| Exam Board | OCR |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming production scheduling |
| Difficulty | Standard +0.8 This is a standard dynamic programming problem requiring systematic state-space exploration across 4 stages with inventory tracking. While methodical, it demands careful bookkeeping of feasible states, storage costs, and optimal substructure—more complex than routine calculus but less conceptually demanding than proof-based or multi-insight problems. |
| Spec | 7.03c Working with algorithms: trace, interpret, adapt |
| No. of Items Produced | 0 | 1 | 2 | 3 |
| Cost in Pounds | 0 | 5500 | 9700 | 13100 |
| Month | March | April | May | June |
| No. of Orders | 1 | 2 | 4 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stage/state table correctly set up with stages 1–4 | M1 A1 | Stage 1 entries correct |
| Stage 2 entries with optimal values marked * | M1 A2 | |
| Stage 3 entries with optimal values marked * | M1 A2 | |
| Stage 4 entries with optimal values marked * | M1 A1 | |
| Should make 2 in March, 3 in April, 3 in May and 0 in June | A1 | (11 total) |
# Question 5:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stage/state table correctly set up with stages 1–4 | M1 A1 | Stage 1 entries correct |
| Stage 2 entries with optimal values marked * | M1 A2 | |
| Stage 3 entries with optimal values marked * | M1 A2 | |
| Stage 4 entries with optimal values marked * | M1 A1 | |
| Should make 2 in March, 3 in April, 3 in May and 0 in June | A1 | **(11 total)** |
---\begin{enumerate}
\item A company wishes to plan its production of a particular item over the coming four months based on its current orders. In each month the company can manufacture up to three of the item with the costs according to how many it makes being as follows:
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
No. of Items Produced & 0 & 1 & 2 & 3 \\
\hline
Cost in Pounds & 0 & 5500 & 9700 & 13100 \\
\hline
\end{tabular}
\end{center}
There are no items in stock at the start of the period and the company wishes to meet all its orders on time and have no stock left at the end of the 4-month period. If any items are not to be supplied in the month they are made there is also a storage cost incurred of $\pounds 400$ per item per month.
The orders for each of the four months being considered are as follows:
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
Month & March & April & May & June \\
\hline
No. of Orders & 1 & 2 & 4 & 1 \\
\hline
\end{tabular}
\end{center}
Use dynamic programming to find how many of the item the company should make in each of these four months in order to minimise the total cost for this period.
\section*{Please hand this sheet in for marking}
\includegraphics[max width=\textwidth, alt={}, center]{df7b056f-1446-43f1-a2fd-c0d56533550e-6_588_1285_504_276}\\
\includegraphics[max width=\textwidth, alt={}, center]{df7b056f-1446-43f1-a2fd-c0d56533550e-6_588_1280_1361_276}
\hfill \mbox{\textit{OCR D2 Q5 [11]}}