| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming production scheduling |
| Difficulty | Challenging +1.2 This is a standard dynamic programming question requiring systematic table completion with state transitions. While it involves multiple cost components and constraints, it follows the textbook D2 format closely with no novel problem-solving required—students apply the learned algorithm methodically through 5 months with clear states (stock levels 0-2). |
| Spec | 7.05e Cascade charts: scheduling and effect of delays |
| Month | March | April | May | June | July |
| Number ordered | 3 | 4 | 2 | 4 | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Part | Scheme | Marks |
| E.g. [Table showing stage-by-stage values and optimal states] | 1M1 1A1 | 1M1: First stage completed. 3 rows, something in each cell. 1A1: CAO condone missing * here. No extra rows. |
| 2M1 2A1 ft | 2M1: Second stage completed with 3 states and at least 6 rows. BoD if something in each cell. 2A1 ft: Any 2 states correct. Fit for their * values or the correct * values. | |
| 3A1 | 3A1: CAO All 3 states correct. No missing/extra rows. | |
| 3M1 4A1 ft | 3M1: 3rd stage completed with 3 states and at least 9 rows. BoD if something in each cell. 4A1 ft: Any state correct. Fit on their * values or the correct * values. | |
| 5A1 | 5A1: CAO All 3 states correct. No missing/extra rows. | |
| 4M1 6A1 | 4M1: 4th stage completed with 3 states and at least 6 rows. BoD if something in each cell. 6A1: CAO All 3 states correct. No missing/extra rows. | |
| 5M1 7A1 | 5M1: 5th stage completed with at least 2 rows. BoD if something in each cell. 7A1: CAO Final, state correct. No missing/extra rows. | |
| 1B1 | 1B1: CAO Must have earned all previous M marks. | |
| 2B1 | 2B1: CAO Must have earned all previous M marks. | |
| 14 marks |
| Part | Scheme | Marks | Guidance |
|------|--------|-------|----------|
| | E.g. [Table showing stage-by-stage values and optimal states] | 1M1 1A1 | 1M1: First stage completed. 3 rows, something in each cell. 1A1: CAO condone missing * here. No extra rows. |
| | | 2M1 2A1 ft | 2M1: Second stage completed with 3 states and at least 6 rows. BoD if something in each cell. 2A1 ft: Any 2 states correct. Fit for their * values or the correct * values. |
| | | 3A1 | 3A1: CAO All 3 states correct. No missing/extra rows. |
| | | 3M1 4A1 ft | 3M1: 3rd stage completed with 3 states and at least 9 rows. BoD if something in each cell. 4A1 ft: Any state correct. Fit on their * values or the correct * values. |
| | | 5A1 | 5A1: CAO All 3 states correct. No missing/extra rows. |
| | | 4M1 6A1 | 4M1: 4th stage completed with 3 states and at least 6 rows. BoD if something in each cell. 6A1: CAO All 3 states correct. No missing/extra rows. |
| | | 5M1 7A1 | 5M1: 5th stage completed with at least 2 rows. BoD if something in each cell. 7A1: CAO Final, state correct. No missing/extra rows. |
| | | 1B1 | 1B1: CAO Must have earned all previous M marks. |
| | | 2B1 | 2B1: CAO Must have earned all previous M marks. |
| | | **14 marks** | |
**Notes for Question 7:** ALL M marks - Must bring earlier optimal results into calculations. Ignore extra rows. Must have right 'ingredients' (– storage costs, overheads, additional space costs) at least once per stage. Penalise lack of * only once per question.
---7. A company assembles microlight aircraft.
They can assemble up to four aircraft in any one month, but if they assemble more than three they will have to hire additional space at a cost of $\pounds 1000$ per month.\\
They can store up to two aircraft at a cost of $\pounds 500$ each per month.\\
The overhead costs are $\pounds 2000$ in any month in which work is done.
Aircraft are delivered at the end of each month. There are no aircraft in stock at the beginning of March and there should be none in stock at the end of July.\\
The order book for aircraft is
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Month & March & April & May & June & July \\
\hline
Number ordered & 3 & 4 & 2 & 4 & 3 \\
\hline
\end{tabular}
\end{center}
Use dynamic programming to determine the production schedule which minimises the costs. Show your working in the table provided in the answer book and state the minimum production cost.\\
(Total 14 marks)\\
\hfill \mbox{\textit{Edexcel D2 2014 Q7 [14]}}