A real-time inventory decision system using Western Electric run rules and ARMA control chart

doi:10.1016/j.eswa.2007.07.019

Expert Systems with Applications

Volume 35, Issue 3, October 2008, Pages 755-761

https://doi.org/10.1016/j.eswa.2007.07.019 Get rights and content

Abstract

Inventory management is an important area of production control. In 1999, Pfohl et al. [Pfohl, H.-C., Cullmann, O., & Stölzle, W. (1999). Inventory management with statistical process control: Simulation and evaluation. Journal of Business Logistics, 20, 101–120] developed a real-time inventory decision support system by using the individual control charts for monitoring the inventory level (i.e., stock quantity) and the market demand, in which a series of decision rules are provided to help the inventory manager to determine the time and the quantity to order. In the present paper, a real-time inventory decision system is proposed by incorporating Western Electric run rules into the decision rules of the system. Since the data of demand sometimes present a pattern of time series (i.e., autocorrelation may exist in the data of demand), in the proposed decision system the ARMA control chart is employed to monitor the market demand and the individual control chart is used to monitor the inventory level. A simulation study is conducted to investigate the effects of demand pattern and autocorrelation on the proposed inventory decision system and to verify the effectiveness of the system. The index “service level” is selected as the key indicator for the system performance. Based on the results of the simulation study, it is shown that the performance of the proposed inventory decision system is quite consistent with service level always greater than 90% for various demand patterns.

Introduction

Among various logistics costs in a company, inventory costs generally amount to almost half of the company’s total distribution dollar expense (Pfohl, Cullmann, & Stölzle, 1999). Many researchers, such as those surveyed by Aggarwal, 1974, Silver, 1981, have developed effective inventory management systems to reduce inventory costs since introduction of Harris’s economic order quantity (EOQ) model in 1915. However, most of these inventory management systems only account for various demand patterns, quantity discounts, stockout costs, lead time variations, and multi-stage and multi-item situations, but few concepts or techniques are suggested for monitoring and diagnosing the performance of the inventory management systems. In their pioneering work, Watts, Hahn, and Sohn (1994) presented a control chart approach for monitoring the performance of a reorder-point inventory system. According to Watts et al. (1994), by monitoring stockouts and control charts for demand and inventory turnover, the inventory manager is able to isolate the causes of system malfunctions such that inventory problems can be identified and resolved quickly and the inventory system can generally be functioning as intended.

Since 1924 when Dr. Shewhart introduced the first control chart, various control chart techniques have been developed and widely applied as a primary tool in statistical process control. The major function of control charting is to detect the occurrence of assignable causes in the process so that the necessary corrective action can be taken before a large quantity of nonconforming product is manufactured. The control chart technique may be considered as the graphical expression and operation of statistical hypothesis testing. Pfohl et al. (1999) developed a real-time inventory decision support system by using the traditional Shewhart control charts for inventory level (i.e., stock quantity) and demand, in which a series of decision rules are provided to help the inventory manager to determine the time and the quantity to order.

Since the data of demand sometimes present a pattern of time series (i.e., autocorrelation may exist in the data of demand), the traditional Shewhart control chart for demand may be inappropriate for practical applications of inventory management. Jiang, Tsui, and Woodall (2000) developed a new control chart, called the auto-regressive moving average (ARMA) control chart, which has been shown suitable for monitoring a set of time-series data. In the present paper, the real-time inventory decision system in Pfohl et al. (1999) is modified, in which the ARMA control chart is applied to monitor the data of demand. Meanwhile, the decision rules given in Western Electric Handbook (1956) are added to the scheme of control charts for enhancing the sensitivity of control charts. In the next section, the real-time inventory decision system given in Pfohl et al. (1999), the ARMA control chart developed by Jiang et al. (2000), and the decision rules by Western Electric Handbook (1956) are briefly reviewed. The proposed modification of the real-time inventory decision system is then presented. A simulation study is conducted to compare the proposed real-time inventory decision system with the inventory decision system of Pfohl et al. (1999). Finally, some conclusions are drawn based on the simulation study.

Section snippets

The inventory decision system

The decision system presented by Pfohl et al. (1999) relied on the assumption that the amounts of inventory and demand quantity are normally distributed. Three standard deviations above and below the means of demand and inventory level are used to construct the upper control limits (UCL) and lower control limits (LCL) for the demand control chart and the inventory level control chart, which will guarantee that for more than 99.73% of all cases, the future ordering and inventory needs can be

Proposed inventory decision system

In the present paper, the concept of inventory decision system presented by Pfohl et al. (1999) is extended by incorporating Western Electric decision rules. In the proposed decision system, the inventory level is monitored by the individual control chart; meanwhile the market demand is monitored by the ARMA control chart.

The proposed inventory decision support system will first check the individual control chart of inventory level at time t. If the chart indicates the inventory level is in

The simulation study

Simulation is a useful technique for studying system behavior with stochastic properties and has been widely applied in various managerial and engineering fields for system improvement, e.g., Chou and Liu, 1999, Chou et al., 2001. In this section, a simulation study is conducted to compare the system performance of the proposed inventory decision system with the system presented by Pfohl et al. (1999). Several indices are selected for the purpose of comparison. The major one is the service

Results and discussion

The simulation results of Pattern 1 (i.e., the data of demand are independently and normally distributed with mean 1000 units and standard deviation 10 units) are shown in Table 1. This is a general data pattern without considering product life cycle and autocorrelation. Based on Table 1, it is noted that the proposed decision system in the present paper obviously has better service level and less cumulative stockout quantity; however, to reach these better performance, the corresponding

Conclusions

Inventory management is an important area of production control. Pfohl et al. (1999) developed an inventory decision system to determine the time and the quantity for ordering by using the individual control charts for monitoring demand and inventory level. In the present paper, a real-time inventory decision system is proposed by incorporating the run rules of Western Electric Handbook (1956) into the decision rules of the system. Since the data of demand sometimes present a pattern of time

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W. Jiang et al.
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View full text

A real-time inventory decision system using Western Electric run rules and ARMA control chart

Abstract

Introduction

Section snippets

The inventory decision system

Proposed inventory decision system

The simulation study

Results and discussion

Conclusions

Computers and Industrial Engineering

A review of current inventory theory and its applications

International Journal of Production Research

Simulation study on the queuing system in a fast-food restaurant

Journal of Restaurant and Foodservice Marketing

A new monitoring method: the ARMA chart

Technometrics