16.5 Exercise
A company produces two types of products T1 and T2, which requires the
following resources to produce each unit of the product:
| Resource | T1 | T2 |
| Labour (hours) | 9 | 6 |
| Pumps (units) | 1 | 1 |
| Tubing (m) | 12 | 16 |
The amount of profit per unit of products are:
-
T1
- £350
- T2
- £300
They have the following resources available: 1566 hours of labour, 200
pumps, and 2880 metres of tubing.
-
Write a program to maximise the profit for the company, using eplex
as a black box solver. Write a predicate that returns the profit and the
values for T1 and T2.
- What program change is required to answer this question:
What profit can be achieved if exactly 150 units of T1 are required?
- What would the profit be if fractional numbers of refrigerators could
be produced?
- Rewrite the program from (1) without optimize/2, using
eplex_solver_setup/1, eplex_solve/1, and eplex_var_get/3.
- In the program from (4), remove the integrality constraints (so that eplex
only sees an LP problem). Solve the integer problem by interleaving
solving of the LP problem with a rounding heuristic:
-
solve the continuous relaxation
- round the solution for T1 to the nearest integer and instantiate it
Initially just return the maximum profit value.
- re-solve the new continuous relaxation
- round the solution for T2 to the nearest integer and instantiate it
- re-solve the new continuous relaxation
What is the result in terms of T1, T2 and Profit?
- Rewrite the program from (5) using eplex_solver_setup/4 and automatic
triggering of the solver instead of explicit calls to eplex_solve/1.
The solver should be triggered whenever variables get instantiated.