Safety stock placement with market selection under load-dependent lead times

A manufacturer with deterministic, load-dependent lead time supplies multiple warehouses, each serving multiple retailers. Each retailer has access to a set of potential markets with different characteristics.

Serving more markets increases revenues, but also increases the manufacturer's lead time, resulting in higher inventory costs. Adopting the Guaranteed Service Approach, we present a nonlinear mixed integer programming model and reformulate it to eliminate integer variables related to service times at warehouses. We then propose a successive piecewise linearization algorithm and a mixed-integer conic quadratic formulation to solve the resulting nonlinear binary formulation.