Analyzing Variability, Cost, and Responsiveness of Base-Stock Inventory Policies with Linear Control Theory

Abstract

The effect of inventory policies on order variability has been extensively analyzed. Two popular means of reducing order variability are demand smoothing and order smoothing. If the objective is minimizing demand variability, demands and orders can be heavily smoothed, resulting in an inventory policy that orders equal amounts in each time period. Such a policy obviously minimizes order variability, but it leads to high cost and low responsiveness of the inventory system. To optimize the overall performance of an inventory system, the effect of the inventory policy on all relevant dimensions of operational performance must be analyzed. We address this issue and analyze the effect of the parameter values of an inventory policy on three main dimensions of operational performance: order variability, expected cost, and responsiveness. The inventory policy we use is the partial correction policy, a policy that can be used to smooth demand and to smooth orders. To analyze this policy, we use linear control theory. We derive the transfer function of the policy and prove the stability of the inventory system under this policy. Then, we determine the effect of the policy parameters on order variability, cost, and responsiveness and discuss how good parameter values can be chosen.

Behavioral causes of the bullwhip effect: An analysis using linear control theory

“…Rather, the dynamic performance of both orders and inventories appears to perform best around the classic base-stock policy area (γ I = γ P = 1). This observation is consistent with Hoberg and Thonemann (2015), who recommend such a policy when excellent dynamic performance is required. Outside this area, the performance is most robust close to the DE-diagonal (γ I = γ P ) and deteriorates rapidly otherwise.…”

“…Such a "real-life" approach would be consistent with, and complement, recent developments in the area that characterize system performance with additional dimensions. For example, in line with Hoberg and Thonemann (2015), additional research can use total cost performance as a complement to order and inventory variability.…”

“…In contrast with the over-reaction to mismatches, order smoothing is often a deliberate decision taken to reduce variability. Hoberg and Thonemann (2015), for example, showed that order smoothing diminishes the stationary bullwhip in DE-APVIOBPCS systems. The same is true for general APVIOBPCS policies.…”

“…Authors consistently report that, whereas forecasting itself induces it, the measured bullwhip depends on the combination of forecasting methodology, ordering policy, and demand distribution; see, for example, the analytical work of Chen, Drezner, Ryan, and Simchi-Levi (2000) and Zhang (2004); system dynamics simulations by Wright and Yuan (2008); and control-theoretic analysis of the topic by Dejonckheere et al (2002). With regards to the specific forecasting methodologies adopted in this article, we refer the reader to and Hoberg et al (2007b) for explicit analyses of the effect of the exponential smoothing parameter α on the magnitude of the bullwhip effect under APVIOBPCS-OUT policies and Hoberg and Thonemann (2015) for the effect of α on DE-APVIOBPCS policies. We analyze the influence of α on general APVIOBPCS policies in a series of numerical experiments presented in Appendix A.…”

“…In terms of model assumptions, we allow for independent pipeline and inventory adjustments, consistent with Dejonckheere et al (2004) and . In terms of performance metrics, we adopt the stationary and dynamic measures of Hoberg et al (2007b) and Hoberg and Thonemann (2015). Conceptually, however, our objective is to relate parameter combinations to different behavioral biases.…”