| Exam Board | Edexcel |
|---|---|
| Module | D2 (Decision Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dynamic Programming |
| Type | Dynamic programming production scheduling |
| Difficulty | Standard +0.8 This is a multi-stage dynamic programming problem requiring backward induction through 5 months with multiple constraints (production capacity, storage limits, demand fulfillment). Students must systematically evaluate feasible states and actions at each stage, calculate costs including conditional overhead and storage fees, and trace back the optimal policy. While the DP framework is standard for D2, the problem requires careful bookkeeping across many possibilities and is more complex than typical textbook exercises. |
| Spec | 7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation |
| Month | May | June | July | August | September |
| Number of motors | 3 | 3 | 7 | 5 | 4 |
| Stage (month) | State (Number in store at start of month) | Action (Number made in month) | Destinatio n (Number in store at end of month) | Value (cost) |
| Month | May | June | July | August | September | ||
|
2. An engineering firm makes motors. They can make up to five in any one month, but if they make more than four they have to hire additional premises at a cost of $\pounds 500$ per month. They can store up to two motors for $\pounds 100$ per motor per month. The overhead costs are $\pounds 200$ in any month in which work is done.\\
Motors are delivered to buyers at the end of each month. There are no motors in stock at the beginning of May and there should be none in stock after the September delivery.
The order book for motors is:
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Month & May & June & July & August & September \\
\hline
Number of motors & 3 & 3 & 7 & 5 & 4 \\
\hline
\end{tabular}
\end{center}
Use dynamic programming to determine the production schedule that minimises the costs, showing your working in the table provided below.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Stage (month) & State (Number in store at start of month) & Action (Number made in month) & Destinatio n (Number in store at end of month) & Value (cost) \\
\hline
& & & & \\
\hline
\end{tabular}
\end{center}
\section*{Production schedule}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Month & May & June & July & August & September \\
\hline
\begin{tabular}{ c }
Number to be \\
made \\
\end{tabular} & & & & & \\
\hline
\end{tabular}
\end{center}
Total cost: $\_\_\_\_$\\
\hfill \mbox{\textit{Edexcel D2 2006 Q2 [12]}}