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-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.

我们研究了兼具市场选择决策的供应链安全库存布设问题。一家采用确定性、依赖负荷提前期模式的制造商为多个仓库供货，每家仓库服务于多家零售商。每家零售商均可接入一组特征各异的潜在市场。
拓展服务的市场数量可提升营收，但同时会延长制造商的提前期，进而推高库存成本。本文采用保障服务法（Guaranteed Service Approach），构建了非线性混合整数规划模型，并通过重构消去了与仓库服务时长相关的整数变量。随后，我们提出了逐次分段线性化算法与混合整数锥二次规划形式，以求解所得的非线性二进制规划模型。计算实验表明，逐次分段线性化算法的性能优于两款当前主流最优求解器——BARON与CPLEX，二者分别用于求解原始规划形式与混合整数锥二次重构形式的算例。当产能相对于可用需求较为紧张时，纳入依赖负荷提前期模型的收益最为显著；当产能紧张且边际收益相对较低时，整合市场选择与安全库存决策的收益最为突出。