 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv4 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv5 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv6 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv7 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv8 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv9 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv10 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv11 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv12 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv13 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv14 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv15 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv16 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv17 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv18 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv19 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv20 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv21 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv22 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv23 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv24 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv25 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv26 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv27 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv28 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv29 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv30 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv31 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv32 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv33 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv34 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 ShipInv35 合計393回の入替え ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv36 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv37 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv38 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv39 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40 ShipInv40

研究目的1 研究目的2 自動車専用船の配置割当て問題に対して安全に輸送活動を行い,積み込み・下ろし時間, 入替え時間を最小化した定式化を表現することに成功した。混合整数計画法は求解時間が非常にかかる実務時間内に求解するためには, どのようなパラメータを与えれば良いのかを数値実験を通して明らかにする。

港の数を減らすことはできない 台数は集約できる品種は高さ・積み込み・下ろし港が同じなら集約できる勝手に発生地,集中地を変更できない造船時点で区画は決定している造船時点で自重は決定している造船時点でモーメント上限値は決定している数値実験の概要1 数理計画法は,問題の規模が大きくなると, 求解時間が非常にかかることが知られている。どのデータが求解を困難にしているのかを明らかにする。 • 港の数 • 台数 • 台数 • 品種 • 需要の発生地,集中地 • 配置場所の区画 • 船の自重 • モーメントの上限値

数値実験概要2 • 数値実験1：品種を固定し,台数の増加によって　台数変化させる。 • 数値実験2：台数を固定し,品種を増加し品種変化させる。 • 数値実験3：総量,品種も増加させる。 • 数値実験4：次の港の積み込み下ろし情報の利用効果の検討する。

数値実験1 • 品種を16品種と固定 • 輸送総量2250～4500台数と変化 • 台数変化による求解時間の比較　（時間設定7200秒） • 台数変化による最適解までの到達％比較

数値実験1～最適解までの求解到達％ 100%の解あるいは,ほぼ100％に近い求解結果を出している

自動車専用船における配置割当て問題に関する研究

自動車専用船における配置割当て問題に関する研究

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