\documentclass[10pt,a4paper]{article}

% Packages
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\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
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\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{vicy12341}
\pdfinfo{
  /Title (oidd.pdf)
  /Creator (Cheatography)
  /Author (vicy12341)
  /Subject (OIDD Cheat Sheet)
}

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% This two commands together give roughly
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% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
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\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{OIDD Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{vicy12341} via \textcolor{DarkBackground}{\uline{cheatography.com/144393/cs/30992/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}vicy12341 \\
  \uline{cheatography.com/vicy12341} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 3rd March, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Lecture 2}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Flow Rate }} & Min between demand and capacity \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Utilization }} = R/Capacity & fraction of time spent working \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Cycle Time }} = 1/ Flow Rate & Time between when units exit process \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
{\bf{Flow Time }} = I/R & Time unit spends in process \tn 
% Row Count 8 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Cost of Direct Labor }} & =(wages per unit of time x \#of workers) / Flow Rate \tn 
% Row Count 11 (+ 3)
% Row 5
\SetRowColor{white}
{\bf{Labor Content }} & sum of processing times involving labor (don't multiply by \#of workers) \tn 
% Row Count 15 (+ 4)
% Row 6
\SetRowColor{LightBackground}
{\bf{Labor Utilization }} & = R / Labor Capacity \tn 
% Row Count 17 (+ 2)
% Row 7
\SetRowColor{white}
{\bf{Labor Capacity }} & = N (\# of workers) / Labor content \tn 
% Row Count 19 (+ 2)
% Row 8
\SetRowColor{LightBackground}
{\bf{Takt Time }} =1/ Demand Rate & Time between when flow units are demanded \tn 
% Row Count 22 (+ 3)
% Row 9
\SetRowColor{white}
{\bf{Target Manpower }} = Labor Content/ Takt Time & = Labor Content/ Takt Time \tn 
% Row Count 25 (+ 3)
% Row 10
\SetRowColor{LightBackground}
{\bf{Goal of Line Balancing }} & Find min cycle time \tn 
% Row Count 27 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Process Flows (Lecture 1)}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Little's Law:}} I = R x T & I= Inventory, R= Flow Rate, T= Flow Time \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Days of Supply }} = I/R = 1/Turns & The "T" in Little's Law (add def) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Inventory Turns }}= 1/T = R/I = COGS/ I} \tn 
% Row Count 5 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{COGS }} = R, the flow rate} \tn 
% Row Count 6 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Gross Margin \%}} = (Price - Cost) / Price} \tn 
% Row Count 7 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Decision trees}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Maximin Decision}} & Find the minimums of each branch, then choose the max of the mins \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
{\bf{Maximax Decision}} & Find the max of each branch, then choose the max of the maxes \tn 
% Row Count 7 (+ 3)
% Row 2
\SetRowColor{LightBackground}
{\bf{Expected value of Perfect info}} & = (expected value of decision w/ perfect info) - (expected value of decision w/o perfect info) \tn 
% Row Count 12 (+ 5)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Baye's Rule}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646260362_IMG_1692.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.69218 cm} x{3.28482 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Queues}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Length of queue at time T}} = T x (Demand - Capacity)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Time to serve Qth person in queue}} = Q/Capacity} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Time to serve customer arriving at time T}} = T x (Demand/Capacity-1)} \tn 
% Row Count 5 (+ 2)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Avg time to serve customers in the queue}} = 1/2 x T x (Demand/Capacity -1)} \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Variables to know}} & a= inter arrival time, m= \# of workers/kiosks, p = avg processing time \tn 
% Row Count 10 (+ 3)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Demand}} = 1/a} \tn 
% Row Count 11 (+ 1)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Capacity}}= m x (1/p)} \tn 
% Row Count 12 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Utilization}} = P / ( a x m)} \tn 
% Row Count 13 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{m = P /( a x utilization)} \tn 
% Row Count 14 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Time spent in system}} = Time in queue + Time in processing} \tn 
% Row Count 16 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Inventory}} = Inventory in queue + Inventory in service} \tn 
% Row Count 18 (+ 2)
% Row 11
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Inventory in queue}} = Time in queue/ a} \tn 
% Row Count 19 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Inventory in service}} = p/a} \tn 
% Row Count 20 (+ 1)
% Row 13
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{CVa}}= Standard deviation inter arrival time / avg inter arrival time} \tn 
% Row Count 22 (+ 2)
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{CVp}}= Standard deviation processing time/ avg processing time} \tn 
% Row Count 24 (+ 2)
% Row 15
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{Time in queue increases dramatically as utilization approaches 100\%} \tn 
% Row Count 26 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Yield and Capacity of Process}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Yield}} = Flow Rate goof output/ Flow rate bad output} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Yield of Process}} = Product of resource yields} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
{\bf{Implied Utilization}} = Demand/ Capacity & Can be over 100\% , bottleneck has highest IU \tn 
% Row Count 6 (+ 3)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Capacity}} = 1/Processing Time} \tn 
% Row Count 7 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Processing Time}} = 1/Capacity} \tn 
% Row Count 8 (+ 1)
% Row 5
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Demand (in min of work)}} = Processing time x Demand} \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Required input}} = Desired output/ Process yield} \tn 
% Row Count 11 (+ 1)
% Row 7
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Required resource capacity}} = Resource's demand with required input} \tn 
% Row Count 13 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Required resource capacity}} = Resource's demand with required input} \tn 
% Row Count 15 (+ 2)
% Row 9
\SetRowColor{white}
{\bf{Finding capacity of process}} & Find capacity of each step and find the bottleneck \tn 
% Row Count 18 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Solving Questions}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{What the question is asking}} & {\bf{Approach to take}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Inventory costs are what percent of purchasing costs?}} & Find Flow Time. Then multiply annual inventory cost percentage by flow time in years and by individual unit cost \tn 
% Row Count 8 (+ 6)
% Row 2
\SetRowColor{LightBackground}
{\bf{Cost to hold inventory for a year}} & Cost of individual unit x annual holding cost percentage \tn 
% Row Count 11 (+ 3)
% Row 3
\SetRowColor{white}
{\bf{What is the avg time...}} & Find flow time \tn 
% Row Count 13 (+ 2)
% Row 4
\SetRowColor{LightBackground}
{\bf{Total time to process 20 customers}} & Time to process 1st customer (sum of processing times) + time to process other customers ( 19 x Cycle Time) \tn 
% Row Count 19 (+ 6)
% Row 5
\SetRowColor{white}
{\bf{Total ordering costs}} & (K x R) / Q \tn 
% Row Count 21 (+ 2)
% Row 6
\SetRowColor{LightBackground}
{\bf{Total holding costs}} & 1/2 x Qh \tn 
% Row Count 23 (+ 2)
% Row 7
\SetRowColor{white}
{\bf{How many individual units should they produce in each batch}} & Use desired capacity to find full batch size. Then multiply batch size by ratio of individual demand/capacity over total demand/capacity \tn 
% Row Count 30 (+ 7)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{5.377cm}{x{2.4885 cm} x{2.4885 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Solving Questions (cont)}}  \tn
% Row 8
\SetRowColor{LightBackground}
{\bf{If company ordered a specific number of cases at a time, what would be their holding and ordering costs}} & Find C(Q) \tn 
% Row Count 6 (+ 6)
% Row 9
\SetRowColor{white}
{\bf{If company ordered a specific number of cases, what would be holding and ordering cost per case}} & Find C(Q)/ R \tn 
% Row Count 11 (+ 5)
% Row 10
\SetRowColor{LightBackground}
{\bf{Quantity of cases per order}} & Find EOQ \tn 
% Row Count 13 (+ 2)
% Row 11
\SetRowColor{white}
{\bf{How long will you wait if you are nth in line}} & Find the time to serve the number of people in front of you. \tn 
% Row Count 16 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Avg Inventory}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646257104_IMG_1690.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Setup Times and Batching}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{ Capacity}}  = Number of units produced/ Time to Produce units} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Utilization (with a setup time)}} = Flow rate x Processing Time} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Capacity}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646257022_IMG_1686.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{EOQ and Quantity Discounts}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Inventory Variables}} & {\bf{Q}}= quantity in each order, {\bf{ R}}=Flow Rate,     {\bf{h}} = inventory holding cost per unit time, {\bf{K}}= fixed vost per order \tn 
% Row Count 6 (+ 6)
% Row 1
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Time between shipments}} = Q/R} \tn 
% Row Count 7 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Avg inventory}} = Q/2} \tn 
% Row Count 8 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Number of orders placed per unit of time}} = R/Q} \tn 
% Row Count 9 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Capacity (in min of work/hr)}} = \#of workers x 60} \tn 
% Row Count 11 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Quantity minimizing ordering and holding costs}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646260891_IMG_1694.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Batch Size}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646256948_IMG_1688.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Ordering plus inventory holding cost per unit time}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646260617_IMG_1693.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Time in Queue}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/vicy12341_1646260021_IMG_1691.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}