313 / 2024-04-24 12:56:41

The Benefits from Service Differentiation: Two-echelon Distribution Network Design with Service Mode Selection

Distribution network design,Service differentiation,Two-echelon inventory replenishment,Submodularity,Polymatroid cutting plane algorithm

（备注：收到了何荣川教授和陆晔教授的邀请）

Classical distribution network design models typically assume exogenous demand and gross profit rate. In practice, however, both demand and profitability depend on various factors such as selling prices, delivery methods, after-sale terms, etc., which are often subject to choices, particularly for companies providing differentiated services. This paper studies the two-echelon distribution network design problem with service differentiation, which is captured by distinct service modes, each could represent any one or any combination of various factors having an impact on demand and profitability. The service modes selection is embedded in network design decisions to simultaneously locate distribution centers (DCs), assign DCs to selected retailers with particular service modes, and replenish inventory for both DCs and retailers, while maximizing the system-wide profit. This problem is formulated as a mixed integer program, which is nonlinear due to the two-echelon inventory replenishment and the impact of service mode selection on demand and profitability. We explore the submodularity of the nonlinear objective function and prove a linearized equivalent reformulation based on the extended polymatroid inequalities. This paper contributes to the literature on general submodular function minimization problems by formally establishing the equivalence between these problems and the extended polymatroid inequalities. To solve the polymatroid reformulation with exponentially many constraints, we employ a cutting plane approach. The corresponding separation problem is efficiently solved in \(O(|I|^2|G|^2)\) (where \(I\) and \(G\) represent the sets of retailers and service modes, respectively) by a tailored algorithm utilizing the structure of its optimal solution. The efficiency of the proposed polymatroid cutting plane algorithm in solving large-size instances is validated in the numerical studies. Through comparisons with benchmarks and sensitivity analysis, the numerical results further demonstrate the benefits from service differentiation in our model and explore the trade-offs between higher and lower degrees of differentiation.