Red Hat Summit3.13. 配送経路
複数の車両を使用して、各顧客の品物を回収し、倉庫まで運びます。1 つの車両で複数の顧客から品物を回収することはできますが、収容できる容量には限りがあります。
基本例 (CVRP) のほかに、時間枠の設定が加わった例 (CVRPTW) もあります。
ハード制約:
- 車両の容量: 車両は、車載容量を超えて品物を運ぶことができない。
時間枠 (CVRPTW のみ):
- 移動時間: 別の場所に移動する場合には時間がかかる。
- 顧客対応の時間: 車両は顧客に対応している時間、顧客先にとどまる必要がある。
- 顧客の準備が整う時間: 顧客の準備が整う前に車両が到着する可能性があるが、準備ができるまで待機してから顧客に対応する必要がある。
- 顧客が設定した締め切り時間: 車両は、顧客が設定した締め切り時間までに到着する必要がある。
ソフト制約:
- 合計距離: 車両が移動する合計距離 (ガソリンの消費量) を最小限に抑える。
CVRP (Capacitated Vehicle Routing Problem) と CVRPTW (Capacitated Vehicle Routing Problem with Time Window) は、VRP Web で定義されています。
図3.8 価値提案
問題の規模
CVRP インスタンス (時間枠なし):
belgium-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-road-km-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-road-km-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-road-km-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-road-km-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-road-km-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-road-time-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-road-time-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-road-time-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-road-time-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-road-time-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. belgium-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74. belgium-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170. belgium-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168. belgium-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607. belgium-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380. A-n32-k5 has 1 depots, 5 vehicles and 31 customers with a search space of 10^40. A-n33-k5 has 1 depots, 5 vehicles and 32 customers with a search space of 10^41. A-n33-k6 has 1 depots, 6 vehicles and 32 customers with a search space of 10^42. A-n34-k5 has 1 depots, 5 vehicles and 33 customers with a search space of 10^43. A-n36-k5 has 1 depots, 5 vehicles and 35 customers with a search space of 10^46. A-n37-k5 has 1 depots, 5 vehicles and 36 customers with a search space of 10^48. A-n37-k6 has 1 depots, 6 vehicles and 36 customers with a search space of 10^49. A-n38-k5 has 1 depots, 5 vehicles and 37 customers with a search space of 10^49. A-n39-k5 has 1 depots, 5 vehicles and 38 customers with a search space of 10^51. A-n39-k6 has 1 depots, 6 vehicles and 38 customers with a search space of 10^52. A-n44-k7 has 1 depots, 7 vehicles and 43 customers with a search space of 10^61. A-n45-k6 has 1 depots, 6 vehicles and 44 customers with a search space of 10^62. A-n45-k7 has 1 depots, 7 vehicles and 44 customers with a search space of 10^63. A-n46-k7 has 1 depots, 7 vehicles and 45 customers with a search space of 10^65. A-n48-k7 has 1 depots, 7 vehicles and 47 customers with a search space of 10^68. A-n53-k7 has 1 depots, 7 vehicles and 52 customers with a search space of 10^77. A-n54-k7 has 1 depots, 7 vehicles and 53 customers with a search space of 10^79. A-n55-k9 has 1 depots, 9 vehicles and 54 customers with a search space of 10^82. A-n60-k9 has 1 depots, 9 vehicles and 59 customers with a search space of 10^91. A-n61-k9 has 1 depots, 9 vehicles and 60 customers with a search space of 10^93. A-n62-k8 has 1 depots, 8 vehicles and 61 customers with a search space of 10^94. A-n63-k9 has 1 depots, 9 vehicles and 62 customers with a search space of 10^97. A-n63-k10 has 1 depots, 10 vehicles and 62 customers with a search space of 10^98. A-n64-k9 has 1 depots, 9 vehicles and 63 customers with a search space of 10^99. A-n65-k9 has 1 depots, 9 vehicles and 64 customers with a search space of 10^101. A-n69-k9 has 1 depots, 9 vehicles and 68 customers with a search space of 10^108. A-n80-k10 has 1 depots, 10 vehicles and 79 customers with a search space of 10^130. F-n45-k4 has 1 depots, 4 vehicles and 44 customers with a search space of 10^60. F-n72-k4 has 1 depots, 4 vehicles and 71 customers with a search space of 10^108. F-n135-k7 has 1 depots, 7 vehicles and 134 customers with a search space of 10^240.
CVRPTW インスタンス (時間枠あり):
belgium-tw-d2-n50-k10 has 2 depots, 10 vehicles and 48 customers with a search space of 10^74. belgium-tw-d3-n100-k10 has 3 depots, 10 vehicles and 97 customers with a search space of 10^170. belgium-tw-d5-n500-k20 has 5 depots, 20 vehicles and 495 customers with a search space of 10^1168. belgium-tw-d8-n1000-k20 has 8 depots, 20 vehicles and 992 customers with a search space of 10^2607. belgium-tw-d10-n2750-k55 has 10 depots, 55 vehicles and 2740 customers with a search space of 10^8380. belgium-tw-n50-k10 has 1 depots, 10 vehicles and 49 customers with a search space of 10^74. belgium-tw-n100-k10 has 1 depots, 10 vehicles and 99 customers with a search space of 10^170. belgium-tw-n500-k20 has 1 depots, 20 vehicles and 499 customers with a search space of 10^1168. belgium-tw-n1000-k20 has 1 depots, 20 vehicles and 999 customers with a search space of 10^2607. belgium-tw-n2750-k55 has 1 depots, 55 vehicles and 2749 customers with a search space of 10^8380. Solomon_025_C101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_C201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_R101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_R201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_RC101 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_025_RC201 has 1 depots, 25 vehicles and 25 customers with a search space of 10^40. Solomon_100_C101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_C201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_R101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_R201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_RC101 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Solomon_100_RC201 has 1 depots, 25 vehicles and 100 customers with a search space of 10^185. Homberger_0200_C1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_C2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_R1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_R2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_RC1_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0200_RC2_2_1 has 1 depots, 50 vehicles and 200 customers with a search space of 10^429. Homberger_0400_C1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_C2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_R1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_R2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_RC1_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0400_RC2_4_1 has 1 depots, 100 vehicles and 400 customers with a search space of 10^978. Homberger_0600_C1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_C2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_R1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_R2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_RC1_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0600_RC2_6_1 has 1 depots, 150 vehicles and 600 customers with a search space of 10^1571. Homberger_0800_C1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_C2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_R1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_R2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_RC1_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_0800_RC2_8_1 has 1 depots, 200 vehicles and 800 customers with a search space of 10^2195. Homberger_1000_C110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_C210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_R110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_R210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_RC110_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840. Homberger_1000_RC210_1 has 1 depots, 250 vehicles and 1000 customers with a search space of 10^2840.
3.13.1. 配送経路のドメインモデル
時間枠ありの配送経路のドメインモデルでは、シャドウ変数の機能を多用します。こうすることで、arrivalTime や departureTime などのプロパティーがドメインモデルで直接利用できるため、制約をより自然に表現できます。
直線距離ではなく道路の距離
車は、直線距離を移動するのではなく、道路や高速道路を使用する必要があります。ビジネスの観点からすると、これは非常に重要です。
最適化アルゴリズムでは、2 点の距離を検索できている (できれば、事前に計算されている) 場合には、これは特に重要ではありません。道路費は距離である必要はありません。また、移動時間、フラッシュコスト、または加重関数を使用することもできます。GraphHopper (埋め込み可能なオフライン Java エンジン)、Open MapQuest (web サービス)、Google Maps Client API (web サービス) など、移動コストを事前に計算する技術があります。
また、Leaflet や Google Maps for developers など、レンダリングする技術も複数あります。
GraphHopper または Google Map Directions を使用して実際の経路をレンダリングすることも可能ですが、高速道路で経路が重なるため、停止する順番を確認するのが困難になります。
2 点間の移動費は、OptaPlanner で使用されるのと同じ最適化条件を使用する点に注意してください。たとえば、GraphHopper はデフォルトで、最短ではなく、最速の経路を返します。最速の GPS 経路の km (またはマイル) の距離を使用して、OptaPlanner で最短の移動を最適化しないようにしてください。以下のように、準最適な解が導き出される可能性があります。
一般的な考え方とは異なり、多くのユーザーは最短の経路ではなく、最速の経路を使用したいと考えます。通常の道路よりも高速道路の使用を好みます。舗装されていない道よりも舗装されている道路を好みます。実際には、最速の経路と、最短の経路が同じであることはほとんどありません。
