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

We study the problem of safety stock placement in a supply chain with market selection decisions. 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. Computational experiments show that the successive piecewise linearization algorithm outperforms two state-of-the-art solvers, BARON and CPLEX, which are used to solve instances of the original formulation and the mixed-integer conic quadratic reformulation, respectively. The value of incorporating load-dependent lead times is greatest when capacity is limited relative to available demand. The benefit of integrating market selection and safety stock decisions is greatest when capacity is limited and marginal revenue is relatively low.