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 analyzed extensively. 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.

Keywords:

• Supply Chain Management
• Control Theory
• Cost Analysis
• Bullwhip Effect

Additional information

Notes on contributors

Kai Hoberg

Kai Hoberg is Associate Professor for Supply Chain and Operations Strategy at Kühne Logistics University in Hamburg, Germany. He held a position as Assistant Professor at the Department of Supply Chain Management and Management Science at the University of Cologne, Germany and earned his Ph.D. degree at Münster University, Germany. He worked as strategy consultant and project manager at Booz & Company and conducted research at the National University of Singapore, at Cornell University and at the Israel Institute of Technology.

Ulrich W. Thonemann

Ulrich W. Thonemann is Professor for Supply Chain Management and Management Science at the University of Cologne, Germany. Prior to joining Cologne University he was Professor for Production and Logistics Management at Münster University, Germany, worked as a management consultant at McKinsey & Company, and was Assistant Professor at Stanford University. He earned his Ph.D. and M.S. degrees in the Department of Management Science and Engineering at Stanford University.