سقوط کوتاه پیش فرض های مدل سازی موجودی مشترک : شبکه های درخت وار، تقاضای پواسون و تقریب تک پله ای

Traditional multi-echelon inventory theory focuses on arborescent supply chains that use a central warehouse which replenishes remote warehouses. The remote warehouses serve customers in their respective regions. Common assumptions in the academic literature include use of the Poisson demand process and instantaneous unit-by-unit replenishment. In the practitioner literature, single-echelon approximations are advised for setting safety stock to deal with lead time, demand, and supply variations in these settings. Using data from a U.S. supplier of home improvement products, we find that neither the assumptions from the academic literature nor the approximations from the practitioner literature necessarily work well in practice. In a variation of the strictly arborescent supply chain, the central warehouse at our real company not only replenishes other warehouses but also meets demand from customers in the region near the central warehouse. In this paper, we study this dual-role central warehouse structure, which we believe is common in practice. Using high and low volume product demand data from this company, we use Monte Carlo simulations to study the impact of (1) the use of a dual-role centralized warehouse, (2) common demand assumptions made in multi-echelon research, and (3) single-echelon approximations for managing a multi-echelon supply chain. We explore each of these under both centralized and decentralized control logic. We find that the common assumptions of theoretical models impede their usefulness and that heuristics that ignore the actual supply chain structure fail to account for additional opportunities to utilize safety stock more effectively. Researchers should be aware of the gap between standard assumptions in traditional literature and actual practice, and critically evaluate their assumptions to find a reasonable balance between tractability and relevance.

The motivation for this article derives from work with a U.S. supplier of home improvement products. BIGCO, as we call it, had been struggling with the management of inventory in its multi-echelon supply chain which serves customers in North America. The firm invested in a state-of-the-art inventory control system that offered nearly real-time inventory information and statistical inventory control logic, but the algorithms were based on traditional assumptions and heuristics that were inconsistent with the actual structure and nature of the company's supply chain. The result was that the firm required large stores of inventory in order to maintain desired service levels. We seek insights into why the theoretical calculations in traditional inventory literature are practically useless in an actual multi-echelon inventory system and how future research might be made more relevant. We introduce an alternate supply chain structure—the dual-role central warehouse—common in industry but ignored in literature. In doing so, we address a problem relevant to academics and practitioners alike. We review existing inventory literature to understand the analytical models available to BIGCO and then develop a simulation with structure and parameter values to reflect its managerial situation. Using historical demand data from this company, we assess BIGCO's current approach compared with exact and heuristic models as suggested by prior literature. We also compare these methods with an optimal policy that we find through simulation. Managing multi-echelon inventory has been a popular topic since a seminal article by Clark and Scarf (1960). A significant part of the literature can be characterized as highly theoretical with a focus on determining the structure of optimal policies or establishing a control logic that balances the flow of inventory between a central warehouse and a set of remote sites that serve regional customers. Although most theoretical inventory literature remains too abstract to be of use in a real-world setting, an interesting and definitive article published by Gallego et al. (2007) prescribes a concrete logic for managing inventory in the common setting of a warehouse that serves a set of satellite warehouses, which in turn support regional customers. This setting is commonly referred to as an arborescent network design. These authors develop scenarios of both local and centralized control and find “fast, transparent, effective, and robust heuristics and approximations” (Gallego et al., 2007, p. 503) for managing these systems. Their article contrasts with most research, in that it provides managers with actual guidance for how to use arborescent inventory systems to determine optimal policies. However, for tractability the authors make some significant assumptions related to the network structure, demand distribution, lot size, lead time, and control logic, comparable to those made by others doing similar research. In our research, we test the applicability of this practical work to a real-world setting with (some significant) differences in the assumptions. Our objective is to evaluate how assumptions significantly influence the relevance of research to real-world applications. Specifically, the key assumptions and policies we test are (1) the supply chain structure, (2) the demand distribution, and (3) the use of a single-echelon approximation to manage a multi-echelon supply chain. The first two of these assumptions are common in the academic literature while the third is common among practitioners. We explore the performance implications of each under both centralized versus decentralized control. In our literature review, we show how these assumptions are used in seminal articles published in the past 50 years. We argue that researchers should be aware of the gap between standard assumptions in traditional inventory literature and actual practice, and evaluate critically their assumptions to find a reasonable balance between tractability and relevance. Our research contributes to actual practices of operations and supply chains by (1) providing a detailed description of the practices in a particular firm that has a common supply structure not addressed in the literature, (2) identifying the lack of theory to explain the observed supply chain structure, and (3) performing simulation experiments to evaluate the impact of various operational changes on performance.

In this research, we test the practical validity of some of the few existing theoretical models that provide operational guidance. We find that analytic models essentially are useless for determining optimal policies for our real-world setting, and for assessing the benefit to our test firm of (1) accounting for the dual role of a central warehouse, (2) not using a single-echelon approximation, and (3) moving to a centralized control system. Our results help identify the lack of theory to provide assistance to managers as they control inventory in a common supply chain structure and thus identifies a problem relevant to academics and practitioners. In addition, our study provides some insights into the advantages of different control structures for managers in a setting with a central warehouse in a dual role, by exploring the effects of alternative structures through use of a simulation of original data from a real company. Using draws from historical demand data from this company, our simulation indicates for this company that (1) moving from a non-dual to a dual role lowers inventory approximately 9% (from 34,967 to 31,695), (2) moving from the single-echelon approximation lowers inventory approximately 32% (from 46,946 to 31,695), and (3) moving to centralized control lowers inventory approximately 3% (from 34,967 to 33,814). Thus, the greatest benefit arises from recognizing the limitations of the single-echelon approximation for setting safety stock levels. Interestingly, the move to a dual role provides more benefit than a move to centralized control. The dual-role central warehouse provides an opportunity for pooling in a manner that has not been studied in the academic literature. While the tool that we use to find these optimal policies would not be of practical value for managing a large scale system, our results suggest that there is an opportunity for academics and practitioners to develop more robust models and tools for real world settings such as that at BIGCO. The current single-echelon approximations that are commonly used in commercial software packages and described in common textbooks fall short; current technology that employs real time multi-echelon data is not being used to the extent possible for the intelligent control of the inventory in these systems. Academic research should focus on developing clever and easily implemented logic that can take advantage of the available information to provide robust solutions. A new type of single level control logic that includes parameters that better capture the actual demand distribution being experienced (such as the median, maximum, and minimum) might be valuable. Systems that use heuristics that “learn” appropriate safety stock levels over time might also be possible. The dual-role structure that we identified reveals some interesting questions that relate to the positioning of inventory in a multi-echelon system. How much volume and what characteristics would indicate that customer demand should be served directly from a central warehouse? We doubt that the best solution is simply to distribute centrally or purely regionally. Rather, customers might need to be segregated, some served centrally and others regionally. Companies appear to be using these hybrid strategies, but this has not been studied in the academic literature. Developing strategies for how to segregate customers and/or products to central and regional sites might be a good avenue for future research. Our simulation is not without limitations. We were unable to get data for actual service levels, and thus had to take for granted our SME's assessment that the company generally achieved its desired 98% service level. In fact, service level data would be helpful to validate our simulation, but also to investigate more deeply the relationship between inventory levels and service levels. In addition, as might be expected in any real-world situation, the data received was not perfectly clean. For example, we were provided inventory levels, order receipts, and shipments and yet, unfortunately, the simple inventory identity “Ending Inventory = Beginning Inventory + Receipts − Shipments” did not always hold. The other key limitation to our simulation is that it is the study of only a couple of products at one firm. While we believe that the supply chain structure at BIGCO is relatively common, our results cannot definitively speak for firms in general and there remain opportunities to explore these issues at other firms. This paper identifies the need to develop solutions to problems that have significant differences from those found in the literature. The assumption of pure arborescent supply chain needs to be relaxed and the dual-role explored. While solving models that assume certain demand distributions solves problem associated with solution tractability, our research shows that more general demand distributions need to be assumed. Finally, practitioners need quick and robust procedures (possibly heuristic) that take advantage of information available in today's ERP systems.