在此研究中，我們探討在C公司的n張訂單與m個供給，其環境為訂單的總需求數量大於公司生產的總供給數量，C公司允諾訂單的機制為採用批次可允諾量以及後向耗用模式，在一固定時間區間內將這一批的顧客需求做拉線的動作以找出哪些訂單是能夠被滿足哪些訂單是不會被滿足的。由於C公司的總供應量小於顧客的總需求量，我們不會允諾全部的需求訂單，所以需要將這些訂單做允諾的優先順序，知道哪些訂單可以被允諾、哪些訂單不會被允諾，以及被允諾的訂單其被供應的數量為多少來達到公司最大的效益，我們的研究目標為在最小持有庫存成本下求最大允諾數量。 為了求出此問題的最佳解，我們使用分支定界演算法以及最小成本最大流量計算最大化的允諾數量以及來計算出我們的目標。 ;Recently, the available-to-promise (ATP) function becomes critical in supply chain management, since it provides appropriate links between production resources and customer orders. In this research, company environment with n demands and m supplies is considered. It is assumed that the total quantity of demands are larger than that of supplies. Batch available-to-promise (batch ATP) and backward consumption mode are applied to commit order promise and fulfillment. Orders are collected periodically, then pegging is at a particular time point in order to find out which order can be promised. The company cannot commit all of demands because the total supplies are smaller than demands which is our assumption. Thus we need to schedule the priority of these orders to find out which order can be accepted or rejected, and the total of accepted demands are then obtained. The company objective is maximizing the committed quantities under minimum inventory holding cost. In order to get the optimal solution for this problem, we present a branch and bound algorithm and the minimum cost maximum flow to get maximum committed quantities.
