To perform sensitivity analysis involving an integer linear program, it is best to

Question

BlackTom AI · Accepted Answer

Integer linear programs (ILPs) are discrete optimization problems; because integrality creates nonconvex feasible sets, many classical LP sensitivity results do not carry over exactly. That is why you should (a) start with LP-based analysis where useful, (b) treat LP duals/shadow prices carefully, and (c) perform multiple re-solves — therefore "all of these are correct."

1. Relevant concepts:
- LP relaxation: solving the continuous version of an ILP gives bounds and insights; simplex sensitivity ranges apply to the LP relaxation.
- Shadow prices (dual values): reflect marginal value for the LP relaxation, not necessarily the true marginal value in the integer problem.
- Scenario analysis/multiple runs: re-solving the ILP under changed parameters is required because integrality can cause discrete jumps in solution structure.

2. Step-by-step reasoning:
- Solve the LP relaxation first. The LP solution and sensitivity ranges tell you how constraints or objective coefficients affect the continuous optimum; this gives a useful starting point.
- Examine shadow prices from the LP relaxation. These indicate marginal worth for small changes, but because the ILP feasible region is discrete, small changes might not change the integer solution at all, or may cause a jump to a very different integer solution. Hence shadow prices must be used very cautiously.
- Conduct multiple computer runs: change RHS values or coefficients and re-solve the ILP to observe actual changes in integer feasibility and objective. This empirical re-solving is the definitive sensitivity test for ILPs.

3. No numeric calculations are needed; the intermediate logical steps are: LP relaxation → interpret duals cautiously → re-solve ILP for each scenario.

4. Why the correct answer is correct:
Each listed tactic contributes essential information. Using LP methods gives quick bounds; shadow prices give approximate marginal values but can mislead; multiple runs capture discrete effects. Combining them is best practice.

5. Why other single options are insufficient:
- Using only LP approach ignores integrality effects.
- Relying solely on shadow prices risks wrong conclusions because they reflect the LP, not the ILP.
- Making multiple runs without LP insight wastes effort and misses useful bounds.

Conclusion: combining these approaches is best, so the correct choice is "all of these are correct," matching the provided answer.

To perform sensitivity analysis involving an integer linear program, it is best to单项选择题

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