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.