The Benefit of Altruistic Behaviour Achieved By the Out Policy With Unmatched Proportional Feedback Gains in a Two-Echelon Supply Chain

Abstract

We study a two echelon supply chain with AR(1) demand and unit replenishment lead-times. Each echelon of the supply chain uses conditional expectation to generate MMSE forecasts. Both echelons use these forecasts inside the "Order-Up-To" policy to generate replenishment orders.

We investigate 3 different scenarios: The first is when each echelon aims to minimize their own inventory holding and backlog costs. The second scenario is concerned with an altruistic retailer who is willing and able to sacrifice some of his own performance for the benefit of the total supply chain. He does this by smoothing the demand he places on the manufacturer by using a matched proportional controller in the inventory and WIP feedback loops. The third scenario is concerned with an altruistic retailer with two unmatched controllers. The matched controller case outperforms the traditional case by 14.1%; the unmatched controller case outperforms the matched controller case by 4.9%.

Keywords: supply chains, multi-echelon inventory, order-up-to policy, collaboration, altruistic behavior

JEL Classification: C22, E23, E27, E37