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feat: work in progress mom
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NotProgramming/MOM/.report_one.tex.swp
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NotProgramming/MOM/.report_one.tex.swp
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\documentclass[12pt]{article}
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\usepackage[polish]{babel}
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\usepackage{float}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath}
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\usepackage{pdfpages}
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\usepackage[T1]{fontenc} % Add this line
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\title{Sprawozdanie z projektu MOM}
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\author{Krzysztof Rudnicki, 307585}
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\date{\today}
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\begin{document}
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\maketitle
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\section{Zadanie 1. Sieć przepływowa}
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\subsection{Model sieciowy}
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\paragraph{Problem do rozwiązania}
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Należy rozwiązać problem najtańszego przepływu \\
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\begin{figure}[htb]
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\caption{Koszty transportowe i przepustowości na poszczególnych odcinkach}
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\begin{center}
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\begin{tabular}{ | c | c | c | c | c | c | }
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\hline
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& D & E & F & G & H \\
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\hline
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A & 4, 15 & 2, 10 & - & - & -\\
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\hline
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B & 4, 4 & 3, 9 & - & 8, 9 & - \\
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\hline
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C & 2, 20 & 6, 10 & - & - & - \\
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\hline
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D & - & - & 3, 10 & 7, 3 & 2, 2 \\
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\hline
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E & 5, 20 & - & 7, 5 & 6, 5 & 3, 5 \\
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\hline
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\end{tabular}
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\end{center}
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\end{figure}
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\begin{figure}[htb]
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\caption{Zdolności wydobywcze kopalń (w tys. ton)}
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\begin{center}
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\begin{tabular}{ | c | c |}
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\hline
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$W_A$ & 10 \\
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\hline
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$W_B$ & 13 \\
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\hline
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$W_C$ & 17 \\
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\hline
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\end{tabular}
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\end{center}
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\end{figure}
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\begin{figure}[htb]
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\caption{Średnie zużycie dobowe węgla przez elektronie (w tys. ton)}
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\begin{center}
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\begin{tabular}{ | c | c |}
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\hline
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$Z_F$ & 15 \\
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\hline
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$Z_G$ & 13 \\
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\hline
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$Z_H$ & 7 \\
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\hline
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\end{tabular}
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\end{center}
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\end{figure}
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\paragraph{Sformułowanie}
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Matematyczne sformułowanie zadania:
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\begin{enumerate}
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\item Parametry \\
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s - źródło \\
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B - Budynki (kopalnie, stacje, elektrownie) \\
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K - kopalnie \\
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$c_{ij}$ - koszt transportu z budynku i do budynku j ($c_{sk}$ = 0) \\
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$W_k$ - zdolność wydobywcza kopalni k [w tonach] \\
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$p_{ij}$ - przepustowość transportu z budynku i do budynku j [w tonach] ($u_{sk}$ = $W_k$) \\
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E - elektrownie \\
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$Z_e$ - średnie zużycie dobowe przez elektrownię e [w tonach] \\
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\item Zmienne decyzyjne
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$f_{ij}$ - przepływ transportu z budynku i do obiektu j \\
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\item Funkcja celu
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\begin{align*}
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Q &= \min\left(\sum_{(i, j) \in B \backslash \{s\}} c_{ij} f_{ij}\right) \\
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&= \min(4f_{AD} + 2f_{AE} + 4f_{BD} + 3f_{BE} + 8f_{BG} + 2f_{CD} \\
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&\quad + 6f_{CE} + 3f_{DF} + 7f_{DG} + 2f_{DH} + 5f_{ED} + 7f_{EF} \\
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&\quad + 6f_{EG} + 3f_{EH})
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\end{align*}
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\item Ograniczenia
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\begin{equation}
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0 \leq f_{sk} \leq W_k, \; k \in K = \{A, B, C\}
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\end{equation}
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\begin{equation}
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f_{si} = 0, \; i \in B \backslash K
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\end{equation}
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\begin{equation}
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f_{is} = 0, \; i \in B
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\end{equation}
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\begin{equation}
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0 \leq f_{ij} \leq p_{uj}, \; (i, j) \in B \backslash \{s\}
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\end{equation}
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\begin{equation}
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f_{is} = 0, \; i \in B
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\end{equation}
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\begin{equation}
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\sum_{b \in B} f_{be} \ge Z_e, \; e \in E = \{F, G, H\}
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\end{equation}
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\begin{equation}
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\sum_{i \in B \backslash \{ s \} } f_{bi} \leq \sum_{j \in B} f_{bn}, \; b \in B \backslash \{s\}
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\end{equation}
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\end{enumerate}
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\paragraph{Narysowanie modelu}
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\includepdf[pages=-]{1flow.pdf}
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\subsection{Rozwiązanie}Z
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\paragraph{Metoda }
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\subsection{Zadanie programowania liniowego}
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\section{Zadanie 2. Zadanie przydziału}
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\subsection{Zadanie 2.1 Planowanie realizacji portfela przy ograniczonych kompetencjach}
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\paragraph{Model sieciowy rysunek}
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\subsubsection{Problem do rozwiązania}
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\paragraph{Rozwiazanie}
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\paragraph{Przydział zespołów do projektów}
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\subsection{Zadanie 2.2 Minimalizacja kosztów realizacji projektów}
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\paragraph{Model sieciowy rysunek}
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\paragraph{Problem do rozwiązania}
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\paragraph{Rozwiazanie}
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\subsection{Zadanie 2.3 Minimalizacja terminu realizacji puli projektów}
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\paragraph{Model programowania liniowego}
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\section{Zadanie 3}
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\paragraph{Model programowania liniowego}
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\end{document}
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BIN
NotProgramming/MOM/1flow.pdf
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BIN
NotProgramming/MOM/1flow.pdf
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Binary file not shown.
49
NotProgramming/MOM/1glpk
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49
NotProgramming/MOM/1glpk
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set StartObiekty;
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set Obiekty;
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set Elektrownie;
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param c{i in StartObiekty, j in Obiekty};
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param u{i in StartObiekty, j in Obiekty};
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param Z{p in Elektrownie};
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var f{i in StartObiekty, j in Obiekty}, >= 0;
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minimize Q: sum {i in Obiekty, j in Obiekty} c[i,j] * f[i,j];
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subject to
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Ogr_1{i in StartObiekty, j in Obiekty}:
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f[i,j] >= 0;
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Ogr_2{i in StartObiekty, j in Obiekty}:
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f[i,j] <= u[i,j];
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Ogr_3{p in Elektrownie}:
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sum {n in StartObiekty} f[n,p] >= Z[p];
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Ogr_4{n in Obiekty}:
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sum {i in Obiekty} f[n,i] <= sum {j in StartObiekty} f[j,n];
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solve;
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display {i in Obiekty, j in Obiekty: f[i,j] > 0}: f[i,j];
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data;
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set StartObiekty := s, A, B, C, D, E, F, G, H;
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set Obiekty := A, B, C, D, E, F, G, H;
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set Elektrownie := F, G, H;
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param c :=
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s A 0 s B 0 s C 0 A D 3 B D 6 B E 2 C D 4 C H 5 D E 3 D F 5 D G 7 D H 3
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E D 3 E F 2 E G 4 s D 0 s E 0 s F 0 s G 0 s H 0 A A 0 A B 0 A C 0 A E 0
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A F 0 A G 0 A H 0 B A 0 B B 0 B C 0 B F 0 B G 0 B H 0 C A 0 C B 0 C C 0
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C E 0 C F 0 C G 0 D A 0 D B 0 D C 0 D D 0 E A 0 E B 0 E C 0 E E 0 E H 0
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0 G A 0 G B 0 G C 0 G D 0
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G E 0 G F 0 G G 0 G H 0 H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param u :=
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s A 10 s B 13 s C 17 A D 9 B D 5 B E 13 C D 6 C H 7 D E 15 D F 11 D G 7 D H 4
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E D 15 E F 10 E G 14 s D 0 s E 0 s F 0 s G 0 s H 0 A A 0 A B 0 A C 0 A E 0
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A F 0 A G 0 A H 0 B A 0 B B 0 B C 0 B F 0 B G 0 B H 0 C A 0 C B 0 C C 0
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C E 0 C F 0 C G 0 D A 0 D B 0 D C 0 D D 0 E A 0 E B 0 E C 0 E E 0 E H 0
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0 G A 0 G B 0 G C 0 G D 0
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G E 0 G F 0 G G 0 G H 0 H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param Z := F 15 G 12 H 8;
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end;
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31
NotProgramming/MOM/1glpk.dat
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NotProgramming/MOM/1glpk.dat
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data;
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set BudynkiNaStart := s, A, B, C, D, E, F, G, H;
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set Budynki := A, B, C, D, E, F, G, H;
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set Elektrownie := F, G, H;
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param c :=
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s A 0 s B 0 s C 0 s D 0 s E 0 s F 0 s G 0 s H 0
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A A 0 A B 0 A C 0 A D 4 A E 2 A F 0 A G 0 A H 0
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B A 0 B B 0 B C 0 B D 4 B E 3 B F 0 B G 8 B H 0
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C A 0 C B 0 C C 0 C D 2 C E 6 C F 0 C G 0 C H 0
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D A 0 D B 0 D C 0 D D 0 D E 0 D F 3 D G 7 D H 2
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E A 0 E B 0 E C 0 E D 5 E E 0 E F 7 E G 6 E H 3
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0
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G A 0 G B 0 G C 0 G D 0 G E 0 G F 0 G G 0 G H 0
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H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param p :=
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s A 10 s B 13 s C 17 s D 0 s E 0 s F 0 s G 0 s H 0
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A A 0 A B 0 A C 0 A D 15 A E 10 A F 0 A G 0 A H 0
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B A 0 B B 0 B C 0 B D 4 B E 9 B F 0 B G 9 B H 0
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C A 0 C B 0 C C 0 C D 20 C E 10 C F 0 C G 0 C H 0
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D A 0 D B 0 D C 0 D D 0 D E 0 D F 10 D G 3 D H 2
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E A 0 E B 0 E C 0 E D 20 E E 0 E F 5 E G 5 E H 5
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0
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G A 0 G B 0 G C 0 G D 0 G E 0 G F 0 G G 0 G H 0
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H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param Z := F 15 G 13 H 7;
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end;
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24
NotProgramming/MOM/1glpk.glp
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24
NotProgramming/MOM/1glpk.glp
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set BudynkiNaStart;
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set Budynki;
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set Elektrownie;
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param c{i in BudynkiNaStart, j in Budynki};
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param u{i in BudynkiNaStart, j in Budynki};
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param Z{e in Elektrownie};
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var f{i in BudynkiNaStart, j in Budynki}, >= 0;
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minimize Q: sum {i in Budynki, j in Budynki} c[i,j] * f[i,j];
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subject to
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Ogr_1{i in BudynkiNaStart, j in Budynki}:
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f[i,j] >= 0;
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Ogr_2{i in BudynkiNaStart, j in Budynki}:
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f[i,j] <= u[i,j];
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Ogr_3{e in Elektrownie}:
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sum {n in BudynkiNaStart} f[n,e] >= Z[e];
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Ogr_4{n in Budynki}:
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sum {i in Budynki} f[n,i] <= sum {j in BudynkiNaStart} f[j,n];
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solve;
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display {i in Budynki, j in Budynki: f[i,j] > 0}: f[i,j];
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49
NotProgramming/MOM/1glpk.glpk
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49
NotProgramming/MOM/1glpk.glpk
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set StartObiekty;
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set Obiekty;
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set Elektrownie;
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param c{i in StartObiekty, j in Obiekty};
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param u{i in StartObiekty, j in Obiekty};
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param Z{p in Elektrownie};
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var f{i in StartObiekty, j in Obiekty}, >= 0;
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minimize Q: sum {i in Obiekty, j in Obiekty} c[i,j] * f[i,j];
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subject to
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Ogr_1{i in StartObiekty, j in Obiekty}:
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f[i,j] >= 0;
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Ogr_2{i in StartObiekty, j in Obiekty}:
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f[i,j] <= u[i,j];
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Ogr_3{p in Elektrownie}:
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sum {n in StartObiekty} f[n,p] >= Z[p];
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Ogr_4{n in Obiekty}:
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sum {i in Obiekty} f[n,i] <= sum {j in StartObiekty} f[j,n];
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solve;
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display {i in Obiekty, j in Obiekty: f[i,j] > 0}: f[i,j];
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data;
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set StartObiekty := s, A, B, C, D, E, F, G, H;
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set Obiekty := A, B, C, D, E, F, G, H;
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set Elektrownie := F, G, H;
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param c :=
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s A 0 s B 0 s C 0 A D 3 B D 6 B E 2 C D 4 C H 5 D E 3 D F 5 D G 7 D H 3
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E D 3 E F 2 E G 4 s D 0 s E 0 s F 0 s G 0 s H 0 A A 0 A B 0 A C 0 A E 0
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A F 0 A G 0 A H 0 B A 0 B B 0 B C 0 B F 0 B G 0 B H 0 C A 0 C B 0 C C 0
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C E 0 C F 0 C G 0 D A 0 D B 0 D C 0 D D 0 E A 0 E B 0 E C 0 E E 0 E H 0
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0 G A 0 G B 0 G C 0 G D 0
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G E 0 G F 0 G G 0 G H 0 H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param u :=
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s A 10 s B 13 s C 17 A D 9 B D 5 B E 13 C D 6 C H 7 D E 15 D F 11 D G 7 D H 4
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E D 15 E F 10 E G 14 s D 0 s E 0 s F 0 s G 0 s H 0 A A 0 A B 0 A C 0 A E 0
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A F 0 A G 0 A H 0 B A 0 B B 0 B C 0 B F 0 B G 0 B H 0 C A 0 C B 0 C C 0
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C E 0 C F 0 C G 0 D A 0 D B 0 D C 0 D D 0 E A 0 E B 0 E C 0 E E 0 E H 0
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F A 0 F B 0 F C 0 F D 0 F E 0 F F 0 F G 0 F H 0 G A 0 G B 0 G C 0 G D 0
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G E 0 G F 0 G G 0 G H 0 H A 0 H B 0 H C 0 H D 0 H E 0 H F 0 H G 0 H H 0;
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param Z := F 15 G 12 H 8;
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end;
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24
NotProgramming/MOM/1glpk.mod
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24
NotProgramming/MOM/1glpk.mod
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set BudynkiNaStart;
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set Budynki;
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set Elektrownie;
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param c{i in BudynkiNaStart, j in Budynki};
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||||||
|
param p{i in BudynkiNaStart, j in Budynki};
|
||||||
|
param Z{e in Elektrownie};
|
||||||
|
|
||||||
|
var f{i in BudynkiNaStart, j in Budynki}, >= 0;
|
||||||
|
|
||||||
|
minimize Q: sum {i in Budynki, j in Budynki} c[i,j] * f[i,j];
|
||||||
|
|
||||||
|
subject to
|
||||||
|
Ograniczenie_1{i in BudynkiNaStart, j in Budynki}:
|
||||||
|
f[i,j] >= 0;
|
||||||
|
Ograniczenie_2{i in BudynkiNaStart, j in Budynki}:
|
||||||
|
f[i,j] <= p[i,j];
|
||||||
|
Ograniczenie_3{e in Elektrownie}:
|
||||||
|
sum {n in BudynkiNaStart} f[n,e] >= Z[e];
|
||||||
|
Ograniczenie_4{n in Budynki}:
|
||||||
|
sum {i in Budynki} f[n,i] <= sum {j in BudynkiNaStart} f[j,n];
|
||||||
|
|
||||||
|
solve;
|
||||||
|
display {i in Budynki, j in Budynki: f[i,j] > 0}: f[i,j];
|
||||||
BIN
NotProgramming/MOM/MOM_proj_1.3.pdf
Normal file
BIN
NotProgramming/MOM/MOM_proj_1.3.pdf
Normal file
Binary file not shown.
243
NotProgramming/MOM/graphs
Normal file
243
NotProgramming/MOM/graphs
Normal file
@ -0,0 +1,243 @@
|
|||||||
|
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|
||||||
|
<diagram name="Page-1" id="8QQrMdNaT32kPHTfEJmi">
|
||||||
|
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|
||||||
|
<root>
|
||||||
|
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|
||||||
|
<mxCell id="1" parent="0" />
|
||||||
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||||||
|
<mxGeometry relative="1" as="geometry">
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||||||
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<Array as="points">
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||||||
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||||||
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</Array>
|
||||||
|
</mxGeometry>
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||||||
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</mxCell>
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||||||
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||||||
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<mxGeometry x="-0.0298" y="1" relative="1" as="geometry">
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||||||
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||||||
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</mxGeometry>
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||||||
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</mxCell>
|
||||||
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-47" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-3" target="ZybQ-fv8Gocl7lNzSQPM-11">
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||||||
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<mxGeometry relative="1" as="geometry" />
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||||||
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</mxCell>
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||||||
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-70" value="3, 9" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-47">
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||||||
|
<mxGeometry x="-0.5404" y="3" relative="1" as="geometry">
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||||||
|
<mxPoint as="offset" />
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||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-48" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-3" target="ZybQ-fv8Gocl7lNzSQPM-5">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
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||||||
|
<mxPoint x="190" y="540" />
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||||||
|
<mxPoint x="600" y="540" />
|
||||||
|
<mxPoint x="600" y="390" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
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||||||
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-71" value="8, 9" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-48">
|
||||||
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<mxGeometry x="-0.4174" y="-2" relative="1" as="geometry">
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||||||
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||||||
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</mxGeometry>
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||||||
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</mxCell>
|
||||||
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-3" value="B" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#f8cecc;strokeColor=#b85450;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="150" y="350" width="80" height="80" as="geometry" />
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||||||
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</mxCell>
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||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-4" value="H" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#fff2cc;strokeColor=#d6b656;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="620" y="550" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-5" value="G" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#fff2cc;strokeColor=#d6b656;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="620" y="350" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-6" value="F" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#fff2cc;strokeColor=#d6b656;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="620" y="140" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-56" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0;entryY=0.5;entryDx=0;entryDy=0;fillColor=#dae8fc;strokeColor=#6c8ebf;" edge="1" parent="1" target="ZybQ-fv8Gocl7lNzSQPM-6">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<mxPoint x="465" y="296" as="sourcePoint" />
|
||||||
|
<mxPoint x="620" y="166" as="targetPoint" />
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="543" y="296" />
|
||||||
|
<mxPoint x="543" y="180" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-74" value="3, 10" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-56">
|
||||||
|
<mxGeometry x="-0.8376" y="-1" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-57" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0.5;entryY=0;entryDx=0;entryDy=0;fillColor=#dae8fc;strokeColor=#6c8ebf;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-7" target="ZybQ-fv8Gocl7lNzSQPM-5">
|
||||||
|
<mxGeometry relative="1" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-75" value="7, 3" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-57">
|
||||||
|
<mxGeometry x="-0.7191" y="-3" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-58" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=1;entryY=0.5;entryDx=0;entryDy=0;fillColor=#dae8fc;strokeColor=#6c8ebf;jumpStyle=arc;jumpSize=12;" edge="1" parent="1" target="ZybQ-fv8Gocl7lNzSQPM-4">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<mxPoint x="465" y="320" as="sourcePoint" />
|
||||||
|
<mxPoint x="700" y="600" as="targetPoint" />
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="780" y="320" />
|
||||||
|
<mxPoint x="780" y="590" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-76" value="2, 2" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-58">
|
||||||
|
<mxGeometry x="-0.1368" y="-2" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-7" value="D" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#dae8fc;strokeColor=#6c8ebf;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="385" y="270" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-43" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-8" target="ZybQ-fv8Gocl7lNzSQPM-7">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="190" y="130" />
|
||||||
|
<mxPoint x="425" y="130" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-67" value="4, 15" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-43">
|
||||||
|
<mxGeometry x="0.0805" y="-4" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-45" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;jumpStyle=arc;jumpSize=12;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-8" target="ZybQ-fv8Gocl7lNzSQPM-11">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="350" y="199" />
|
||||||
|
<mxPoint x="350" y="410" />
|
||||||
|
<mxPoint x="425" y="410" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-68" value="2, 10" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-45">
|
||||||
|
<mxGeometry x="-0.5088" y="-3" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-8" value="A" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#f8cecc;strokeColor=#b85450;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="150" y="140" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-41" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;fillColor=#d5e8d4;strokeColor=#82b366;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-9" target="ZybQ-fv8Gocl7lNzSQPM-3">
|
||||||
|
<mxGeometry relative="1" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-65" value="0, 13" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#B9E0A5;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-41">
|
||||||
|
<mxGeometry x="-0.3333" y="-5" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-52" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0;entryY=0.5;entryDx=0;entryDy=0;fillColor=#d5e8d4;strokeColor=#82b366;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-9" target="ZybQ-fv8Gocl7lNzSQPM-8">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="50" y="180" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-64" value="0, 10" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#B9E0A5;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-52">
|
||||||
|
<mxGeometry x="-0.2074" y="-2" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-53" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0;entryY=0.5;entryDx=0;entryDy=0;fillColor=#d5e8d4;strokeColor=#82b366;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-9" target="ZybQ-fv8Gocl7lNzSQPM-10">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="50" y="590" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-66" value="0, 17" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#B9E0A5;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-53">
|
||||||
|
<mxGeometry x="-0.2769" y="3" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-9" value="s" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#d5e8d4;strokeColor=#82b366;" vertex="1" parent="1">
|
||||||
|
<mxGeometry x="10" y="350" width="80" height="80" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-50" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0.5;entryY=1;entryDx=0;entryDy=0;jumpStyle=arc;jumpSize=12;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-10" target="ZybQ-fv8Gocl7lNzSQPM-7">
|
||||||
|
<mxGeometry relative="1" as="geometry">
|
||||||
|
<Array as="points">
|
||||||
|
<mxPoint x="190" y="640" />
|
||||||
|
<mxPoint x="500" y="640" />
|
||||||
|
<mxPoint x="500" y="370" />
|
||||||
|
<mxPoint x="425" y="370" />
|
||||||
|
</Array>
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-73" value="2, 20" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-50">
|
||||||
|
<mxGeometry x="-0.6993" y="-5" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-51" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0.5;entryY=1;entryDx=0;entryDy=0;jumpStyle=arc;jumpSize=12;fillColor=#f8cecc;strokeColor=#b85450;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-10" target="ZybQ-fv8Gocl7lNzSQPM-11">
|
||||||
|
<mxGeometry relative="1" as="geometry" />
|
||||||
|
</mxCell>
|
||||||
|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-72" value="6, 10" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontSize=14;fontColor=#F19C99;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-51">
|
||||||
|
<mxGeometry x="-0.5564" y="-3" relative="1" as="geometry">
|
||||||
|
<mxPoint as="offset" />
|
||||||
|
</mxGeometry>
|
||||||
|
</mxCell>
|
||||||
|
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<mxGeometry relative="1" as="geometry">
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<Array as="points">
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<mxPoint x="480" y="470" />
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<mxPoint x="480" y="338" />
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</Array>
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</mxGeometry>
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-78" value="5, 20" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-60">
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<mxGeometry x="-0.1581" y="3" relative="1" as="geometry">
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<mxPoint as="offset" />
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</mxGeometry>
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-61" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;entryX=0.5;entryY=0;entryDx=0;entryDy=0;jumpStyle=arc;jumpSize=12;fillColor=#dae8fc;strokeColor=#6c8ebf;" edge="1" parent="1" target="ZybQ-fv8Gocl7lNzSQPM-6">
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<mxPoint x="465" y="462" as="sourcePoint" />
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<mxPoint x="660" y="132" as="targetPoint" />
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<Array as="points">
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<mxPoint x="570" y="462" />
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<mxPoint x="570" y="112" />
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<mxPoint x="660" y="112" />
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</Array>
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</mxGeometry>
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-79" value="7, 5" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-61">
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<mxPoint as="offset" />
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-62" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;fillColor=#dae8fc;strokeColor=#6c8ebf;jumpStyle=arc;jumpSize=12;" edge="1" parent="1" target="ZybQ-fv8Gocl7lNzSQPM-5">
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<mxGeometry relative="1" as="geometry">
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<mxPoint x="465" y="480" as="sourcePoint" />
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<mxPoint x="660" y="440" as="targetPoint" />
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</mxGeometry>
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-80" value="6, 5" style="edgeLabel;html=1;align=center;verticalAlign=middle;resizable=0;points=[];fontColor=#A9C4EB;fontSize=14;" vertex="1" connectable="0" parent="ZybQ-fv8Gocl7lNzSQPM-62">
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<mxPoint as="offset" />
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</mxGeometry>
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</mxCell>
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|
<mxCell id="ZybQ-fv8Gocl7lNzSQPM-63" style="edgeStyle=orthogonalEdgeStyle;rounded=0;orthogonalLoop=1;jettySize=auto;html=1;jumpStyle=arc;jumpSize=12;fillColor=#dae8fc;strokeColor=#6c8ebf;" edge="1" parent="1" source="ZybQ-fv8Gocl7lNzSQPM-11" target="ZybQ-fv8Gocl7lNzSQPM-4">
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<mxGeometry relative="1" as="geometry">
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<Array as="points">
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<mxPoint x="660" y="500" />
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</Array>
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</mxGeometry>
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</mxCell>
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<mxPoint as="offset" />
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</mxGeometry>
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</mxCell>
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<mxCell id="ZybQ-fv8Gocl7lNzSQPM-11" value="E" style="whiteSpace=wrap;html=1;aspect=fixed;shape=ellipse;perimeter=ellipsePerimeter;fontSize=48;fillColor=#dae8fc;strokeColor=#6c8ebf;" vertex="1" parent="1">
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<mxGeometry x="385" y="430" width="80" height="80" as="geometry" />
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</mxCell>
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</root>
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</mxGraphModel>
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|
</diagram>
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||||||
|
</mxfile>
|
||||||
@ -1,6 +1,10 @@
|
|||||||
\documentclass[12pt]{article}
|
\documentclass[12pt]{article}
|
||||||
\usepackage[polish]{babel}
|
\usepackage[polish]{babel}
|
||||||
|
\usepackage{float}
|
||||||
\usepackage[utf8]{inputenc}
|
\usepackage[utf8]{inputenc}
|
||||||
|
\usepackage{amsmath}
|
||||||
|
\usepackage{pdfpages}
|
||||||
|
\usepackage[T1]{fontenc} % Add this line
|
||||||
\title{Sprawozdanie z projektu MOM}
|
\title{Sprawozdanie z projektu MOM}
|
||||||
\author{Krzysztof Rudnicki, 307585}
|
\author{Krzysztof Rudnicki, 307585}
|
||||||
\date{\today}
|
\date{\today}
|
||||||
@ -8,12 +12,108 @@
|
|||||||
|
|
||||||
\maketitle
|
\maketitle
|
||||||
\section{Zadanie 1. Sieć przepływowa}
|
\section{Zadanie 1. Sieć przepływowa}
|
||||||
\subsection{Model sieciowy}
|
|
||||||
\paragraph{Sformułowanie}
|
|
||||||
\paragraph{Narysowanie modelu}
|
|
||||||
\paragraph{Problem do rozwiązania}
|
|
||||||
|
|
||||||
\subsection{Rozwiązanie}
|
\subsection{Model sieciowy}
|
||||||
|
\paragraph{Problem do rozwiązania}
|
||||||
|
Należy rozwiązać problem najtańszego przepływu \\
|
||||||
|
\begin{figure}[htb]
|
||||||
|
\caption{Koszty transportowe i przepustowości na poszczególnych odcinkach}
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ | c | c | c | c | c | c | }
|
||||||
|
\hline
|
||||||
|
& D & E & F & G & H \\
|
||||||
|
\hline
|
||||||
|
A & 4, 15 & 2, 10 & - & - & -\\
|
||||||
|
\hline
|
||||||
|
B & 4, 4 & 3, 9 & - & 8, 9 & - \\
|
||||||
|
\hline
|
||||||
|
C & 2, 20 & 6, 10 & - & - & - \\
|
||||||
|
\hline
|
||||||
|
D & - & - & 3, 10 & 7, 3 & 2, 2 \\
|
||||||
|
\hline
|
||||||
|
E & 5, 20 & - & 7, 5 & 6, 5 & 3, 5 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
\begin{figure}[htb]
|
||||||
|
\caption{Zdolności wydobywcze kopalń (w tys. ton)}
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ | c | c |}
|
||||||
|
\hline
|
||||||
|
$W_A$ & 10 \\
|
||||||
|
\hline
|
||||||
|
$W_B$ & 13 \\
|
||||||
|
\hline
|
||||||
|
$W_C$ & 17 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
\begin{figure}[htb]
|
||||||
|
\caption{Średnie zużycie dobowe węgla przez elektronie (w tys. ton)}
|
||||||
|
\begin{center}
|
||||||
|
\begin{tabular}{ | c | c |}
|
||||||
|
\hline
|
||||||
|
$Z_F$ & 15 \\
|
||||||
|
\hline
|
||||||
|
$Z_G$ & 13 \\
|
||||||
|
\hline
|
||||||
|
$Z_H$ & 7 \\
|
||||||
|
\hline
|
||||||
|
\end{tabular}
|
||||||
|
\end{center}
|
||||||
|
\end{figure}
|
||||||
|
\paragraph{Sformułowanie}
|
||||||
|
Matematyczne sformułowanie zadania:
|
||||||
|
\begin{enumerate}
|
||||||
|
\item Parametry \\
|
||||||
|
s - źródło \\
|
||||||
|
B - Budynki (kopalnie, stacje, elektrownie) \\
|
||||||
|
K - kopalnie \\
|
||||||
|
$c_{ij}$ - koszt transportu z budynku i do budynku j ($c_{sk}$ = 0) \\
|
||||||
|
$W_k$ - zdolność wydobywcza kopalni k [w tonach] \\
|
||||||
|
$p_{ij}$ - przepustowość transportu z budynku i do budynku j [w tonach] ($u_{sk}$ = $W_k$) \\
|
||||||
|
E - elektrownie \\
|
||||||
|
$Z_e$ - średnie zużycie dobowe przez elektrownię e [w tonach] \\
|
||||||
|
\item Zmienne decyzyjne
|
||||||
|
$f_{ij}$ - przepływ transportu z budynku i do obiektu j \\
|
||||||
|
\item Funkcja celu
|
||||||
|
\begin{align*}
|
||||||
|
Q &= \min\left(\sum_{(i, j) \in B \backslash \{s\}} c_{ij} f_{ij}\right) \\
|
||||||
|
&= \min(4f_{AD} + 2f_{AE} + 4f_{BD} + 3f_{BE} + 8f_{BG} + 2f_{CD} \\
|
||||||
|
&\quad + 6f_{CE} + 3f_{DF} + 7f_{DG} + 2f_{DH} + 5f_{ED} + 7f_{EF} \\
|
||||||
|
&\quad + 6f_{EG} + 3f_{EH})
|
||||||
|
\end{align*}
|
||||||
|
|
||||||
|
\item Ograniczenia
|
||||||
|
\begin{equation}
|
||||||
|
0 \leq f_{sk} \leq W_k, \; k \in K = \{A, B, C\}
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
f_{si} = 0, \; i \in B \backslash K
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
f_{is} = 0, \; i \in B
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
0 \leq f_{ij} \leq p_{uj}, \; (i, j) \in B \backslash \{s\}
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
f_{is} = 0, \; i \in B
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
\sum_{b \in B} f_{be} \ge Z_e, \; e \in E = \{F, G, H\}
|
||||||
|
\end{equation}
|
||||||
|
\begin{equation}
|
||||||
|
\sum_{i \in B \backslash \{ s \} } f_{bi} \leq \sum_{j \in B} f_{bn}, \; b \in B \backslash \{s\}
|
||||||
|
\end{equation}
|
||||||
|
|
||||||
|
\end{enumerate}
|
||||||
|
\paragraph{Narysowanie modelu}
|
||||||
|
\includepdf[pages=-]{1flow.pdf}
|
||||||
|
|
||||||
|
\subsection{Rozwiązanie}Z
|
||||||
\paragraph{Metoda }
|
\paragraph{Metoda }
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user