D2 January 2006 Q2
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 £500 per month. They can store up to two motors for £100 per motor per month. The overhead costs are £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:
| Month | May | June | July | August | September |
|---|---|---|---|---|---|
| Number of motors | 3 | 3 | 7 | 5 | 4 |
Use dynamic programming to determine the production schedule that minimises the costs, showing your working in a table with the headings
| Stage (month) | State (Number in store at start of month) | Action (Number made in month) | Destination (Number in store at end of month) | Value (cost) |
|---|
Production schedule
| Month | May | June | July | August | September |
|---|---|---|---|---|---|
| Number to be made |
Total cost: ………… (12)
| Scheme | Marks | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
e.g.
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| M1 A1ft | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cost £2300 | A1ft (3) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| (12 marks) |
Notes
The scheme gives no individual marks against the table; the 3 marks shown are for the schedule and cost (the remaining marks of the 12 are not itemised in the printed scheme).
(Corrected from the printed mark scheme: in stage 5 (May) the State, Action and Dest columns are printed as 0, 1, 0 / 5, 4, 5 / 2, 2, 2; the values shown match State 0 with Action 5, 4, 3 and Dest 2, 1, 0.)