基于批量销售的分布式库存管理研究

Optimal and heuristic policies for distribution inventory systems with batch ordering

随着互联网销售、新零售等模式的发展,分布式库存系统在实践中的应用越来越广泛。为加强顾客体验,解决消费者的即时性购物需求,互联网公司通常采用“中心仓+前置仓”模式。前置仓进行小仓囤货以满足消费者即时性需求,并且前置仓库存由中心仓来补货。同时,出于运输方便、规模经济等原因,批量销售也尤为常见。在批量销售情形下,如何同时管理中心仓和前置仓的库存水平已经成为电商企业的痛点。本文首次研究了基于批量销售的分布式库存管理系统,通过建立相应的动态规划模型,证明了在平衡假设下系统具有可分性,即原问题可以分解成若干单级库存管理系统。在刻画了若干强Q-跳凸函数性质的前提下,本文证明可分系统的目标函数具有强Q-跳凸性,从而刻画了在平衡假设下的系统最优策略服从(r,Q)策略。尽管系统可分性大大降低了问题求解的计算量,但是对于大规模问题仍然面临求解困难。因此,本文进一步提出了基于可分性的近视策略,并且证明了该策略的最优条件。

Distribution inventory systems are becoming more and more popular in reality with the development of internet sales and new retailing. As e-retailers rush to fulfill demand, such as next-day and same-day delivery, urban facilities with ready access to major population centers are being rapidly set up, which replenish from distribution centers. The establishment of lead warehouses can meet the personalized needs of consumers and have obvious advantages in quick response of orders and reducing distribution costs. However, due to the uncertainty of demand, the e-retailers who operate lead warehouses face the challenging of inventory management and allocation among different echelons. An effective inventory management can significantly improve the system efficiency, whereas implementing inappropriate inventory policies may result in huge inventory costs. For e-commerce, one of the main problems of operating distribution inventory systems is how to design an efficient and easy-to-implement inventory policy according to the demand information from each echelon. It includes how to make the replenishment policies from the central warehouse to the external suppliers, how to make the replenishment policies from the lead warehouses to the central warehouse, and how to make the inventory distribution policies from the central warehouse to the lead warehouses when the inventory of the central warehouse is limited. At the same time, due to the convenience of transportation and economies of scale, batch orders are particularly common in practice. Therefore, it is of great practical significance to study the distribution inventory systems based on batch ordering. In this paper, we aim to characterize the optimal policy for classic distribution systems with batch ordering. Understanding the structure of the optimal policy can help us to design efficient heuristic policies for more general and complicated distribution systems.In this paper, we study for the first time distribution inventory systems with batch ordering, which consists of a central warehouse and multiple lead warehouses. The lead warehouses replenish inventory from the central warehouse, which can order from the external suppliers. Assuming that the external supplier has no capacity restriction, the sequence of events in each period is as follows:(1) each echelon i places an order for its upstream echelon i+1;(2) each echelon i receives orders from its upstream echelon i+1 placed in advance of Lperiods;(3) random demand of the current period is realized;(4) all echelons meet the demand from their downstream echelons with the inventory on hand as much as possible and pay the corresponding inventory costs. When formulating the problem, we use the following cost accounting scheme for each echelon i: at time t, we charge the inventory holding/shortage cost of echelon i incurred at time t+ L. This cost accounting scheme only switches inventory costs across time periods, so it does not affect the total inventory holdings and shortage costs in the system over the whole planning horizon.By formulating the problem as a dynamic planning model, we show that the original system is decomposable under the balance assumption, that is, the original problem can be decomposed into several single-stage inventory systems. By exploring new properties of strong Q-jump convexity, we can prove that the objective functions of these subsystems are strong Q-jump convex. These new properties may also be helpful to analyze other complicated inventory systems. Based on strong Q-jump convexity of the objective functions, we further characterize the optimal policy of distribution inventory systems with batch ordering, which requires each echelon to implement the classic(r, Q) policy. Specifically, when the inventory level drops below the critical value r, it is optimal to raise the total inventory level as close to the range of [r, r+Q) as possible;otherwise, it is optimal not to order. Although the decomposition property of the system greatly reduces computation efforts, it is still difficult to solve large-scale problems. Therefore, we also propose an approximate policy with less computation complexity and identify its optimal conditions.The theoretical results of this paper are based on the balance assumption. However, the transfer between the lead warehouses is not necessarily immediate and free. Therefore, it is of practical and theoretical significance to study more general distribution inventory systems. Furthermore, the demand of multi-channel is considered, that is, both the lead warehouses and the central warehouses can meet the online and offline demand at the same time, but the experience of consumers is different. How to make reasonable inventory policies according to the different demands of customers and timely inventory level is also a direction for future study.