Impact of timing in post-warning prepositioning decisions on performance measures of disaster management: A real-life application

•Timing decision is made for relief pre-positioning in disasters with prior warning.•The impacts of timing on the cost and relief operation's speed are investigated.•Using a graph-theoretic conversion, the developed model is implemented on real data.•Tradeoffs between the logistics cost and relief operation's speed are extracted.•The best timing for different types of decision-makers is suggested.