When bullwhip increases in the lead time: An eigenvalue analysis of ARMA demand

Problem definition. The impact of lead times on the bullwhip effect produced by order-up-to (OUT) replenishment policy is studied. Practical relevance. Under general auto-regressive moving average (ARMA) demand, we investigate when OUT possesses an always-increasing-in-the-lead-time and it does not. Methodology. A measure based difference between demand order variance combined with a novel analysis eigenvalues impulse response ARMA process. Contribution. We show positive necessary sufficient condition for increasing in time effect. ordering zeros poles (the eigenvalue ordering) z-transform transfer function process reveals positive. To provide further insight, study ARMA(2,2) which contains six different orderings. Two these orderings satisfy (positive particular order) response. inverse this do not possess final two condition, nor its inverse, but contain responses. Managerial implications. Our findings are important as reducing lead-times often advocated improvement action to reduce By identifying characteristics that increases offer prescriptive advice when, not, invest reduction.