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"# Scheduling Problems\n",
"\n",
"本章ではいくつかの典型的スケジューリング問題の例とその定式化について扱います。\n"
]
},
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"metadata": {},
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"source": [
"from amplify_sched import *\n",
"\n",
"token = \"xxxxxxxxxxxxxxxxxxxxxxxxx\""
]
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"source": [
"## Flow Shop Scheduling\n",
"\n",
"Flow Shop Scheduling はスケジューリング問題の一種で以下のように定義されます\n",
"\n",
"**定義**\n",
"\n",
"- m 台の Machine(M_1, M_2, ..., M_m)で n 個の Job(J_1, J_2, ..., J_n)を処理する\n",
"- 各 Job は m 台すべての Machine を$M_1$から順に処理し、これらの Machine の処理順序はすべての Job で同一である\n",
"- 各 Job の各 Machine における処理時間はそれぞれ与えられる\n",
"- このとき与えられた評価尺度を最適にするような Job の処理順序を求める問題\n",
"\n",
"### 定式化例\n",
"\n",
"下記の Flow Shop Scheduling の定式化とメイクスパンの最適化を Amplify Sched で行います。\n",
"\n",
"| Job name | Process | Machine name | Processing Time |\n",
"| -------- | ------- | ------------ | --------------- |\n",
"| J1 | 0 | M1 | 10 |\n",
"| J1 | 1 | M2 | 15 |\n",
"| J1 | 2 | M3 | 20 |\n",
"| J2 | 0 | M1 | 15 |\n",
"| J2 | 1 | M2 | 20 |\n",
"| J2 | 2 | M3 | 10 |\n",
"| J3 | 0 | M1 | 10 |\n",
"| J3 | 1 | M2 | 20 |\n",
"| J3 | 2 | M3 | 15 |\n"
]
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"\n",
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"model.jobs.add(\"J2\")\n",
"model.jobs.add(\"J3\")\n",
"\n",
"model.machines.add(\"M1\")\n",
"model.machines.add(\"M2\")\n",
"model.machines.add(\"M3\")\n",
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"model.jobs[\"J1\"].append(Task())\n",
"model.jobs[\"J1\"][0].processing_times[\"M1\"] = 10\n",
"model.jobs[\"J1\"].append(Task())\n",
"model.jobs[\"J1\"][1].processing_times[\"M2\"] = 15\n",
"model.jobs[\"J1\"].append(Task())\n",
"model.jobs[\"J1\"][2].processing_times[\"M3\"] = 20\n",
"\n",
"model.jobs[\"J2\"].append(Task())\n",
"model.jobs[\"J2\"][0].processing_times[\"M1\"] = 15\n",
"model.jobs[\"J2\"].append(Task())\n",
"model.jobs[\"J2\"][1].processing_times[\"M2\"] = 20\n",
"model.jobs[\"J2\"].append(Task())\n",
"model.jobs[\"J2\"][2].processing_times[\"M3\"] = 10\n",
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"model.jobs[\"J3\"].append(Task())\n",
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"model.jobs[\"J3\"].append(Task())\n",
"model.jobs[\"J3\"][1].processing_times[\"M2\"] = 20\n",
"model.jobs[\"J3\"].append(Task())\n",
"model.jobs[\"J3\"][2].processing_times[\"M3\"] = 15\n",
"gantt = model.solve(token=token, timeout=1)\n",
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"source": [
"## Job Shop Scheduling\n",
"\n",
"Job Shop Scheduling はスケジューリング問題の一種で以下のように定義されます。\n",
"\n",
"**定義**\n",
"\n",
"- m 台の Machine(M_1, M_2, ..., M_m)で n 個の Job(J_1, J_2, ..., J_n)を処理する。\n",
"- 各 Job はすべての Machine で一度ずつ処理されるが、その処理順序は Job ごとに異なってもよい\n",
"- 各 Job の各 Machine における処理時間はそれぞれ与えられる\n",
"- このとき与えられた評価尺度を最適にするような各 Task の開始時刻を求める問題\n",
"\n",
"### 定式化例\n",
"\n",
"下記の Job Shop Scheduling の定式化とメイクスパンの最適化を Amplify Sched で行います。\n",
"\n",
"| Job name | Process | Machine name | Processing Time |\n",
"| -------- | ------- | ------------ | --------------- |\n",
"| Job A | 0 | Machine X | 10 |\n",
"| Job A | 1 | Machine Y | 20 |\n",
"| Job A | 2 | Machine Z | 15 |\n",
"| Job B | 0 | Machine Y | 10 |\n",
"| Job B | 1 | Machine Z | 20 |\n",
"| Job B | 2 | Machine X | 15 |\n",
"| Job C | 0 | Machine Z | 10 |\n",
"| Job C | 1 | Machine X | 20 |\n",
"| Job C | 2 | Machine Y | 15 |\n",
"| Job D | 0 | Machine Z | 10 |\n",
"| Job D | 1 | Machine Y | 20 |\n",
"| Job D | 2 | Machine X | 15 |\n"
]
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"model = Model()\n",
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"model.jobs.add(\"Job B\")\n",
"model.jobs.add(\"Job C\")\n",
"model.jobs.add(\"Job D\")\n",
"\n",
"model.machines.add(\"Machine X\")\n",
"model.machines.add(\"Machine Y\")\n",
"model.machines.add(\"Machine Z\")\n",
"\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine X\"] = 10\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine Y\"] = 20\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][2].processing_times[\"Machine Z\"] = 15\n",
"\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine Y\"] = 10\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine Z\"] = 20\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][2].processing_times[\"Machine X\"] = 15\n",
"\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][0].processing_times[\"Machine Z\"] = 10\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][1].processing_times[\"Machine X\"] = 20\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][2].processing_times[\"Machine Y\"] = 15\n",
"\n",
"model.jobs[\"Job D\"].append(Task())\n",
"model.jobs[\"Job D\"][0].processing_times[\"Machine Z\"] = 10\n",
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"model.jobs[\"Job D\"].append(Task())\n",
"model.jobs[\"Job D\"][2].processing_times[\"Machine X\"] = 15\n",
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"source": [
"## Flexible Job Shop Scheduling\n",
"\n",
"Flexible Job Shop Scheduling はスケジューリング問題の一種で以下のように定義されます\n",
"\n",
"**定義**\n",
"\n",
"- m 台の Machine(M_1, M_2, ..., M_m)で n 個の Job(J_1, J_2, ..., J_n)を処理する\n",
"- 各 Job の各 Process は指定されたの Machine で処理される。このときその Process を処理できる Machine の候補を複数定義できる\n",
"- 各 Job の各 Machine における処理時間はそれぞれ与えられる\n",
"- このとき与えられた評価尺度を最適にするような各 Task の開始時刻と Machine の割り当てを求める問題\n",
"\n",
"### 定式化例\n",
"\n",
"下記の Flexible Job Shop Scheduling の定式化とメイクスパンの最適化を Amplify Sched で行います。\n",
"\n",
"| Job name | Process | Machine name | Processing Time |\n",
"| -------- | ------- | ------------ | --------------- |\n",
"| Job A | 0 | Machine X | 10 |\n",
"| Job A | 0 | Machine Y | 5 |\n",
"| Job B | 0 | Machine X | 15 |\n",
"| Job B | 0 | Machine Y | 2 |\n",
"| Job C | 0 | Machine Z | 10 |\n",
"| Job C | 0 | Machine Y | 1 |\n",
"| Job A | 1 | Machine X | 20 |\n",
"| Job A | 1 | Machine Y | 10 |\n",
"| Job B | 1 | Machine Z | 20 |\n",
"| Job B | 1 | Machine Y | 10 |\n",
"| Job C | 1 | Machine X | 20 |\n",
"| Job C | 1 | Machine Z | 10 |\n",
"| Job A | 2 | Machine Z | 15 |\n",
"| Job B | 2 | Machine X | 15 |\n",
"| Job C | 2 | Machine Y | 15 |\n"
]
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"\n",
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"model.machines.add(\"Machine Y\")\n",
"model.machines.add(\"Machine Z\")\n",
"\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine X\"] = 10\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine Y\"] = 5\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine X\"] = 15\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine Y\"] = 2\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][0].processing_times[\"Machine Z\"] = 10\n",
"model.jobs[\"Job C\"][0].processing_times[\"Machine Y\"] = 1\n",
"\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine X\"] = 20\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine Y\"] = 10\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine Z\"] = 20\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine Y\"] = 10\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][1].processing_times[\"Machine X\"] = 20\n",
"model.jobs[\"Job C\"][1].processing_times[\"Machine Z\"] = 10\n",
"\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][2].processing_times[\"Machine Z\"] = 15\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][2].processing_times[\"Machine X\"] = 15\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][2].processing_times[\"Machine Y\"] = 15\n",
"\n",
"\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline(machine_view=True)"
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},
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