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An Exact Analysis of a Joint Production-Inventory Problem in Two-Echelon Inventory Systems

机译：两级库存系统中联合生产库存问题的精确分析

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摘要

We consider a two-echelon inventory system with a manufacturer operating from a warehouse supplying multiple distribution centers (DCs) that satisfy the demand originating from multiple sources. The manufacturer has a finite production capacity and production times are stochastic. Demand from each source follows an independent Poisson process. We assume that the transportation times between the warehouse and DCs may be positive which may require keeping inventory at both the warehouse and DCs. Inventory in both echelons is managed using the base-stock policy. Each demand source can procure the product from one or more DCs, each incurring a different fulfilment cost. The objective is to determine the optimal base-stock levels at the warehouse and DCs as well as the assignment of the demand sources to the DCs so that the sum of inventory holding, backlog, and transportation costs is minimized. We obtain a simple equation for finding the optimal base-stock level at each DC and an upper bound for the optimal base-stock level at the warehouse. We demonstrate several managerial insights including that the demand from each source is optimally fulfilled entirely from a single distribution center, and as the system's utilization approaches 1, the optimal base-stock level increases in the transportation time at a rate equal to the demand rate arriving at the DC.
机译：我们考虑一个两级库存系统，其制造商在一个仓库中运作，该仓库提供满足多个来源需求的多个配送中心（DC）。制造商的生产能力有限，生产时间是随机的。每个来源的需求都遵循独立的泊松过程。我们假设仓库和配送中心之间的运输时间可能是正数，这可能需要在仓库和配送中心都保持库存。两个梯队的库存均使用基本库存策略进行管理。每个需求源都可以从一个或多个配送中心采购产品，每个配送中心产生不同的履行成本。目的是确定仓库和配送中心的最佳基本库存水平，并确定配送中心的需求来源，以使库存持有，积压和运输成本之和最小。我们获得一个简单的方程式，用于找到每个配送中心的最佳基础库存水平以及仓库中最佳基础库存水平的上限。我们展示了一些管理方面的见解，包括可以完全从单个配送中心完全满足每个来源的需求，并且随着系统利用率的接近1，最优的基础库存水平在运输时间中以等于到达需求率的速率增加在DC。

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