What is the extent of the "drug problem" in Singapore and what is your source for this information?
Singapore does not have an obvious drug problem, but then neither do many cities in the US where drugs are most certainly flowing pretty readily -- drugs are rarely a visible problem in affluent regions. Statistics of drug use and annual arrests in Singapore do not look terribly dissimilar to other modern countries.
Given that ~0.1% of Singapore's population gets busted for drug offenses every year, it appears that the drug trade is alive and well in that city. My source of information, other than from the statistics the government publishes, is from being there, knowing people that lived there, and even knowing a (stupid) girl whose boyfriend there was a drug dealer. While they do have harsh laws with respect to illegal drugs, it hasn't made much of a dent in usage.