䝽䘱䘀䗃ѝⲴ䖖䖶䐟 䰞仈⹄ウ㔬䘠
㾱˖䝽䘱䘀䗃ѝⲴ䖖䖶䐟 䰞仈аⴤ 䘀ㆩ 亶 Ⲵ⹄ウ✝⛩ѻаDŽ Ҿ䖖䖶䐟 䰞仈Ⲵ ⭘㛼 ˈ 㓣 㔃Ҷ ㊫䰞仈 ≲䀓㇇⌅Ⲵ⹄ウ䘋 ˈ 䎻 ˈѪ 䢤DŽ
䭞䇽˖⢙⍱䝽䘱˗䖖䖶䐟 䰞仈˗䙊⭘ ㇇⌅˗㔬䘠DŽ
The Current Situation and Development Trends on Vehicle Routing Problems of distribution management
Abstract: Vehicle routing problem is one of the attractive research area in the circles of operations research. In this paper, on the basis of introducing briefly the application background, the research classified the vehicle routing problem, analyzed and summarized the progress of different type of problems and solution algorithms. Furthermore, the research progress of the problems is also discussed. It is expected to provide inference for relevant research work.
Key words: distribution management; vehicle routing problem; heuristics; overview.
䀶
䲿⵰㓿⍾Ⲵ 、 Ⲵ䘋↕ˈ⢙⍱ӗъ䗵䙏 ˈ Ѫ ≁㓿⍾ Ⲵ 㜹 ӗъˈ ≤ 㺑䟿ањ ⧠ԓ 〻 㔬 Ⲵ䟽㾱 ḷDŽкц㓚80 ԓԕ ˈ ⢙⍱ӗъⲴ ˈ⢙⍱ъ Ѫањ⤜・Ⲵӗъ䗵䙏 䎧DŽ❦㘼ˈ ⢙⍱ъӽ Ҿ 㓗䱦⇥ˈо 䗮 ∄䘈 а Ⲵ 䐍ˈ ѝ ケ Ⲵ䰞仈 ⢙⍱ 䖳儈DŽ 㔏䇑[1]ˈ ⢙⍱ 䍩⭘Ѫ7.1зӯ ˈ GDPⲴ∄䟽Ѫ17.8%ˈ㘼 㖾 ㅹ 䗮 ⢙⍱ 㓖 GDPⲴ10%ˈ丙 ㅹѝㅹ 䗮 Ⲵ∄䟽㓖Ѫ15%DŽ䗷儈Ⲵ⢙⍱ Ѫ 㓖 ≁㓿⍾ Ⲵ䟽㾱 ㍐DŽ ↔ˈ 儈⢙⍱ъⲴ、 ㇑⨶≤ ǃ䱽վ⢙⍱ ӏ䴰䀓 Ⲵ 䭞 䰞仈DŽ
䘀䗃 ⢙⍱ Ⲵ䟽㾱㓴 䜘 DŽ 䘀䗃 ⢙⍱ 䍩⭘Ⲵ∄ 䖳儈ˈ㓖Ѫ50%[1]DŽ䱽վ䘀䗃 ˈ 儈䘀䗃 ⦷ǃ 䘋⢙⍱ъ 㔝 Ⲵ䟽㾱䙄 DŽ
Ѫ⢙⍱䝽䘱ѝⲴ 䭞а⧟ˈ䖖䖶䐟 䰞仈˄Vehicle Routing Problem, VRP˅ 䘀䗃㓴㓷Ո ⲴṨ 䰞仈ѻаDŽ㠚1959 Dantzig Ramser[2]俆⅑ ԕ ˈVRP Ѫ䘀ㆩ 㓴 Ո 亶 Ⲵ ⋯о⹄ウ✝⛩ѻаDŽ⧠ ⭏ӗѝˈ䛞 䘀䗃ǃ 䖖 ⊭䖖䈳 ㅹ䈨 䰞仈䜭 ԕ 䊑ѪVRPDŽ ↔ˈ VRPⲴ␡ ⹄ウˈ ⵰䟽㾱Ⲵ、 ѹ 〻 ⭘ԧ DŽ 㓣 㔃ҶVRP Ⲵ⹄ウ䘋 ˈ ҶVRPⲴ 䎻 ˈѪ 㓿傼 䐟DŽ
1. 䖜䖼䐥 䰤从Ⲻ 䘦
Ր㔏кˈ 䖖䖶䐟 䰞仈Ⲵа㡜 䘠Ѫ[3, 4]˖ а㌫ 㔉 Ⲵ ˄䘱䍗⛩ 䍗⛩˅ˈ⺞ 䘲 Ⲵ䝽䘱䖖䖶㹼傦䐟㓯ˈ Ӿ䝽䘱ѝ ˈ ⅑ 䇯䰞 њ ⛩ˈ 䘄 䝽䘱ѝ ˈ ┑䏣а Ⲵ㓖 Ԧл˄ 䖖䖶䖭䍗䟿ǃ 䴰≲䟿ǃ 䰤デ䲀 ㅹ˅ˈ 䘀䗃 ˄ ⭘䖖䖶 ǃ䖖䖶㹼傦䐟〻 䰤˅䗮 DŽ 1 ⽪ˈ ѝⲴ Ṷ㺘⽪䖖䖶 ⛩˄ 䖖 䝽䘱ѝ ˅ˈ ⛩㺘⽪䴰㾱䇯䰞Ⲵ ⛩ˈ㓯⇥㺘⽪є⛩ѻ䰤Ⲵ䘎 䐟⇥ˈ ѝ⇿ 㓯⇥ ⵰ањ䍩⭘˄ 䐍 㹼傦 䰤˅DŽ
1 䖜䖼䐥 䰤从⽰
Fig.1 Schematic figure of VRP
Ⲵ䖖䖶䐟 䰞仈ѫ㾱 ԕлṨ 㾱㍐[5]˖䚃䐟㖁㔌˄Road Network˅ǃ ˄Customer˅ǃ䝽䘱ѝ ˄䖖 ˅˄Distribution Center, Depot˅ǃ䖖䖶˄Vehicle˅ǃ傮傦 ˄Driver˅ǃ䲀 Ԧǃ㹼傦䍩⭘ 㹼傦 䰤ˈԕ Ո ⴞḷ˄Objective˅DŽ њ㾱㍐Ⲵ⢩ 㿱㺘1DŽ
㺞1 䖜䖼䐥 䰤从Ⲻ㓺 㾷㍖
Tab. 1 Key elements of VRP
㓴 㾱㍐⢩
䚃䐟㖁㔌1. VRPⲴṨ 㾱㍐ѻа˗
2. 䙊 ⭡ 㢲⛩ 㓴 Ⲵ䍻 㺘⽪DŽ 㺘⽪䐟⇥ˈ⛩㺘⽪䚃䐟Ӕ ⛩ǃ
䝽䘱ѝ ˗
3. ṩ 䐟㖁㚄є⛩䰤Ⲵ䚃䐟⢩ ˈ Ⲵ Ѫ ˗ 䍻Ҹ⇿ 䶎䍏Ⲵ䍩⭘ 䟽ˈ є⛩䰤Ⲵ䘀㹼䐍ˈ䘀㹼 䰤ㅹDŽ
1. VRPѝ䖖䖶 Ⲵ 䊑ˈ Ҿ㖁㔌 ѝⲴ ⛩˗
2. ⛩Ⲵ ㊫ ˖䘱䍗 ˄Delivery˅ǃ 䍗 ˄Pickup˅ є㘵
˗
3. ⛩Ⲵ 䴰≲䟿˖а⅑┑䏣ˈ ˄Split˅;
4. ⛩Ⲵ 䰤˖䖖䖶 ӔԈ 䍗⢙ 㣡䍩Ⲵ 䰤˗
5. ⛩Ⲵ 䰤デ˖ 㾱≲ Ⲵ 䰤 䲀ˈ Ѫ⺜ 䰤デ[6]
䖟 䰤デ[7]˗
6. ⛩ Ⲵ ⅑ ˖ Ո 㓗˗ ㊫ 亪
ˈ 䘱䍗 䍗˗
7. ⛩Ⲵ ㌫˖ ḀӋ лˈ ⛩Ⲵ䝽 ㌫ˈ Ӿањ 䍗❦ 䘱 оѻ䝽 Ⲵ⢩ 䘱䍗 ⛩DŽ
䝽䘱ѝ 1. ⇿ 䖖䖶䐟㓯Ⲵ䎧⛩ 㓸⛩ˈ Ҿ㖁㔌 ѝⲴ ⛩˗
2. 䖖 䟿˖ањ䖖 њ䖖 ˗
3. 䖖䖶 䘄 䖖 ˖ VRP[5, 8]ˈ䰝 VRP˗
4. 䖖 䰤デ˖ḀӋ лˈ䖖 䲀 ⢩↺㾱≲˄ Ⲵ 䰤 䰤˅˗
5. 䖖 ѻ䰤Ⲵ ㌫˖ḀӋ лˈ䖖 䰤 䝽 ㌫ˈ Ӿањ䖖 䛓䟼 Ⲵ䖖䖶 享 оѻ䝽 Ⲵ Ⲵ䖖 DŽ
䖖䖶1. 䖖䖶 㠚 䘈 』ˈ ԫ 䘄 ˗
2. 䖖䖶㊫ ˖ VRPѝ 䇮䖖䖶Ѫ а㊫ ˈն 䱵䝽䘱㇑⨶ѝˈ䖖䱏 ⭡ н 㻵䖭㜭 ǃн ԕ Ⲵ 䖖䖶㓴 ˗
3. 䖖䖶Ⲵ㻵䖭㜭 ˖䖖䖶 Ⲵ䖭䟽䟿 Ⲵ㻵䖭 䟿ㅹ˗
4. 䖖䖶 ˖䖖䖶Ⲵ ˈ 䖖䖶䍝㖞䍩⭘ㅹ˗ ⭘ ս 䟼Ⲵ䍩⭘ ս 䰤Ⲵ䍩⭘ 㺑䟿˗
5. 䖖䖶Ⲵ 㔝 ˄Duration˅˖䖖䖶 Ⲵ 䇨㹼傦䐍 䰤DŽ
傮傦 1. 㔉傮傦 䘱䍗ԫ ˈ 享ㅖ 䰤Ⲵ 㿴 DŽ 傮傦 䲀 Ԧа㡜䜭 Ⲵ䖖䖶䲀 ԦѝDŽ
䲀 Ԧ1. 䖖䖶Ⲵ 䍏䖭н㜭䎵䗷䖖䖶Ⲵ㻵䖭㜭 ˗
2. 㾱≲䘱䍗ǃ 䍗ǃ 䘱䍗 ˗
3. 㾱≲Ⲵ 䰤デ 傮傦 Ⲵ 䰤 ˗
4. 䇯䰞 Ⲵ亪 㾱≲DŽ
㹼傦䍩⭘
㹼傦 䰤
1. ⛩о ⛩ѻ䰤ǃ䝽䘱ѝ о ⛩ѻ䰤Ⲵ㹼傦䐍 㹼傦 䰤DŽ
Ո ⴞḷ1. 䘀䗃 ˈ Ҿ 䴰Ⲵ䖖䖶 ˄ 㓯䐟 ˅ǃ 㹼傦䐍˄ 䰤˅˗
2. о Ⲵн ㅹ Ⲵ 㖊 ˗
3. 㺑 㓯䐟кⲴ㹼傦 䰤 䖖䖶䖭䟽䟿DŽ
2. 䖜䖼䐥 䰤从Ⲻ ㊱
䙊䗷 к䘠VRPṨ 㾱㍐䱴 н Ⲵ⢩ 䘲 Ⲵ ˈ 㹽⭏ ⿽н Ⲵ䖖䖶䐟 䰞仈㊫ DŽ ⹄ウ[5, 9, 10]ˈ 㿱ⲴVRP ㊫ 㹽⭏㊫ DŽ VRP㊫ 㻵䖭㜭 ⲴVRPǃ 䐟〻䮯 ⲴVRPǃ 䰤デⲴVRPǃ 〻䘀䗃ⲴVRPˈԕ 䘱䍗ⲴVRP˗ ⁑ Ⲵ кˈ㔃 н Ⲵ㓖 Ԧˈ ҶVRPⲴ㹽⭏㊫ ˈ 䲿 VRPǃ⁑㋺VRPǃ VRPㅹDŽ њ㊫ Ⲵ⢩ 㿱㺘2DŽ
