THEORY-1303: For an uncertain linear program, a decision fixed before the data are revealed must satisfy every realization at once (the robust counterpart, ∃ solution ∀ data), while a decision that may adjust after them need only have a feasible adjustment for each (the adjustable robust counterpart, ∀ data ∃ adjustment); the second is never more conservative and can be feasible where the first is not, the two coincide when each constraint's uncertainty is its own, and decisions may be restricted between them by what part of the data they read or by the form of the rule

Source

Ben-Tal et al. (2004), LIT-1975, Math. Program. 99: 351–376; read in NOTE-1503.

What was actually shown

• Definitions (eqs. 5–6): RC min_u {cᵀu : ∃v ∀ζ ∈ Z: Uu + Vv ≤ b}; ARC min_u {cᵀu : ∀ζ ∈ Z ∃v: Uu + Vv ≤ b}.
• Strict gaps (Example 1.2; the example after Theorem 2.1): RC infeasible where ARC is feasible for every u; RC value 0 against ARC −1. Both checked.
• Theorem 2.1: constraint-wise uncertainty (rows depending on disjoint blocks of a product set) and bounded adjustments make RC = ARC; proved by a minimax argument (appendix).
• Two intermediate restrictions. An information basis, “a prescribed portion ζᵢ of the true data” (p. 353), and the affine rule v = w + Wζ (AARC, eq. 8), “in-between” RC and ARC and tractable with fixed recourse (Theorem 3.1).
• Inventory (Table 2, θ = 20%, 100 simulations): cost 34,583 with on-line information, 35,121 with past demands, infeasible with a four-period delay and with none.

What this does not say

• That the information-basis case has been worked out beyond the black-and-white case and Remark 4.1’s linear maps.
• That the AARC equals the ARC.
• Bearing: CLAIM-537’s conditions I and II are this paper’s ARC and RC in a feasibility problem; its III is an information basis given by a general h; CLAIM-354’s legibility-limited policies are this paper’s information bases.