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zRJwQcHD@_=&L!&FjSA{}FHgm#%3Up5nr1Z+BOV=j;@DLcVQvnto&Qxy5|A8Vwo=ua~6)%A@R;SgRr!w z*2Xp2lvR%CR8Q0LasYsX??R5GsqtGxNkbc$SG*C&SbvkGG2Z2cvG2 z33BeaQ*cy_=%Yy?EVO4o5_W&w8#-jq7%}u;9BlDhtV`5I_$2{wTL1bP((ZdTOy|Oj zuNRMR-b73&zDE%KNJ#4JUhesB{Jw*u) zi6=9TG`qW1H1M|A6MHR7F6!}zD_rAT3OC6}2LC6V>9Mo@voG5lTOkPuFsr#cm@#Xq zn3*%nNazZfbMUg7v4c#w*-cDL*m*dNIatkE&3Jf093WnH9#$5i|MNx?dK~PRkF4zM zNvv_O6aYK#e=%h^{|?bhf<6yi?l-N?dyVPUSZ9>Gx9+)X(C~A~+PolhQ6Mg=Xq@%S zD&xl63@I=SMn?pi7BH+}oDEYXN>c@qG3#(SNIP~7O}tviGO17#i>Nm=#kZe zw>A>A2~ennt?y!5fNB9TV@YBGAgtpz??sGC5;QhRa2~r0TT{j#9wY2HPia~7@St3W z=0 \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months \\ p \in products}} produce[m][p] >=0 \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months \\ p \in products}} sell[m][p] >=0 \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months \\ p \in products}} stock[m][p] >=0 \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ i \in scenarios \\ m \in months \\ p \in products}} lowerProfit[i][m][p] >=0 @@ -199,52 +222,52 @@ Zmienne decyzyjne stanowią wartości kontrolowane przez podmiot podejmujący de \item Ograniczenie czasowe pracy maszyn - Każda maszyna może pracować maksymalnie \textit{numberOfHoursInFactory} godzin w miesiącu, zatem łączny czas pracy wszystkich maszyn danego typu nie może przekroczyć iloczynu liczby dostępnych maszyn tego typu i czasu \textit{numberOfHoursInFactory}. \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ mc \in machines}} \sum_{p \in products} (workTime[m][mc][p] <= machineCount[mc]*numberOfHoursInFactory) \end{equation} \item Ograniczenie wiążące czas pracy maszyn z produkcją - czas wykorzystania określonego typu maszyny jest równy sumie iloczynów liczby wytworzonych jednostek każdego produktu i czasu potrzebnego na obróbkę jednej jednostki tego produktu na danej maszynie: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ mc \in machines\\ p \in products}} workTime[m][mc][p] == produce[m][p]*timeToProduce[mc][p] \end{equation} \item Ograniczenie maksymalnej sprzedaży wynikające z pojemności rynku w danym miesiącu: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} sell[m][p] == maxProductsInMonth[m][p] \end{equation} \item Warunki definiujące zmienną binarną przy przekroczeniu 80 procent chłonności rynku: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} sell[m][p] <= 0.8*maxProductsInMonth[m][p] + 1000000 * if80prec[m][p] \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} sell[m][p] >= 0.8*maxProductsInMonth[m][p] * if80prec[m][p] \end{equation} \item Ograniczenia linearyzujące oddziaływanie zmiennych binarnych na funkcję celu: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ i \in scenarios\\ m \in months\\ p \in products}} lowerProfit[i][m][p] <= 1000000 * if80prec[m][p] \end{equation} \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ i \in scenarios\\ m \in months\\ p \in products}} lowerProfit[i][m][p] <= 0.2 * sell[m][p]*sellProfit[i][p] \end{equation} \begin{multline} - \bigforall_{\substack{ + \forall{\substack{ i \in scenarios\\ m \in months\\ p \in products}} 0.2 * sell[m][p]*sellProfit[i][p] - lowerProfit[i][m][p] +\\ 1000000 * if80prec[m][p] <= 1000000; @@ -252,35 +275,36 @@ Zmienne decyzyjne stanowią wartości kontrolowane przez podmiot podejmujący de \item Ograniczenie sprzedaży do liczby sztuk wyprodukowanych oraz dostępnych w magazynie. Dla pierwszego miesiąca ograniczenie przyjmuje formę: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} sell[m][p] <= produce[m][p]+storageStart[p] \end{equation} Dla każdego następnego miesiąca: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} sell[m][p] <= produce[m][p] + stock[m-1][p] \end{equation} \item Ograniczenie określające stan magazynu na koniec miesiąca jako różnicę między sumą produktów wyprodukowanych i dostępnych na początku miesiąca a liczbą sprzedanych jednostek. Dla pierwszego miesiąca: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} stock[m][p]==(produce[m][p] + storageStart[p])-sell[m][p] \end{equation} Dla każdego następnego miesiąca: \begin{equation} - \bigforall_{\substack{ + \forall{\substack{ m \in months\\ p \in products}} stock[m][p]==(produce[m][p] + stock[m-1][p])-sell[m][p] \end{equation} \end{itemize} \subsection{Funkcja celu} +\addcontentsline{toc}{subsection}{Funkcja celu} Funkcja celu w modelu jednokryterialnym polega na maksymalizacji wartości oczekiwanej zysku ze wszystkich analizowanych scenariuszy. W każdym ze scenariuszy zastosowano funkcję zysku o następującej postaci \begin{multline} -\bigforall_{\substack{ +\forall{\substack{ i