Your original question asks about decision-analysis limitations without clarifying what type of organization would be making the decision.  Practical management problems occur in both profit and not-for-profit organizations, and there are strengths and limitations of decision analysis in both.

Decision analysis is a quantitative assessment of different decisions based on relative value.  Understanding the strengths and limitations of decision analysis when making a decision or facing an economic challenge in both for profit and not for profit organizations can be challenging.  What follows are general points to consider across all decision-analysis models.

Strengths

• Systemically creates components of multi-faceted problems.
• Values are measured or inferred.
• Uncertainties and assumptions can be defined.
• Better-defined decisions may lead to preferred outcomes.
• Formulates well-informed policy decisions.

Limitations

• A myriad of decision-making models exist: rapid decision making (RPD), meta-analysis, multi-criteria, goal programming, etc.  
• The selection of a decision model might slow the use of decision analysis, and the decision itself.
• The cognitive processes of the people making the decisions may limit the analysis outcome.
• Management of axioms, paradoxes, proofs, and cognitive limitations while making a decision in a group may lead to conflict, cost overruns, and deferred decision making.  
• Categorizing the normative and descriptive aspects of a problem, or the ought and the is, may be difficult, if not impossible.
• Different attributes may be emphasized by different people making the decision, which may also create conflict.
• Measurements and inferences may vary among decision makers.

While original the question asks about decision-analysis limitations, the practical answer to your question is to include both polarities, or strengths, as well as limitations.  

In summary, the strengths and limitations are multi-faceted.  The strengths include the systemic measurement of values leading to more defined policies in profit and not-for-profit organizations.  The limitations include selection of a decision-analysis model, time-frame needed to make a decision, and individual and group cognitive process(es).