On the relationship between entropy, demand uncertainty, and expected loss

•Provide theoretical justification for the increasing use of entropy in the operations management literature.•Establish that expected loss in general stochastic inventory problems is non-increasing as demand uncertainty measured using entropy is reduced.•Present insightful comparisons among various methods of measuring demand uncertainty.

We analyze the effect of demand uncertainty, as measured by entropy, on expected costs in a stochastic inventory model. Existing models studying demand variability’s impact use either stochastic ordering techniques or use variance as a measure of uncertainty. Due to both axiomatic appeal and recent use of entropy in the operations management literature, this paper develops entropy’s use as a demand uncertainty measure. Our key contribution is an insightful proof quantifying how costs are non-increasing when entropy is reduced.