| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Network Flows |
| Type | Transportation problem: add dummy |
| Difficulty | Moderate -0.8 This is a standard textbook transportation problem requiring routine application of the dummy variable method and stepping-stone algorithm. Parts (a)-(c) test basic understanding of balancing supply/demand, while part (d) requires mechanical application of a taught algorithm with clear structure provided. No novel insight or complex problem-solving required. |
| Spec | 7.04f Network problems: choosing appropriate algorithm |
| J | K | Supply | |
| A | 12 | 15 | 9 |
| B | 8 | 17 | 13 |
| C | 4 | 9 | 12 |
| Demand | 9 | 11 |
| J | K | L | Supply | |
| A | 12 | 15 | 9 | |
| B | 8 | 17 | 13 | |
| C | 4 | 9 | 12 | |
| Demand | 9 | 11 | 34 |
| J | K | L | |
| A | 9 | 0 | |
| B | 11 | 2 | |
| C | 12 |
| J | K | L | |
| A | 8 | 1 | |
| B | 13 | ||
| C | 9 | 3 |
4. The following minimising transportation problem is to be solved.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& J & K & Supply \\
\hline
A & 12 & 15 & 9 \\
\hline
B & 8 & 17 & 13 \\
\hline
C & 4 & 9 & 12 \\
\hline
Demand & 9 & 11 & \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Complete the table below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
& J & K & L & Supply \\
\hline
A & 12 & 15 & & 9 \\
\hline
B & 8 & 17 & & 13 \\
\hline
C & 4 & 9 & & 12 \\
\hline
Demand & 9 & 11 & & 34 \\
\hline
\end{tabular}
\end{center}
\item Explain why an extra demand column was added to the table above.
A possible north-west corner solution is:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& J & K & L \\
\hline
A & 9 & 0 & \\
\hline
B & & 11 & 2 \\
\hline
C & & & 12 \\
\hline
\end{tabular}
\end{center}
\item Explain why it was necessary to place a zero in the first row of the second column.
After three iterations of the stepping-stone method the table becomes:
\begin{center}
\begin{tabular}{ | c | c | c | c | }
\hline
& J & K & L \\
\hline
A & & 8 & 1 \\
\hline
B & & & 13 \\
\hline
C & 9 & 3 & \\
\hline
\end{tabular}
\end{center}
\item Taking the most negative improvement index as the entering square for the stepping stone method, solve the transportation problem. You must make your shadow costs and improvement indices clear and demonstrate that your solution is optimal.
\end{enumerate}
\hfill \mbox{\textit{Edexcel D2 2006 Q4 [16]}}