-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathnotebook.tex
961 lines (696 loc) · 65.1 KB
/
notebook.tex
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{model}
% Pygments definitions
\makeatletter
\def\PY@reset{\let\PY@it=\relax \let\PY@bf=\relax%
\let\PY@ul=\relax \let\PY@tc=\relax%
\let\PY@bc=\relax \let\PY@ff=\relax}
\def\PY@tok#1{\csname PY@tok@#1\endcsname}
\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
\expandafter\def\csname PY@tok@c\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.74,0.48,0.00}{##1}}}
\expandafter\def\csname PY@tok@k\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.69,0.00,0.25}{##1}}}
\expandafter\def\csname PY@tok@o\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@ow\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
\expandafter\def\csname PY@tok@nb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@nf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@nc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@nn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@ne\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.82,0.25,0.23}{##1}}}
\expandafter\def\csname PY@tok@nv\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@no\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@nl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.63,0.00}{##1}}}
\expandafter\def\csname PY@tok@ni\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.60,0.60,0.60}{##1}}}
\expandafter\def\csname PY@tok@na\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.49,0.56,0.16}{##1}}}
\expandafter\def\csname PY@tok@nt\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@nd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.67,0.13,1.00}{##1}}}
\expandafter\def\csname PY@tok@s\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sd\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@si\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
\expandafter\def\csname PY@tok@se\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.13}{##1}}}
\expandafter\def\csname PY@tok@sr\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.40,0.53}{##1}}}
\expandafter\def\csname PY@tok@ss\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@sx\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@m\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@gh\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@gu\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.50,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@gd\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.63,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@gi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.63,0.00}{##1}}}
\expandafter\def\csname PY@tok@gr\endcsname{\def\PY@tc##1{\textcolor[rgb]{1.00,0.00,0.00}{##1}}}
\expandafter\def\csname PY@tok@ge\endcsname{\let\PY@it=\textit}
\expandafter\def\csname PY@tok@gs\endcsname{\let\PY@bf=\textbf}
\expandafter\def\csname PY@tok@gp\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,0.50}{##1}}}
\expandafter\def\csname PY@tok@go\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.53,0.53,0.53}{##1}}}
\expandafter\def\csname PY@tok@gt\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.27,0.87}{##1}}}
\expandafter\def\csname PY@tok@err\endcsname{\def\PY@bc##1{\setlength{\fboxsep}{0pt}\fcolorbox[rgb]{1.00,0.00,0.00}{1,1,1}{\strut ##1}}}
\expandafter\def\csname PY@tok@kc\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kd\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kn\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@kr\endcsname{\let\PY@bf=\textbf\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@bp\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.50,0.00}{##1}}}
\expandafter\def\csname PY@tok@fm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.00,0.00,1.00}{##1}}}
\expandafter\def\csname PY@tok@vc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@vg\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@vi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@vm\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.10,0.09,0.49}{##1}}}
\expandafter\def\csname PY@tok@sa\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sc\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@dl\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@s2\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@sh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@s1\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.13,0.13}{##1}}}
\expandafter\def\csname PY@tok@mb\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mf\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mh\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mi\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@il\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@mo\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.40,0.40,0.40}{##1}}}
\expandafter\def\csname PY@tok@ch\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cm\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cpf\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@c1\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
\def\PYZbs{\char`\\}
\def\PYZus{\char`\_}
\def\PYZob{\char`\{}
\def\PYZcb{\char`\}}
\def\PYZca{\char`\^}
\def\PYZam{\char`\&}
\def\PYZlt{\char`\<}
\def\PYZgt{\char`\>}
\def\PYZsh{\char`\#}
\def\PYZpc{\char`\%}
\def\PYZdl{\char`\$}
\def\PYZhy{\char`\-}
\def\PYZsq{\char`\'}
\def\PYZdq{\char`\"}
\def\PYZti{\char`\~}
% for compatibility with earlier versions
\def\PYZat{@}
\def\PYZlb{[}
\def\PYZrb{]}
\makeatother
% Exact colors from NB
\definecolor{incolor}{rgb}{0.0, 0.0, 0.5}
\definecolor{outcolor}{rgb}{0.545, 0.0, 0.0}
% Prevent overflowing lines due to hard-to-break entities
\sloppy
% Setup hyperref package
\hypersetup{
breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
}
% Slightly bigger margins than the latex defaults
\geometry{verbose,tmargin=1in,bmargin=1in,lmargin=1in,rmargin=1in}
\begin{document}
\maketitle
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}1}]:} \PY{k+kn}{from} \PY{n+nn}{gurobipy} \PY{k}{import} \PY{o}{*}
\PY{o}{\PYZpc{}}\PY{k}{run} data.ipynb
\end{Verbatim}
\section{create a new model.}\label{create-a-new-model.}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}2}]:} \PY{n}{m} \PY{o}{=} \PY{n}{Model}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{scheduling}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Academic license - for non-commercial use only
\end{Verbatim}
\section{Creating a Binary Variables}\label{creating-a-binary-variables}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}3}]:} \PY{n}{vars\PYZus{}tup} \PY{o}{=} \PY{p}{[}\PY{p}{(}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{)} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{]}
\end{Verbatim}
Creating the Binary varibale indicates whether task \(j\) of appliance
\(i\) of user \(u\) at time slot \(k\) processed by only electricity or
not; 1 = processed, 0 = not processed denoted by \(y_{k, u, i, j}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}4}]:} \PY{n}{x} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{vars\PYZus{}tup}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{BINARY}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{x}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
Creating the binary varibale indicated whether task \(j\) of appliances
\(i\) of user \(u\) at time slot \(k\) processed by both electricity and
hotwater or not; 1 = processed, 0 = not processed denoted by
\(y_{k, u, i, j}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}5}]:} \PY{n}{y} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{vars\PYZus{}tup}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{BINARY}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{y}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
Creating the binary varibale indicated whether task \(j\) of appliances
\(i\) of user \(u\) at time slot \(k\) processed by natural gas or not;
1 = processed, 0 = not processed denoted by \(z_{k, u, i, j}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}6}]:} \PY{n}{z} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{vars\PYZus{}tup}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{BINARY}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{z}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
Creating a binary variable indicated the On and Off status of the CHP at
time slot k; 1 = On or 0 = off denoted by \(s_k^{Boiler}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}7}]:} \PY{n}{s} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{BINARY}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{s}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
\section{Auxiliary Decision
variable.}\label{auxiliary-decision-variable.}
Binary variable that takes value 1, if the task \(j\) of appliances
\(i\) of user \(u\) starts running at time \(k\), Or 0 if it doesn't
start denoted by \(\delta_{k, u, i, j}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}8}]:} \PY{c+c1}{\PYZsh{} delta = m.addVars(vars\PYZus{}tup, vtype = GRB.BINARY, name = \PYZsq{}delta\PYZsq{})}
\end{Verbatim}
Binary variable that takes value 1, if the task \(j\) of appliance \(i\)
of user \(u\) at time slot \(k\) is already finished, or 0 if it is not
yet finished indicated by \(\beta_{k, u, i, j}\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}9}]:} \PY{c+c1}{\PYZsh{} beta = m.addVars(vars\PYZus{}tup, vtype = GRB.BINARY, name = \PYZdq{}beta\PYZdq{})}
\end{Verbatim}
\section{Creating the Variables for the
Model}\label{creating-the-variables-for-the-model}
Electricity imported by task \(j\) of appliances \(i\) of user \(u\) at
time slot \(k\) from grid or send to the grid denoted by
\(E_{k, u, i, j}^{grid}\)(Wh).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}10}]:} \PY{c+c1}{\PYZsh{} grid\PYZus{}electricity = m.addVars(vars\PYZus{}tup, vtype = GRB.CONTINUOUS, name = \PYZsq{}grid\PYZus{}electricity\PYZsq{})}
\end{Verbatim}
Amount of hotwater available in the storage tank at time slot \(k\)
denoted by \(H_{k}^{available}\)(litres).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}11}]:} \PY{n}{available\PYZus{}hotwater\PYZus{}storagetank} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{,} \PY{n}{lb} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ub} \PY{o}{=} \PY{l+m+mi}{31719} \PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{CONTINUOUS}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{available\PYZus{}hotwater\PYZus{}storagetank}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
The time slot at which appliance \(i\) starts its operation denoted by
\(t_{i}\).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}12}]:} \PY{n}{timeslot\PYZus{}appliance\PYZus{}start} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{appliances}\PY{p}{,} \PY{n}{lb} \PY{o}{=}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ub} \PY{o}{=} \PY{l+m+mi}{96}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{INTEGER}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{timeslot\PYZus{}appliance\PYZus{}start}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
Electricity produced by the CHP at time slot \(k\) denoted by
\(E_k^{CHP}\)(Wh).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}13}]:} \PY{c+c1}{\PYZsh{} CHP\PYZus{}produced\PYZus{}electricity = m.addVars(time\PYZus{}slots, vtype = GRB.CONTINUOUS, name =\PYZdq{}CHP\PYZus{}produced\PYZus{}electricity\PYZdq{})}
\end{Verbatim}
Thermal output of the Boiler at time slot \(k\) denoted by
\(T_k^{Boiler}\)(wh).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{boiler\PYZus{}produced\PYZus{}thermal} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{,} \PY{n}{lb} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ub} \PY{o}{=} \PY{l+m+mi}{21250} \PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{CONTINUOUS}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{boiler\PYZus{}produced\PYZus{}thermal}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
Hotwater Produced by Boiler at time slot \(k\) denoted by
\(H_k^{Boiler}\)(litres).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}15}]:} \PY{n}{boiler\PYZus{}produced\PYZus{}hotwater} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{,} \PY{n}{lb} \PY{o}{=}\PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ub} \PY{o}{=} \PY{l+m+mi}{21250} \PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{CONTINUOUS}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{boiler\PYZus{}produced\PYZus{}hotwater}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
Electricity produced by Solar panel at time slot \(k\) denoted by
\(E_k^{solar}\)(wh).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}16}]:} \PY{c+c1}{\PYZsh{} solar\PYZus{}produced\PYZus{}electricity = m.addVars(time\PYZus{}slots, vtype = GRB.CONTINUOUS, name = \PYZdq{}solar\PYZus{}produced\PYZus{}electricity\PYZdq{})}
\end{Verbatim}
Amount of gas required by Boiler at time slot \(k\) denoted by
\(G_k^{Boiler}\) (\(Wh\)).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}17}]:} \PY{n}{boiler\PYZus{}required\PYZus{}gas} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addVars}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{,} \PY{n}{lb} \PY{o}{=} \PY{l+m+mi}{0}\PY{p}{,} \PY{n}{ub} \PY{o}{=} \PY{l+m+mi}{19125}\PY{p}{,} \PY{n}{vtype} \PY{o}{=} \PY{n}{GRB}\PY{o}{.}\PY{n}{CONTINUOUS}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{boiler\PYZus{}required\PYZus{}gas}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}18}]:} \PY{n}{m}\PY{o}{.}\PY{n}{update}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\section{Set the Objective Function}\label{set-the-objective-function}
Objective is to minimize the CO2 emission from the group of users who
has same set of the household appliances.
\begin{multline} \label{eq1}
minimize \sum_{k=1}^{96}\sum_{u=1}^{50}\sum_{i=1}^N\sum_{j=1}^{n_i} C_{k}^{electricity} E_{k,u,i,j}^{high} x_{k,u,i,j}+ [C_{k}^{electricity} E_{k,u,i,j}^{low}
+C_{k}^{gas} H_{k,u,i,j}] y_{k,u,i,j}+ C_{k}^{gas}[ G_{k,u,i,j} z_{k,u,i,j}+G_{K}^{Boiler}]
\end{multline}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}19}]:} \PY{n}{obj} \PY{o}{=} \PY{n}{quicksum}\PY{p}{(}\PY{n}{co2\PYZus{}factor\PYZus{}electricity}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{*} \PY{n+nb}{float}\PY{p}{(}\PY{n}{electricity\PYZus{}high\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{x}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+}
\PY{n}{co2\PYZus{}factor\PYZus{}electricity}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{*} \PY{n+nb}{float}\PY{p}{(}\PY{n}{electricity\PYZus{}low\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{l+m+mf}{0.469} \PY{o}{*} \PY{n+nb}{float}\PY{p}{(}\PY{n}{hotwater\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+}
\PY{l+m+mf}{0.469} \PY{o}{*} \PY{n+nb}{float}\PY{p}{(}\PY{n}{gas\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{z}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u} \PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{l+m+mf}{0.469} \PY{o}{*} \PY{n}{boiler\PYZus{}required\PYZus{}gas}\PY{p}{[}\PY{n}{t}\PY{p}{]}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}20}]:} \PY{n}{m}\PY{o}{.}\PY{n}{setObjective}\PY{p}{(}\PY{n}{obj}\PY{p}{,} \PY{n}{GRB}\PY{o}{.}\PY{n}{MINIMIZE}\PY{p}{)}
\end{Verbatim}
Update the Model.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}21}]:} \PY{n}{m}\PY{o}{.}\PY{n}{update}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\section{Create the Constraints for the
model}\label{create-the-constraints-for-the-model}
Subject to Constraints
The appliances can to use electricity or both electricity and hotwater
or Gas energy carrier at a time to process its task.
\(x_{k,u,i,j}+ y_{k,u,i,j}+ z_{k,u,i,j} \leq 1\)
\(\forall k, u, i, j, \{X_{k,u,i,j}, Y_{k,u,i,j}, Z_{k,u,i,j}\} \in \{0,1\}\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}22}]:} \PY{n}{energy\PYZus{}carrier} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{n}{z}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{l+m+mi}{1}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{energy\PYZus{}carrier}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The amount of electricity or hot water or natural gas required by the
task of the appliances should be satisfied.
\begin{equation} \label{eq3}
\sum_{k=1}^{96} E_{k,u,i,j}^{high} x_{k,u,i,j} = E_{i,j}^{high} \quad \forall k, u, i, j, x_{k,u,i,j} \in \{0,1\}
\end{equation}
\begin{equation} \label{eq3a}
\sum_{k=1}^{96} (E_{k,u,i,j}^{low} + H_{k, u, i, j}^{demand}) y_{k,u,i,j} = E_{i,j}^{low} + H_{i,j} \quad \forall k, u, i, j, y_{k,u,i,j} \in \{0,1\}
\end{equation}
\begin{equation} \label{eq3b}
\sum_{k=1}^{96} G_{k,u,i,j}^{demand} z_{k,u,i,j} = G_{i,j} \quad \forall k, u, i, j, z_{k,u,i,j} \in \{0,1\}
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}23}]:} \PY{n}{balance\PYZus{}energy1} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{n+nb}{float}\PY{p}{(}\PY{n}{electricity\PYZus{}high\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{x}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)} \PY{o}{==}
\PY{n+nb}{float}\PY{p}{(}\PY{n}{task\PYZus{}only\PYZus{}electricity\PYZus{}req}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{[}\PY{n}{task}\PY{p}{]}\PY{p}{)}
\PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{balance\PYZus{}energy1}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{balance\PYZus{}energy2} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{p}{(}\PY{n+nb}{float}\PY{p}{(}\PY{n}{electricity\PYZus{}low\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{+}\PY{n+nb}{float}\PY{p}{(}\PY{n}{hotwater\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)}\PY{p}{)} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)} \PY{o}{==}
\PY{n+nb}{float}\PY{p}{(}\PY{n}{task\PYZus{}low\PYZus{}electricity\PYZus{}req}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{[}\PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{+} \PY{n+nb}{float}\PY{p}{(}\PY{n}{task\PYZus{}hotwater\PYZus{}req}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{[}\PY{n}{task}\PY{p}{]}\PY{p}{)}
\PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{balance\PYZus{}energy2}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\PY{n}{balance\PYZus{}energy3} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{n+nb}{float}\PY{p}{(}\PY{n}{gas\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{o}{*} \PY{n}{z}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots} \PY{p}{)} \PY{o}{==}
\PY{n+nb}{float}\PY{p}{(}\PY{n}{task\PYZus{}gas\PYZus{}req}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{[}\PY{n}{task}\PY{p}{]}\PY{p}{)} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{balance\PYZus{}energy3}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The task of the appliance has to use same energy carrier/s untill the
end of the task completion. It means, the task should not change its
energy carrier inbetween the task operation.
\$x\_\{k, u, i, j\}\le x\_\{(k+o\_\{i,j\}), u, i , j\}+1-\delta\_\{k, u,
i, j\} \quad \forall k, u, i, j \$
\(x_{k, u, i, j} \le \delta_{k, u , i, j} +x_{k-1, u, i, j} \quad \forall t, u, i, j\)
If task \(j\) starts at time \(t\) then \(x_{k-1, u, i, j}\) = 0,
\(x_{k, u, i, j}\) = 1 and this imposes \(\delta_{k, u , i, j}\) = 1 in
eq(2).
This way, if electricity starts at time \(t\) \(x_{k, u, i, j}\),
\(\delta_{k, u , i, j}\) = 1 eq(1) imposes
\(x_{(k+o_{i,j}), u, i, j}=1\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}24}]:} \PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}electricity1 = m.addConstrs((x[time\PYZus{}slots[t\PYZus{}index], u, app, task]\PYZlt{}= x[time\PYZus{}slots[t\PYZus{}index + each\PYZus{}task\PYZus{}time], u, app, task]+ 1 \PYZhy{} delta[time\PYZus{}slots[t\PYZus{}index], u , app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] for each\PYZus{}task\PYZus{}time in range(int(task\PYZus{}time[app][task])) if t\PYZus{}index \PYZlt{} (len(time\PYZus{}slots)\PYZhy{} task\PYZus{}time[app][task])),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}electricity1\PYZdq{})}
\PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}electricity2 = m.addConstrs((x[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= delta[time\PYZus{}slots[t\PYZus{}index], u, app, task] + x[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}electricity2\PYZdq{})}
\end{Verbatim}
\$y\_\{k, u, i, j\}\le y\_\{(k+o\_\{i,j\}), u, i , j\}+1-\delta\_\{k, u,
i, j\} \quad \forall k, u, i, j \$
\(y_{k, u, i, j} \le \delta_{k, u , i, j} +y_{k-1, u, i, j} \quad \forall t, u, i, j\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}25}]:} \PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}electricity\PYZus{}hotwater1 = m.addConstrs((y[time\PYZus{}slots[t\PYZus{}index], u, app, task]\PYZlt{}= y[time\PYZus{}slots[t\PYZus{}index + each\PYZus{}task\PYZus{}time], u, app, task]+ 1 \PYZhy{} delta[time\PYZus{}slots[t\PYZus{}index], u , app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] for each\PYZus{}task\PYZus{}time in range(int(task\PYZus{}time[app][task])) if t\PYZus{}index \PYZlt{} (len(time\PYZus{}slots)\PYZhy{} task\PYZus{}time[app][task])),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}electricity\PYZus{}hotwater1\PYZdq{})}
\PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}electricity\PYZus{}hotwater2 = m.addConstrs((y[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= delta[time\PYZus{}slots[t\PYZus{}index], u, app, task] + y[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}electricity\PYZus{}hotwater2\PYZdq{})}
\end{Verbatim}
\$z\_\{k, u, i, j\}\le z\_\{(k+o\_\{i,j\}), u, i , j\}+1-\delta\_\{k, u,
i, j\} \quad \forall k, u, i, j \$
\(z_{k, u, i, j} \le \delta_{k, u , i, j} +z_{k-1, u, i, j} \quad \forall t, u, i, j\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}26}]:} \PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}gas1 = m.addConstrs((z[time\PYZus{}slots[t\PYZus{}index], u, app, task]\PYZlt{}= z[time\PYZus{}slots[t\PYZus{}index + each\PYZus{}task\PYZus{}time], u, app, task]+ 1 \PYZhy{} delta[time\PYZus{}slots[t\PYZus{}index], u , app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] for each\PYZus{}task\PYZus{}time in range(int(task\PYZus{}time[app][task])) if t\PYZus{}index \PYZlt{} (len(time\PYZus{}slots)\PYZhy{} task\PYZus{}time[app][task])),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}gas1\PYZdq{})}
\PY{c+c1}{\PYZsh{} task\PYZus{}end\PYZus{}gas2 = m.addConstrs((z[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= delta[time\PYZus{}slots[t\PYZus{}index], u, app, task] + z[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}task\PYZus{}end\PYZus{}gas2\PYZdq{})}
\end{Verbatim}
The task of the appliances are not interupptible it means it can't be
stop untill it finishes it's task.
\(x_{k, u, i, j} \le 1- \beta_{k, u, i, j}\) \(\forall k, u, i, j\)
\$x\_\{k-1, u, i, j\}- x\_\{k, u, i, j\} \le \beta\_\{k, u, i, j\} \$ \$
\forall u, i, j k= 2, 3 . . .96\$
\(\beta_{k-1, u, i, j} \le \beta_{k, u, i, j}\)
\(\forall u, i, j, k = 2,3,4 . . .96\)
\(x_{k, u, i, j} = x_{k-1, u, i, j-1}\)
\(y_{k, u, i, j} = y_{k-1, u, i, j-1}\)
\(z_{k, u, i, j} = z_{k-1, u, i, j-1}\)
\(\forall u, i, j = 2, 3, ... , k = 2,3,4 . . .96\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}27}]:} \PY{c+c1}{\PYZsh{} electricity\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((x[t, u, app, task] \PYZlt{}= 1\PYZhy{} beta[t, u, app, task] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task in task\PYZus{}appliances[app]), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}task\PYZus{}uniterupptible2 = m.addConstrs((x[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZhy{} x[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task]}
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}task\PYZus{}uniterupptible2\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}task\PYZus{}uniterupptible3 = m.addConstrs((beta[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}task\PYZus{}uniterupptible3 \PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((x[time\PYZus{}slots[t\PYZus{}index], u, app, task\PYZus{}appliances[app][task\PYZus{}index]] == }
\PY{c+c1}{\PYZsh{} x[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app])}
\PY{c+c1}{\PYZsh{} if t\PYZus{}index != 0 and task\PYZus{}index !=0), name = \PYZdq{}electricity\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((y[time\PYZus{}slots[t\PYZus{}index], u, app, task\PYZus{}appliances[app][task\PYZus{}index]] == }
\PY{c+c1}{\PYZsh{} y[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app])}
\PY{c+c1}{\PYZsh{} if t\PYZus{}index != 0 and task\PYZus{}index !=0), name = \PYZdq{}electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\PY{c+c1}{\PYZsh{} gas\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((z[time\PYZus{}slots[t\PYZus{}index], u, app, task\PYZus{}appliances[app][task\PYZus{}index]] == }
\PY{c+c1}{\PYZsh{} z[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app])}
\PY{c+c1}{\PYZsh{} if t\PYZus{}index != 0 and task\PYZus{}index !=0), name = \PYZdq{}gas\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\end{Verbatim}
\(y_{k, u, i, j} \le 1- \beta_{k, u, i, j}\) \(\forall k, u, i, j\)
\$y\_\{k-1, u, i, j\}- y\_\{k, u, i, j\} \le \beta\_\{k, u, i, j\} \$ \$
\forall u, i, j k= 2, 3 . . .96\$
\(\beta_{k-1, u, i, j} \le \beta_{k, u, i, j}\)
\(\forall u, i, j, k = 2,3,4 . . .96\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}28}]:} \PY{c+c1}{\PYZsh{} electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((y[t, u, app, task] \PYZlt{}= 1\PYZhy{} beta[t, u, app, task] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task in task\PYZus{}appliances[app]), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible2 = m.addConstrs((y[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZhy{} y[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task]}
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible2\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible3 = m.addConstrs((beta[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}hotwater\PYZus{}task\PYZus{}uniterupptible3\PYZdq{})}
\end{Verbatim}
\(z_{k, u, i, j} \le 1- \beta_{k, u, i, j}\) \(\forall k, u, i, j\)
\$z\_\{k-1, u, i, j\}- z\_\{k, u, i, j\} \le \beta\_\{k, u, i, j\} \$ \$
\forall u, i, j k= 2, 3 . . .96\$
\(\beta_{k-1, u, i, j} \le \beta_{k, u, i, j}\)
\(\forall u, i, j, k = 2,3,4 . . .96\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}29}]:} \PY{c+c1}{\PYZsh{} gas\PYZus{}task\PYZus{}uniterupptible1 = m.addConstrs((z[t, u, app, task] \PYZlt{}= 1\PYZhy{} beta[t, u, app, task] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task in task\PYZus{}appliances[app]), }
\PY{c+c1}{\PYZsh{} name = \PYZdq{}gas\PYZus{}task\PYZus{}uniterupptible1\PYZdq{})}
\PY{c+c1}{\PYZsh{} gas\PYZus{}task\PYZus{}uniterupptible2 = m.addConstrs((z[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZhy{} z[time\PYZus{}slots[t\PYZus{}index], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task]}
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}gas\PYZus{}task\PYZus{}uniterupptible2\PYZdq{})}
\PY{c+c1}{\PYZsh{} gas\PYZus{}task\PYZus{}uniterupptible3 = m.addConstrs((beta[time\PYZus{}slots[t\PYZus{}index\PYZhy{}1], u, app, task] \PYZlt{}= beta[time\PYZus{}slots[t\PYZus{}index], u, app, task] }
\PY{c+c1}{\PYZsh{} for t\PYZus{}index, t in enumerate(time\PYZus{}slots) for u in users for app in appliances for task in task\PYZus{}appliances[app] if t\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}gas\PYZus{}task\PYZus{}uniterupptible3\PYZdq{})}
\end{Verbatim}
The task of the appliances has to be sequential. It means task can't
start unless it's previous task finishes it's operation.
\(x_{k, u, i, j} \le \beta_{k, u, i, (j-1)}\)
\(y_{k, u, i, j} \le \beta_{k, u, i, (j-1)}\)
\(z_{k, u, i, j} \le \beta_{k, u, i, (j-1)}\)
\$\forall {i, j = 2, 3 . .}, k, u \$
\(x_{k, u, i, j} \le x_{k, u, i, (j-1)}\)
\(y_{k, u, i, j} \le y_{k, u, i, (j-1)}\)
\(z_{k, u, i, j} \le z_{k, u, i, (j-1)}\) \$\forall {i, j = 2, 3 . .},
k, u \$
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}30}]:} \PY{c+c1}{\PYZsh{} electricity\PYZus{}task\PYZus{}sequential = m.addConstrs((x[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index]] \PYZlt{}= x[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app]) if task\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}task\PYZus{}sequential\PYZdq{})}
\PY{c+c1}{\PYZsh{} electricity\PYZus{}hotwater\PYZus{}task\PYZus{}sequential = m.addConstrs((y[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index]] \PYZlt{}= y[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app]) if task\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}electricity\PYZus{}hotwater\PYZus{}task\PYZus{}sequential\PYZdq{})}
\PY{c+c1}{\PYZsh{} gas\PYZus{}task\PYZus{}sequential = m.addConstrs((z[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index]] \PYZlt{}= z[t, u, app, task\PYZus{}appliances[app][task\PYZus{}index\PYZhy{}1]] }
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for u in users for app in appliances for task\PYZus{}index, task in enumerate(task\PYZus{}appliances[app]) if task\PYZus{}index != 0),}
\PY{c+c1}{\PYZsh{} name = \PYZdq{}gas\PYZus{}task\PYZus{}sequential\PYZdq{})}
\end{Verbatim}
The amount of electricity demand at any time slot should not exceed the
\(PEAK\) electricity threshold of the distribution grid.
\begin{multline} \label{eq5}
\sum_{u=1}^{50}\sum_{i=1}^{N}\sum_{j=1}^{n_i} E_{k,u,i,j}^{high} * x_{k,u,i,j} +E_{k, u, i, j}^{low} * y_{k, u, i, j} \leq PEAK \qquad \forall k , x_{k,u,i,j}, y_{k, u, i, j} \in \{0,1\}
\end{multline}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}31}]:} \PY{n}{peak\PYZus{}constraint} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{n}{electricity\PYZus{}high\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{*} \PY{n}{x}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{n}{electricity\PYZus{}low\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}
\PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{PEAK} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{peak\PYZus{}constraint}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The amount of hot water demand by all tasks of the appliances at any
time slot should not exceed the capacity of the hot water storage tank.
\begin{multline} \label{eq4}
\sum_{i=1}^N \sum_{j=1}^{n_i} H_{k,u,i,j} * y_{k,u,i,j} \leq C_{ST} \qquad \forall k , u , y_{k,u,i,j} \in \{0,1\}
\end{multline}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}32}]:} \PY{n}{hotwater\PYZus{}demand\PYZus{}constarint} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{n}{hotwater\PYZus{}demand}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{t}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{tank\PYZus{}capacity}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users}\PY{p}{)}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{hotwater\PYZus{}demand\PYZus{}constarint}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
All the appliances have to be scheduled within a user-specified time
slots.
\(t_{st, i} \leq t_i + r_i \leq t_{end, i}\) \(\forall i\)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}33}]:} \PY{c+c1}{\PYZsh{} appliance\PYZus{}schedule = m.addConstrs((starting\PYZus{}time\PYZus{}slot[app] \PYZlt{}= timeslot\PYZus{}appliance\PYZus{}start[app] + run\PYZus{}time[app] \PYZlt{}= endind\PYZus{}time\PYZus{}slot[app]}
\PY{c+c1}{\PYZsh{} for t in time\PYZus{}slots for app in appliances), name = \PYZdq{}appliance\PYZus{}schedule\PYZdq{})}
\end{Verbatim}
The amount of gas required by Boiler to produce thermal power measured
in Wh.
\begin{equation} \label{eq8}
G_{k}^{Boiler} = \frac {T_{k}^{Boiler}}{\eta_{th}}
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}34}]:} \PY{n}{boiler\PYZus{}gas} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{boiler\PYZus{}required\PYZus{}gas}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{==} \PY{p}{(}\PY{n}{boiler\PYZus{}produced\PYZus{}thermal}\PY{p}{[}\PY{n}{t}\PY{p}{]}\PY{o}{/}\PY{n}{boiler\PYZus{}efficiecny}\PY{p}{)} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{boiler\PYZus{}gas}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
Convert the thermal power produced by the boiler into the hotwater. For
instance, the water temperature rise from 0 degree to 65 degree. Hence
the \(\textit{Temp}\) is 65 degree. Where 4 being a 1/4th of hour and
3412 being a given constant. This formula tells the amount of hot water
produced by thermal energy of the boiler in 15 minute.
\begin{equation} \label{eq8a}
H_{k}^{Boiler} = \frac {T_{k}^{Boiler} * 3412 } {2.22 * 65 * 4}
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}35}]:} \PY{n}{boiler\PYZus{}hotwater} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{boiler\PYZus{}produced\PYZus{}hotwater}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{==} \PY{p}{(}\PY{n}{boiler\PYZus{}produced\PYZus{}thermal}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{*} \PY{l+m+mi}{3412}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{l+m+mf}{2.22} \PY{o}{*} \PY{l+m+mi}{65} \PY{o}{*} \PY{l+m+mi}{4}\PY{p}{)}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{boiler\PYZus{}hotwater}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The amount of thermal energy produced by boiler should not exceeds its
maximum thermal output at time slot t.
\$ 0\textless{}=T\_\{k, u\}\^{}\{Boiler\} \textless{}=
s\_\{k\}\^{}\{Boiler\}. T\_\{max\}\^{}\{Boiler\}\$
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}36}]:} \PY{n}{Boiler\PYZus{}capacity} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{0} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{boiler\PYZus{}produced\PYZus{}thermal}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{s}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{*} \PY{l+m+mi}{21250} \PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{Boiler\PYZus{}capacity}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The amount of hot water available in the storage tank at time slot k is
equal to the amount stored at k-1 plus the hot water produced by the
boiler minus hot water consumed by the appliances.
\begin{equation} \label{10a}
H_{k}^{a} = H_{k-1}^{a} + H_{k}^{Boiler} - \sum_{i=1}^{N} \sum_{j=1}^{n_i} H_{k,u,i,j} * y_{k,u,i,j} \\ \forall u,i,j, k= {2, 3, .. }
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}37}]:} \PY{n}{available\PYZus{}hotwater} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{available\PYZus{}hotwater\PYZus{}storagetank}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{]} \PY{o}{==}
\PY{n}{available\PYZus{}hotwater\PYZus{}storagetank}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{o}{\PYZhy{}}\PY{l+m+mi}{1}\PY{p}{]}\PY{p}{]} \PY{o}{+} \PY{n}{boiler\PYZus{}produced\PYZus{}hotwater}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{]} \PY{o}{\PYZhy{}}
\PY{n}{quicksum}\PY{p}{(}\PY{n}{hotwater\PYZus{}demand}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{*} \PY{n}{y}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}
\PY{k}{for} \PY{n}{t\PYZus{}index}\PY{p}{,} \PY{n}{t} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{)} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{if} \PY{n}{t\PYZus{}index} \PY{o}{!=} \PY{l+m+mi}{0}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
Hot water storage tank capacity has to be maintained at any time slot.
\begin{equation} \label{eq10b}
0 \leq H_{k}^a \leq C_{ST} \qquad \forall k = \{1,2,. . .96\}
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}38}]:} \PY{n}{available\PYZus{}hotwater\PYZus{}capacity} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{l+m+mi}{0} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{available\PYZus{}hotwater\PYZus{}storagetank}\PY{p}{[}\PY{n}{t}\PY{p}{]} \PY{o}{\PYZlt{}}\PY{o}{=} \PY{n}{tank\PYZus{}capacity}
\PY{k}{for} \PY{n}{t} \PY{o+ow}{in} \PY{n}{time\PYZus{}slots}\PY{p}{)}\PY{p}{,} \PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{available\PYZus{}hotwater\PYZus{}capacity}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
The task of the appliances should not be performed outside the
user-specified time window.
\begin{equation} \label{eq12}
\sum_{k\in m-[t_{st,i}, t_{end,i}]} X_{k,u,i,j} + Y_{k,u,i,j} + Z_{k,u,i,j} = 0
\end{equation}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}39}]:} \PY{n}{not\PYZus{}perform\PYZus{}task} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{addConstrs}\PY{p}{(}\PY{p}{(}\PY{n}{quicksum}\PY{p}{(}\PY{n}{x}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]} \PY{o}{+} \PY{n}{y}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}\PY{o}{+} \PY{n}{z}\PY{p}{[}\PY{n}{time\PYZus{}slots}\PY{p}{[}\PY{n}{t\PYZus{}index}\PY{p}{]}\PY{p}{,} \PY{n}{u}\PY{p}{,} \PY{n}{app}\PY{p}{,} \PY{n}{task}\PY{p}{]}
\PY{k}{for} \PY{n}{t\PYZus{}index}\PY{p}{,} \PY{n}{t} \PY{o+ow}{in} \PY{n+nb}{enumerate}\PY{p}{(}\PY{n}{time\PYZus{}slots}\PY{p}{)} \PY{k}{if} \PY{n}{t\PYZus{}index} \PY{o+ow}{not} \PY{o+ow}{in} \PY{n+nb}{range}\PY{p}{(}\PY{n}{starting\PYZus{}time\PYZus{}slot}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{,} \PY{n}{endind\PYZus{}time\PYZus{}slot}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{)}
\PY{o}{==} \PY{l+m+mi}{0} \PY{k}{for} \PY{n}{u} \PY{o+ow}{in} \PY{n}{users} \PY{k}{for} \PY{n}{app} \PY{o+ow}{in} \PY{n}{appliances} \PY{k}{for} \PY{n}{task} \PY{o+ow}{in} \PY{n}{task\PYZus{}appliances}\PY{p}{[}\PY{n}{app}\PY{p}{]}\PY{p}{)}\PY{p}{,}
\PY{n}{name} \PY{o}{=} \PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{not\PYZus{}perform\PYZus{}task}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
\section{Update the Model}\label{update-the-model}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}40}]:} \PY{n}{m}\PY{o}{.}\PY{n}{update}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\section{Call the Optimize}\label{call-the-optimize}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}41}]:} \PY{n}{m}\PY{o}{.}\PY{n}{optimize}\PY{p}{(}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Optimize a model with 66511 rows, 186246 columns and 470783 nonzeros
Variable types: 384 continuous, 185862 integer (185856 binary)
Coefficient statistics:
Matrix range [3e-01, 2e+04]
Objective range [1e-01, 9e+02]
Bounds range [1e+00, 3e+04]
RHS range [3e-01, 3e+04]
Presolve removed 17032 rows and 89808 columns
Presolve time: 0.89s
Presolved: 49479 rows, 96438 columns, 226032 nonzeros
Variable types: 118 continuous, 96320 integer (96320 binary)
Found heuristic solution: objective 101775.35000
Root relaxation: objective 1.016900e+05, 1762 iterations, 0.05 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
* 0 0 0 101690.01250 101690.012 0.00\% - 1s
Explored 0 nodes (1762 simplex iterations) in 1.52 seconds
Thread count was 8 (of 8 available processors)
Solution count 2: 101690 101775
Optimal solution found (tolerance 1.00e-04)
Best objective 1.016900125000e+05, best bound 1.016900125000e+05, gap 0.0000\%
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}42}]:} \PY{n}{status} \PY{o}{=} \PY{n}{m}\PY{o}{.}\PY{n}{status}
\PY{k}{if} \PY{n}{status} \PY{o}{==} \PY{n}{GRB}\PY{o}{.}\PY{n}{Status}\PY{o}{.}\PY{n}{UNBOUNDED}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{The model cannot be solved because it is unbounded}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{exit}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)}
\PY{k}{if} \PY{n}{status} \PY{o}{==} \PY{n}{GRB}\PY{o}{.}\PY{n}{Status}\PY{o}{.}\PY{n}{OPTIMAL}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{The optimal objective is }\PY{l+s+si}{\PYZpc{}g}\PY{l+s+s1}{\PYZsq{}} \PY{o}{\PYZpc{}} \PY{n}{m}\PY{o}{.}\PY{n}{objVal}\PY{p}{)}
\PY{n}{exit}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)}
\PY{k}{if} \PY{n}{status} \PY{o}{!=} \PY{n}{GRB}\PY{o}{.}\PY{n}{Status}\PY{o}{.}\PY{n}{INF\PYZus{}OR\PYZus{}UNBD} \PY{o+ow}{and} \PY{n}{status} \PY{o}{!=} \PY{n}{GRB}\PY{o}{.}\PY{n}{Status}\PY{o}{.}\PY{n}{INFEASIBLE}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Optimization was stopped with status }\PY{l+s+si}{\PYZpc{}d}\PY{l+s+s1}{\PYZsq{}} \PY{o}{\PYZpc{}} \PY{n}{status}\PY{p}{)}
\PY{n}{exit}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
The optimal objective is 101690
Optimization was stopped with status 2
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}43}]:} \PY{c+c1}{\PYZsh{} copy1 = m.copy()}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}44}]:} \PY{c+c1}{\PYZsh{} if m.status == GRB.INFEASIBLE:}
\PY{c+c1}{\PYZsh{} copy1.feasRelaxS(1, True, False, True)}
\PY{c+c1}{\PYZsh{} copy1.optimize()}
\end{Verbatim}
\section{DO IIS}\label{do-iis}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}45}]:} \PY{n+nb}{print}\PY{p}{(}\PY{n}{m}\PY{o}{.}\PY{n}{status}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{The model is infeasible; computing IIS}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n}{m}\PY{o}{.}\PY{n}{computeIIS}\PY{p}{(}\PY{p}{)}
\PY{k}{if} \PY{n}{m}\PY{o}{.}\PY{n}{IISMinimal}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{IIS is minimal}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{k}{else}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{IIS is not minimal}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+se}{\PYZbs{}n}\PY{l+s+s1}{The following constraint(s) cannot be satisfied:}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{k}{for} \PY{n}{c} \PY{o+ow}{in} \PY{n}{m}\PY{o}{.}\PY{n}{getConstrs}\PY{p}{(}\PY{p}{)}\PY{p}{:}
\PY{k}{if} \PY{n}{c}\PY{o}{.}\PY{n}{IISConstr}\PY{p}{:}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+si}{\PYZpc{}s}\PY{l+s+s1}{\PYZsq{}} \PY{o}{\PYZpc{}} \PY{n}{c}\PY{o}{.}\PY{n}{constrName}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
2
The model is infeasible; computing IIS
IIS runtime: 1.09 seconds
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
---------------------------------------------------------------------------
GurobiError Traceback (most recent call last)
<ipython-input-45-67a93a689b17> in <module>()
1 print(m.status)
2 print('The model is infeasible; computing IIS')
----> 3 m.computeIIS()
4 if m.IISMinimal:
5 print('IIS is minimal\textbackslash{}n')
model.pxi in gurobipy.Model.computeIIS (../../src/python/gurobipy.c:58013)()
GurobiError: Cannot compute IIS on a feasible model
\end{Verbatim}
\section{Save the Model}\label{save-the-model}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor} }]:} \PY{n}{m}\PY{o}{.}\PY{n}{write}\PY{p}{(}\PY{l+s+s2}{\PYZdq{}}\PY{l+s+s2}{model.ilp}\PY{l+s+s2}{\PYZdq{}}\PY{p}{)}
\end{Verbatim}
% Add a bibliography block to the postdoc
\end{document}