考慮搬運產能限制下之最佳分區設計與合併補貨問題

Abstract

合併補貨問題(Joint Replenishment Problem, JRP)藉由決定各產品之補貨週期、補貨數量與補貨次數，使平均總成本最小化。本研究將探討在一般整數策略下，「考量搬運產能限制下之最佳分區設計與合併補貨問題」，探討如何對於補貨的需求點/顧客進行最佳的分區設計，對於每一分區中的所有需求點進行合併補貨。而且在每一分區的合併補貨問題中，本研究加入搬運設備運轉產能時數上限的考量；即每一分區的JRP數學模式中，必須增加搬運產能的限制式。針對上述的決策情境，本研究將提出考量搬運產能限制下之最佳分區設計與合併補貨問題之數學模式，進行完整的理論分析，並提出一混合式基因演算法為整體求解架構，不僅求解最佳分區，同時結合自行發展的一套搜尋最佳分區JRP批量與排程之演算機制，求得在滿足搬運產能可行性限制之下的最佳分區及各分區之最佳基本週期(B值)，每個需求點/顧客對各產品的補貨週期乘數與對應之補貨排程期別。運用隨機數據實驗，驗證本研究所提出演算法為求解考量搬運產能限制下之最佳分區設計與合併補貨問題的一個有效率的求解方法。

The joint replenishment problem (JRP) determines the replenishment cy-cle time and lot size of each item so as to minimize the total costs per unit time. In this study, we investigate a problem that combines the delivery zone-design problem for all demand sites/customers and the joint replenishment problem under the general-integer policy. Different from the conventional JRP, we consider that the material handling facility has a capacity limit. Therefore, for each delivery-zone, the mathematical model for the JRP problem is augmented with a set of capacity constraints. We formulate a mathematical model for the concerned problem, and conduct full theoretical analysis for the mathematical model. Our results facilitate in proposing a hybrid genetic algorithm (GA) that not only seeks for an optimal zone design, but also incorporates with a search procedure for solving the JRP with material-handling capacity constraints. Following our numerical experiments, we demonstrate that the proposed hybrid GA is an effective solution approach for solving the concerned problem.