Inventory control with and without deliveries in several pieces
研究复合泊松需求下，允许自动分批交货（有成本）与禁止分批交货两种库存系统的成本差异，并比较标准模型，为管理者选择交货策略提供依据。
An inventory system is operated as a base stock system under a compound Poisson demand process. Besides having inventory and backorder costs, also a cost is incurred for each order that is delivered in several pieces to the customer (irrespective of whether some items in the order are delivered on time, or whether they are all delivered late but at different times). The possible split deliveries are assumed to happen automatically, meaning that there cannot at the same time be a positive on-hand inventory and a positive backlog. We develop a mathematical cost expression for this system to be optimized, denoted Model 1. We compare Model 1 to another model, denoted Model 2, where it is forbidden to make any of these split deliveries; thus at the same time, there can be a positive on-hand inventory and a positive backlog. We compare Model 2 to the standard textbook model, denoted Model 0, where split deliveries occur automatically and are costless. Thereby, we address a claim made by Zipkin (Foundations of inventory management. McGraw-Hill, Boston, 2000). We also examine the threshold value for the delivery split cost, which makes Model 1 and 2 perform equally well, and we examine how this threshold value depends on the other common parameters of the models.