Optimal operational service levels in vendor managed inventory contracts - an exact approach

Abstract

Vendor Managed Inventory (VMI) contracts are anchored on a fill rate at which the vendor is expected to meet the end-customer demand. Violations of this contracted fill rate due to excess and insufficient inventory are both penalized, often in a linear, but asymmetric manner. To minimize these costs, the vendor needs to maintain an operational fill rate that is different from the contracted fill rate. We model, analyze and solve an optimization problem that determines this operational fill rate and the associated optimal inventory decision. We establish that, for some special, yet popular, models of demand (e.g. truncated normal, gamma, Weibull and uniform distributions), the optimal solution can be derived in closed form and computed precisely. For other demand distributions, either the optimization problem becomes ill-defined or we may need to use approximate solution methods. An extensive computational study reveals that, for realistic values of problem parameters, the operational fill rate is often larger (by as much as 20%) than the contracted service level, possibly explaining the inventory glut commonly observed in real-world VMI systems.