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"## release_time, deadline\n",
"\n",
"各Taskには開始可能時刻(Release Time)と終了締め切り時刻(Deadline)を与えることができます。\n",
"\n",
"\n",
"\n",
"下記例では`Job A`の0番目のプロセスの開始時間は10以上、終了時間は20以下であることを指定します。"
]
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"source": [
"from amplify_sched import *\n",
"\n",
"token = \"xxxxxxxxxxxxxxxxxxxxxxxxx\"\n",
"\n",
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.machines.add(\"Machine X\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine X\"] = 10\n",
"model.jobs[\"Job A\"][0].release_time = 10\n",
"model.jobs[\"Job A\"][0].deadline = 20\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline()"
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"source": [
"## transportation_time\n",
"\n",
"ある Machine からある Machine への輸送時間(transportation_time)を Task ごとに設定できます。輸送時間が設定されている場合、その時間より短い間隔では次の Task を開始できません。\n",
"\n",
"\n",
"\n",
"\n",
"下記例では`Machine A` から`Machine B`に`Job A`の0番目のプロセスの輸送時間を10に設定しています。"
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"model.machines.add(\"Machine B\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 7\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine B\"] = 5\n",
"model.jobs[\"Job A\"][0].transportation_times.append((10, \"Machine A\", \"Machine B\"))\n",
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"## setup_time\n",
"\n",
"ある Machine において、ある Task からある Task への切り替えにかかる準備時間(setup_time)を設定できます。準備時間が設定されている場合、その時間より短い間隔では次の Task を開始できません\n",
"\n",
"\n",
"\n",
"下記例では`Machine A` において、`Task[Job A, 0]`<->`Task[Job B,1]`の切り替えにかかる準備時間を10に設定しています。"
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},
"text/html": [
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],
"source": [
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.machines.add(\"Machine A\")\n",
"model.machines.add(\"Machine B\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 7\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine B\"] = 7\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine A\"] = 5\n",
"model.machines[\"Machine A\"].setup_times.append((10, model.jobs[\"Job A\", 0], model.jobs[\"Job B\", 1]))\n",
"model.machines[\"Machine A\"].setup_times.append((10, model.jobs[\"Job B\", 1], model.jobs[\"Job A\", 0]))\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline(machine_view=True)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## maintenance_time\n",
"\n",
"ある Machine が稼働できない時間区間を設定できます。設定した時間区間ではその Machine では Task を行うことはできません。\n",
"\n",
"\n",
"\n",
"\n",
"下記例では`Machine A`は10~15をmaintenance_timeにしています。"
]
},
{
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"execution_count": 4,
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},
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"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"caxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"title": {
"x": 0.05
},
"xaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
},
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"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
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},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"xaxis": {
"anchor": "y",
"domain": [
0,
1
],
"type": "linear"
},
"yaxis": {
"anchor": "x",
"categoryarray": [
"Machine B",
"Machine A"
],
"categoryorder": "array",
"domain": [
0,
1
],
"title": {
"text": "Machine"
}
}
}
},
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
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],
"source": [
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.jobs.add(\"Job C\")\n",
"model.machines.add(\"Machine A\")\n",
"model.machines.add(\"Machine B\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 7\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine B\"] = 7\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine A\"] = 5\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][0].processing_times[\"Machine A\"] = 10\n",
"model.machines[\"Machine A\"].maintenance_times.append(TimeRange(10, 15))\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline(machine_view=True)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## buffer\n",
"\n",
"ある Machine で終了した Task を、次の Machine での処理が始まるまで保管する倉庫を考えます。このとき、各 Machine の倉庫の容量と各 Task が占有するサイズを設定することができます。これらが設定されている場合、各時刻において倉庫の容量を超えるようなスケジュールは許されません。\n",
"\n",
"\n",
"\n",
"\n",
"下記例では`Machine A`のバッファを1に、`Task[\"Job A\",0]`,`Task[\"Job B\",0]`,`Task[\"Job C\",1]`の要求バッファサイズを1に設定しています。"
]
},
{
"cell_type": "code",
"execution_count": 46,
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},
"bgcolor": "#E5ECF6",
"caxis": {
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"ticks": ""
}
},
"title": {
"x": 0.05
},
"xaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
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},
"zerolinecolor": "white",
"zerolinewidth": 2
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"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
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"source": [
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.jobs.add(\"Job C\")\n",
"model.machines.add(\"Machine A\")\n",
"model.machines.add(\"Machine B\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 1\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine B\"] = 3\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine A\"] = 1\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine B\"] = 2\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][0].processing_times[\"Machine A\"] = 1\n",
"model.jobs[\"Job C\"].append(Task())\n",
"model.jobs[\"Job C\"][1].processing_times[\"Machine B\"] = 7\n",
"model.jobs[\"Job A\"][1].deadline = 4\n",
"model.jobs[\"Job B\"][1].deadline = 6\n",
"model.machines[\"Machine A\"].buffer_size = 1\n",
"model.machines[\"Machine A\"].maintenance_times.append(TimeRange(3, 6))\n",
"model.jobs[\"Job A\"][0].required_buffer_size = 1\n",
"model.jobs[\"Job B\"][0].required_buffer_size = 1\n",
"model.jobs[\"Job C\"][0].required_buffer_size = 1\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline(machine_view=True)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## resource\n",
"\n",
"各 Task を行うために必要なリソースを定義できます。各リソースには同時使用上限数が定められ、その数を超える複数の Task で同時にリソースを使用できません。\n",
"\n",
"\n",
"\n",
"\n",
"下記例は`Task[Job A,0]`,`Task[Job B,0]`が`Resource A`を使用します。"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
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"text/html": [
""
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],
"source": [
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.machines.add(\"Machine A\")\n",
"model.machines.add(\"Machine B\")\n",
"model.resources.add(\"Resource A\")\n",
"model.resources[\"Resource A\"].capacity = 1\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 10\n",
"model.jobs[\"Job A\"][0].required_resources.append(\"Resource A\")\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine B\"] = 10\n",
"model.jobs[\"Job B\"][0].required_resources.append(\"Resource A\")\n",
"\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline(machine_view=True)"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## no_wait\n",
"\n",
"各 Job に no-wait フラグを設定できます。no-wait が設定された Job は一度 Task を始めたら、全 Task が終了するまで連続で Task を行う必要があります。\n",
"\n",
"\n",
"\n",
"下記例は`Job B`に`no_wait=True`を設定しています。"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
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"source": [
"model = Model()\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.machines.add(\"Machine A\")\n",
"model.machines.add(\"Machine B\")\n",
"model.machines.add(\"Machine C\")\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][0].processing_times[\"Machine A\"] = 10\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][1].processing_times[\"Machine B\"] = 10\n",
"model.jobs[\"Job A\"].append(Task())\n",
"model.jobs[\"Job A\"][2].processing_times[\"Machine C\"] = 10\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][0].processing_times[\"Machine B\"] = 10\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][1].processing_times[\"Machine A\"] = 15\n",
"model.jobs[\"Job B\"].append(Task())\n",
"model.jobs[\"Job B\"][2].processing_times[\"Machine C\"] = 10\n",
"model.jobs[\"Job B\"].no_wait = True\n",
"gantt = model.solve(token=token, timeout=1)\n",
"gantt.timeline()"
]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"## dependent_jobs\n",
"\n",
"各 Job ごとに依存する Job を複数定義できます。依存する Job が定義されている場合、それらがすべて完了しないとその Job は開始できません。\n",
"\n",
"\n",
"\n",
"\n",
"下記例は`Job B`は`Job A`に依存すると設定しています。"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
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"## 複数の制約がある場合\n",
"\n",
"### transportation_time + setup_time\n",
"transportation_time と setup_time が両方設定されている場合、それぞれ独立に制約を課します。すなわちある Machine における切り替え準備は前後の Task の輸送時間中にも行うことができます。\n",
"\n",
"\n",
"\n",
"\n",
"### transportation_time + no_wait\n",
"no-wait フラグと transportation_time が両方設定されている場合、no-wait フラグが設定されている Job の連続する 2 つの Task(j, p), Task(j,p+1)について、Task(j,p+1) の処理開始時刻 = Task(j,p) の処理終了時刻 + transportation_time[Task(j,p), Machine A, Machine B] となります。\n",
"\n",
"\n",
"\n",
"\n",
"### transportation_time + dependent_jobs\n",
"dependent_jobs によって Job A -> Job C という順序関係が定義されている場合、Job A の最後の工程に対して transportation_time を設定することができ、Job C の最初の工程は Job A の最後の工程から transportaion_time 以上経過しないと開始できません。\n",
"\n",
"\n",
"\n",
"\n",
"### transportation_time + buffer\n",
"buffer と transportation_time が両方設定されている場合、Task は輸送時間中には倉庫を使用しないとし、輸送直後に次のタスクが開始されると考えます。\n",
"\n",
"\n",
"\n"
]
}
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