{
"cells": [
{
"attachments": {},
"cell_type": "markdown",
"metadata": {},
"source": [
"# Getting started\n",
"\n",
"## はじめに\n",
"Amplify Schedはスケジューリング問題の定式化をサポートするライブラリです。Amplify Schedで定式化されたスケジューリング問題はAmplify Scheduling Engineにてスケジュールの最適化を行うことができます。\n",
"\n",
"\n",
"## スケジューリング問題\n",
"\n",
"スケジューリング問題とは、複数のジョブ (Job) とそれらを処理する複数のマシン (Machine) のスケジュールを決定する問題です。\n",
"1つのジョブは、指定されたマシンで指定された時間、複数の処理 (Task) を実行し、すべてのタスクが完了するとジョブが完了します。\n",
"\n",
"### Job\n",
"\n",
"複数の Task から構成されます。Job 内の各 Task には順序関係が定められており、その順序で処理を行う必要があります。また同時に複数の Task を行うことはできません。Job 内の Task の順番を Process 1, Process 2, ...と呼びます。\n",
"\n",
"\n",
"\n",
"\n",
"### Task\n",
"\n",
"Task は Job と Process から一意に決まります。Task の変数として、処理開始時刻、処理終了時刻、処理を行う Machine があります。\n",
"処理を行うことができる Machine ごとに、Task の処理時間を設定します。\n",
"\n",
"\n",
"\n",
"\n",
"### Machine\n",
"\n",
"Task を処理する機械です。複数の Task を同時に処理することはできません。\n",
"\n",
"\n",
"\n",
"\n",
"## スケジューリング問題の評価尺度\n",
"\n",
"### Makespan\n",
"\n",
"すべての Job の最後の処理終了時間(メイクスパン)を最小にするスケジュールを探索します。\n",
"\n",
"\n",
"\n",
"## Amplify Schedによるスケジューリング問題の定式化\n",
"\n",
"Amplify Schedで下記の問題の定式化を行います。\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"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from amplify_sched import *"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# define Model\n",
"model = Model()\n",
"\n",
"# define Jobs\n",
"model.jobs.add(\"Job A\")\n",
"model.jobs.add(\"Job B\")\n",
"model.jobs.add(\"Job C\")\n",
"model.jobs.add(\"Job D\")\n",
"\n",
"# define Machines\n",
"model.machines.add(\"Machine X\")\n",
"model.machines.add(\"Machine Y\")\n",
"model.machines.add(\"Machine Z\")\n",
"\n",
"# add Task to Jobs\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",
"model.jobs[\"Job D\"].append(Task())\n",
"model.jobs[\"Job D\"][1].processing_times[\"Machine Y\"] = 20\n",
"model.jobs[\"Job D\"].append(Task())\n",
"model.jobs[\"Job D\"][2].processing_times[\"Machine X\"] = 15"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Enter your token for Amplify Scheduling Engine.\n",
"token = \"xxxxxxxxxxxxxxxxxxxxxxxxxxx\"\n",
"gantt = model.solve(token=token, timeout=1)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"alignmentgroup": "True",
"base": [
0,
40,
10,
55
],
"customdata": [
[
"Machine X",
0
],
[
"Machine X",
2
],
[
"Machine X",
1
],
[
"Machine X",
2
]
],
"hovertemplate": "Machine=%{customdata[0]}
Start=%{base}
Finish=%{x}
Job=%{y}
Process=%{customdata[1]}",
"legendgroup": "Machine X",
"marker": {
"color": "#636efa",
"pattern": {
"shape": ""
}
},
"name": "Machine X",
"offsetgroup": "Machine X",
"orientation": "h",
"showlegend": true,
"textposition": "auto",
"type": "bar",
"x": [
10,
15,
20,
15
],
"xaxis": "x",
"y": [
"Job A",
"Job B",
"Job C",
"Job D"
],
"yaxis": "y"
},
{
"alignmentgroup": "True",
"base": [
10,
0,
50,
30
],
"customdata": [
[
"Machine Y",
1
],
[
"Machine Y",
0
],
[
"Machine Y",
2
],
[
"Machine Y",
1
]
],
"hovertemplate": "Machine=%{customdata[0]}
Start=%{base}
Finish=%{x}
Job=%{y}
Process=%{customdata[1]}",
"legendgroup": "Machine Y",
"marker": {
"color": "#EF553B",
"pattern": {
"shape": ""
}
},
"name": "Machine Y",
"offsetgroup": "Machine Y",
"orientation": "h",
"showlegend": true,
"textposition": "auto",
"type": "bar",
"x": [
20,
10,
15,
20
],
"xaxis": "x",
"y": [
"Job A",
"Job B",
"Job C",
"Job D"
],
"yaxis": "y"
},
{
"alignmentgroup": "True",
"base": [
40,
20,
0,
10
],
"customdata": [
[
"Machine Z",
2
],
[
"Machine Z",
1
],
[
"Machine Z",
0
],
[
"Machine Z",
0
]
],
"hovertemplate": "Machine=%{customdata[0]}
Start=%{base}
Finish=%{x}
Job=%{y}
Process=%{customdata[1]}",
"legendgroup": "Machine Z",
"marker": {
"color": "#00cc96",
"pattern": {
"shape": ""
}
},
"name": "Machine Z",
"offsetgroup": "Machine Z",
"orientation": "h",
"showlegend": true,
"textposition": "auto",
"type": "bar",
"x": [
15,
20,
10,
10
],
"xaxis": "x",
"y": [
"Job A",
"Job B",
"Job C",
"Job D"
],
"yaxis": "y"
}
],
"layout": {
"barmode": "overlay",
"legend": {
"title": {
"text": "Machine"
},
"tracegroupgap": 0
},
"margin": {
"t": 60
},
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "bar"
}
],
"barpolar": [
{
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "barpolar"
}
],
"carpet": [
{
"aaxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"baxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"type": "carpet"
}
],
"choropleth": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "choropleth"
}
],
"contour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "contour"
}
],
"contourcarpet": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "contourcarpet"
}
],
"heatmap": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "heatmap"
}
],
"heatmapgl": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "heatmapgl"
}
],
"histogram": [
{
"marker": {
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "histogram"
}
],
"histogram2d": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "histogram2d"
}
],
"histogram2dcontour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "histogram2dcontour"
}
],
"mesh3d": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "mesh3d"
}
],
"parcoords": [
{
"line": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "parcoords"
}
],
"pie": [
{
"automargin": true,
"type": "pie"
}
],
"scatter": [
{
"fillpattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
},
"type": "scatter"
}
],
"scatter3d": [
{
"line": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatter3d"
}
],
"scattercarpet": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattercarpet"
}
],
"scattergeo": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattergeo"
}
],
"scattergl": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattergl"
}
],
"scattermapbox": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scattermapbox"
}
],
"scatterpolar": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterpolar"
}
],
"scatterpolargl": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterpolargl"
}
],
"scatterternary": [
{
"marker": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"type": "scatterternary"
}
],
"surface": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"type": "surface"
}
],
"table": [
{
"cells": {
"fill": {
"color": "#EBF0F8"
},
"line": {
"color": "white"
}
},
"header": {
"fill": {
"color": "#C8D4E3"
},
"line": {
"color": "white"
}
},
"type": "table"
}
]
},
"layout": {
"annotationdefaults": {
"arrowcolor": "#2a3f5f",
"arrowhead": 0,
"arrowwidth": 1
},
"autotypenumbers": "strict",
"coloraxis": {
"colorbar": {
"outlinewidth": 0,
"ticks": ""
}
},
"colorscale": {
"diverging": [
[
0,
"#8e0152"
],
[
0.1,
"#c51b7d"
],
[
0.2,
"#de77ae"
],
[
0.3,
"#f1b6da"
],
[
0.4,
"#fde0ef"
],
[
0.5,
"#f7f7f7"
],
[
0.6,
"#e6f5d0"
],
[
0.7,
"#b8e186"
],
[
0.8,
"#7fbc41"
],
[
0.9,
"#4d9221"
],
[
1,
"#276419"
]
],
"sequential": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
],
"sequentialminus": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
],
[
0.8888888888888888,
"#fdca26"
],
[
1,
"#f0f921"
]
]
},
"colorway": [
"#636efa",
"#EF553B",
"#00cc96",
"#ab63fa",
"#FFA15A",
"#19d3f3",
"#FF6692",
"#B6E880",
"#FF97FF",
"#FECB52"
],
"font": {
"color": "#2a3f5f"
},
"geo": {
"bgcolor": "white",
"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
"align": "left"
},
"hovermode": "closest",
"mapbox": {
"style": "light"
},
"paper_bgcolor": "white",
"plot_bgcolor": "#E5ECF6",
"polar": {
"angularaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"radialaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"scene": {
"xaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"yaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"zaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
}
},
"shapedefaults": {
"line": {
"color": "#2a3f5f"
}
},
"ternary": {
"aaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"baxis": {
"gridcolor": "white",
"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
},
"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"xaxis": {
"anchor": "y",
"domain": [
0,
1
],
"type": "linear"
},
"yaxis": {
"anchor": "x",
"categoryarray": [
"Job D",
"Job C",
"Job B",
"Job A"
],
"categoryorder": "array",
"domain": [
0,
1
],
"title": {
"text": "Job"
}
}
}
},
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gantt.timeline()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "scheduling-engine-sdk-IShfnD0Q",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.6"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}