بهینه سازی تصمیمات گروه بندی موجودی ABC

Inventory managers often group inventory items into classes to manage and control them more efficiently. The well-known ABC inventory classification approach categorizes inventory items into A, B and C classes according to their sales and usage volume. In this paper, we present an optimization model to enhance the quality of inventory grouping. Our model simultaneously optimizes the number of inventory groups, their corresponding service levels and assignment of SKUs to groups, under limited inventory spending budget. Our methodology provides inventory and purchasing managers with a decision-support tool to optimally exploit the tradeoff among service level, inventory cost and net profit. The model and solution are applied for an inventory classification project of a real-life company, and outperform the traditional ABC method. Computational experiments are performed to obtain managerial insights on optimal inventory grouping decisions.

A manufacturer often keeps inventory of various raw materials and components to meet production needs. A repair shop needs to ensure availability of different parts for replacement and maintenance work. A retailer usually holds certain amount of various merchandize to satisfy market demand. A hospital must keep sufficient medical supplies of all kinds for its clinical and operational needs. In the above inventory systems, the number of stock keeping units (SKUs) may be so large that it is often not practical to control them individually (Ernst and Cohen, 1990). One way to manage a large number of SKUs is to aggregate them into different groups, and set common inventory control policies for each group (Chakravarty, 1981). Grouping provides management with more effective means for specifying, monitoring and controlling inventory performance. From the operational perspective, grouping may achieve more efficient inventory management by reducing the overhead of managing each inventory group. Inventory policies also align better with item groups than each individual item. For instance, inventory groups with different service levels often reflect a company's order fulfillment strategy and customer relationship policies, e.g., the service level agreement (SLA). Service levels have a direct impact on the company's revenue and profit. A well-known implementation of the inventory grouping idea is the ABC classification method widely used in industry. It was first developed by GE in the 1950s (cf. Flores and Whybark, 1986 and Guvenir and Erel, 1998). In a typical ABC approach, one classifies inventory items according to their transaction volume or value. A small number of items may account for a large share of volume; an intermediate category may have a moderate percentage of volume; and a large number of items may occupy a low proportion of volume. These categories are labeled A, B and C. Taking insights from Pareto (1971), it is often found that a small percentage of the inventory items contribute to the majority of a company's sales and revenue. This has led to the 80–20 rule. That is, the top 20% of items are given the A classification, the next 30% of items the B classification and the bottom 50% the C classification ( Flores and Whybark, 1986). Alternatively, Juran (1954) claims that A-items are the highest 5% of the items in dollar value, C-items are the bottom 75% and B items are the middle 20%. Practitioners often employ the ABC classification scheme in a three-step approach to control inventory. First, SKUs are grouped into categories according to their sales volume. Second, inventory policies, e.g. the target service levels, are determined for each group. A common wisdom to determine the service level is that one should concentrate on the A category to enhance managerial effectiveness. As a rule-of-thumb, the A-class items get the highest service level settings and C-class the lowest (Armstrong, 1985). Finally, inventory managers, in collaboration with sales management and finance, need to make sure that the inventory control policy is feasible within the available inventory and management budget. The above ABC inventory grouping and control approach has several disadvantages. (a) According to Teunter et al. (2010), there is no clear guideline in the literature to determine the service level for each group. (b) Since the grouping decision is made independent from and before the service level decision, their interactions have not been exploited, thus neither of the two decisions can be optimal. (c) Because the available budget was not considered until the last step, there is no guarantee that the grouping and/or service level decisions made in the first two steps are feasible. Thus one often needs to iteratively revise the grouping and/or service level decisions until feasibility is reached. This can be a tedious process for a large number of SKUs, and may lead to sub-optimal solutions. These deficiencies have motivated us to develop a new optimization approach to enhance the existing ABC inventory grouping and control decisions. Our model and solution will help inventory and operations managers to simultaneously optimize: (i) the number of classification groups for the SKUs; (ii) optimal assignment of each SKU to a group; (iii) target service level for each group; and (iv) optimal allocation of available inventory budget to groups of SKUs. These decisions are made to maximize the total net profit, subject to explicit inventory budget constraints. We have implemented our methodology for an industrial products’ distributor using real-life inventory data. The remainder of this paper is organized as follows. Section 2 reviews the related research literature and highlights contribution of our work. Section 3 formally describes the addressed optimization problem and presents a mixed-integer linear programming (MILP) formulation to model it. In Section 4, we provide a case study of our approach on a real-world inventory grouping application. A comprehensive computational experiment is conducted to further examine the behavior and performance of our model when problem parameters vary. The computational results and managerial insights are presented in Section 5. Finally, Section 6 draws conclusion and discusses future research directions.

In this paper, we have developed an optimization model to simultaneously determine inventory groups, their corresponding service levels and assignment of SKUs to groups. It generalizes and enhances the well-known ABC inventory grouping approach by offering integrated, automated and optimized solutions. Our model differs from the existing optimization models in the literature with two distinctive features. First, rather than minimizing inventory cost, our model maximizes the profitability of a company. Second, our solution optimizes the tradeoff between inventory cost and profit, and optimally allocates the inventory budget to SKUs. Our approach may also serve as an SKU rationalization tool to help inventory managers decide which SKUs should better to be kept out of stock. Our optimization model and solution are applicable to companies and organizations in various industries: manufacturing, distribution, retail and health care. We have implemented our methodology for a real-life company who distributes thousands of industrial products to business customers. Solution offered by our model has improved the company's total net profit by 3.85%, compared with past ABC solution implemented at the company. Our solution helps better manage inventories by optimally assigning service levels to SKUs and determining with SKUs should be rationalized out of stock. Moreover, the sensitivity analysis provided by our approach helps inventory managers to quantify the impact of inventory spending and inventory group management cost on the optimal inventory grouping decision and profitability. Through a comprehensive computational experiment, we have obtained several managerial insights about optimal inventory grouping and control strategy. (i) When the management cost per group can be reduced, it is optimal to differentiate service levels for SKUs by classifying them into more granular groups. (ii) Our solution shows a diminishing return of inventory spending on the net profit, and can help a company quantify and justify the benefit of increasing inventory budget. (iii) We find that there is more incentive to increase the number of inventory groups when the available inventory budget is tight; whereas when there is plenty of budget available, it might be acceptable to aggregate SKUs into a small number of groups as in the traditional ABC approach. The capability of being able to optimally allocate limited inventory spending among SKUs is of importance in today's completive business environment. Our work has the following limitations, which also opens the door for future study. Firstly, our current model is a one-period static model. Although it can be implemented in a rolling horizon fashion as shown in Section 5.2, it will be interesting to develop a multi-period dynamic inventory grouping model that directly optimizes the grouping decisions taking the future demand projection and trend into consideration. Secondly, the current model is based on a deterministic optimization approach, which can be improved by an integrated simulation–optimization approach to optimize inventory grouping decisions under uncertainty. In addition, due to limited availability of data, our computational study has focused on the model with single-objective. We plan to continue working with our industrial partners on inventory grouping optimization with multiple criteria. It is also our plan to consider other practical inventory management settings such as quantity discounts, perishable SKUs, and variable overhead management cost per inventory group as a function of the number of groups, the number of SKUs or volumes in each group.