Evaluation of Diverse Inventory Policies Using Simulation and Design of Experiment

Transcription

1 Evaluation of Diverse Inventory Policies Using Simulation and Design of Experiment Siri-on Setamanit Faculty of Commerce and Accountancy, Chulalongkorn University, Bangkok, Thailand Abstract--The importance of inventory management has been evident for a long time since inventories are not only necessary for operations, but they also contribute to customer satisfaction. However, holding inventory comes with costs such as inventory carrying cost and opportunity cost. Therefore, it is vital for a firm to find way to manage its inventory to maximize customer service, minimize total investment, and maintaining operation efficiency. Unfortunately, these three objectives are frequently in conflict with each other. In this paper, the author presents a simulation-based approach to evaluate the impact of continuous and periodic review policies on supply chain performance measures including cost and service level. This simulation model is served as an experimental platform for manager to evaluate diverse inventory policies for different products under different circumstances. For the case study company, continuous and periodic review policies provide relatively the same costs given the same service level. Furthermore, this paper also applies Design of Experiment (DOE) to an inventory simulation model. DOE is used to investigate factors that affect performance including variation in demand, lead time, and review interval, and to analyze the interaction of these factors. All three factors affect total costs but in different magnitude. Interaction between lead time and review interval is also significant. The results of the experimentation enables managers to gain better understanding of different inventory policies and be able to select the configuration that best suit the company s objective. I. INTRODUCTION The importance of inventory management has been evident for a long time since inventories are not only necessary for operations, but they also contribute to customer satisfaction. Generally, inventory is one of the important investments in all firms, ranging from a merchandise distributor to a manufacturer. Most of the firms including manufacturing and service companies will carry some amount of inventories. The main reason is that each of these firms needs to hold inventory in order to satisfy its customers or production requirements. Nevertheless, at the same time it is also trying to reduce inventory level held in order to minimize total inventory costs, which include: 1) Holding or carrying costs which are related to physically having items in storage, 2) Ordering costs which are the costs incurred when ordering and receiving inventories, and 3) Shortage or stockout costs which incurred when demand from customer exceeds the supply of inventory on hand One can see that it is very important for a firm to find way to manage its inventory to maximize customer service while trying to minimize total costs. To satisfy these objectives, manager usually needs to answer 2 questions which are when an order for additional items should be placed and how many items should be ordered each time [3, 6]. There are several inventory control models being developed to help determine the appropriate inventory policy that will answer the above questions. The two popular inventory policies are continuous review policy or (Q, r) policy and periodic review policy or (s, S) policy [10]. With continuous review policy, the inventory level will be reviewed continuously and the order will be placed when the inventory level reaches a particular level or reorder point (r). The order quantity (Q) is usually predetermined by using several models such as basic economic order quantity (EOQ) model. In general, computerized inventory systems are needed in order to review inventory at all time. On the other hand, under periodic review policy, inventory will be reviewed at regular intervals such as every day or week. Then, appropriate quantity is ordered after each review. The quantity ordered is equal to the difference between S (order-up-to level) and the current inventory level. If the current inventory level is more than s (reorder point), no order will be placed. This inventory policy is usually employed when it is impossible or inconvenient to frequently review inventory and place orders if necessary. In general, continuous review policy is believed to be more flexible and tends to provide lower total costs than periodic review policy, especially when demands are dynamic. However, periodic review policy is more preferable in practice since it is easier to manage and control. The saving in the administrative costs could make up for higher inventory carrying costs [7]. In order to determine which inventory policy would be appropriate for an organization, a simulation model can be use to evaluate the effect of these policies, thus, providing information for manager to make a decision. There are many studies that use computer simulation to study and analyze inventory control systems. For example, Cerda and Monteros used simulation to evaluate a (R,s,Q,c) multi-item inventory replenishment policy for a cardboard box marketing firm and found that the proposed policy can reduce total investment and maximize customer service, while maintaining the business efficiency [2]. Merkuryeva and Vecherinska used simulation to compare between (s, Q) and (R, S) replenishment policies in multi-echelon supply chains [7]. Larson used simulation to investigate the impact of different inventory and production policies [4]. Morrice et al. used simulation model to explore the relationship between on-time delivery in the major supply chain segments and on-time delivery to the customer where there are significant inventory and WIP level changes and also evaluate supply chain production and inventory control 2345

2 policies and the impact of lead time reductions [8]. Xudong et al. developed a simulation-based approach to evaluate the impact of different configuration of inventory policies on total supply chain cost and customer service level [12]. These studies used simulation to evaluate different configurations and attempt to identify the most suitable configuration for the inventory system by answering what if questions. However, to identify the optimal or most suitable configuration, one has to manually vary decision variables, run simulation, obtain performance result, and redo the process again until one is satisfied. This process is more or less similar to trial and error and requires extensive time and effort, and may not yield optimal result. In an attempt to overcome these weaknesses, a new methodology called simulation optimization has been introduced. Simulation optimization is used to determine the best values for the decision variables of the system that maximize or minimize a single or multiple performance measures. It is a process of searching for the best decision variable values from among all possibilities without performing a complete evaluation search [1]. This makes it easier and quicker for researchers and practitioners to identify the optimal inventory policy under different conditions/circumstances. In author s previous research [9], a simulation optimization method was used to identify the optimal parameters for periodic inventory policy for a case study company. The simulation model was developed by using ARENA simulation package together with OptQuest. The study shows that the configuration suggested by simulation optimization results in approximately 35% saving in total costs comparing to solution developed by analytical model, given the same service level. This paper is a continuous work which will use a simulation-based approach to analyses the impact of continuous and periodic review policies on case study company s performance including cost and service level. Furthermore, Design of Experiment (DOE) will also be used to identify important factors that affect inventory performance and analyze the interaction of these factors. This will help manager gain better understanding of different inventory policies and be able to select the configuration that best suit the company s objective. The rest of this paper is organized as follow: Section 2 describes a background of a case study company and a simulation model. Section 3 shows the comparison of the performance using continuous and periodic review policies. Section 4 discusses the use of DOE and the findings. Conclusions are provided in Section 5. II. CASE STUDY BACKGROUND A case study company is a beverage manufacturer which produces and sells more than 40 products all over the country. There products are distributed via company owned distribution center (DC). In general, the DC orders products from the factory, stores them at its facility, and waits for customers (agents or retailers), who then sell the products to consumers, to pick them up. There are 6 items that are distributed via this DC. Based on the ABC analysis, there is 1 item that represents 75% of the annual sale value. The current inventory policy used is periodic review or fixed order interval system (s, S). At the beginning of each week, the manager of the DC reviews weekly sale forecast together with the space available in the DC, and decides on the quantity to order by using his/her own experience. Most of the managers tend to maintain high level of inventory to prevent stockout problem. In previous study [9], simulation optimization method was used to identify the optimal values for reorder point (s) and target inventory or order-up-to-level (S). It was found that the parameters suggested by simulation optimization can help the company reduce total costs while maintaining the service level. For this study, the company would like to further examine whether the company should consider using continuous review policy or (Q, r) policy as often suggested by the literatures. In addition, the company also would like to better understand the impact of different factors/conditions on performance measures such as costs and service level. This can help company make better decision on its inventory policy. A. A Simulation Model The discrete-event simulation software package, ARENA, is used to construct a simulation model for a case study company s inventory management system. There are 2 models to represent different inventory policies. The first model is constructed to represent periodic review policy where DC evaluates its inventory level every certain period (predetermined 1 week in this case) and place an order. The quantity order will be equal to the difference between S (order-up-to level) and the current inventory level. If the current inventory level is more than s (reorder point), no order will be placed. Detailed information on how this model works can be found in [9]. For continuous review or (Q, r) model, inventory level will be evaluate every time the demand (the transaction) occurs. The company places an order when current inventory level is equal to or less than the reorder point (r). The quantity order is fixed at Q units every time an order is placed. For this study, simulation model will be run for 52 weeks (approximately a year) for both cases. Note that the parameters including s, S, Q, and r will be determined by using OptQuest (optimization tool). B. Data Collection Weekly customer demand was collected for 2 years (104 data points). The weekly demand is normally distribution with a mean of 157,812 units and a standard deviation of 38,566. The lead time is uniformly distributed with a minimum of 1.5 weeks and a maximum of 2 weeks. For cost information, the ordering cost and the inventory carrying cost were calculated using information from the company annual performance report. Ordering cost is 766 Baht per order, while inventory carrying cost is estimated to be 0.47% of the unit cost (or 1.65 Baht) per unit per week. Shortage cost was 2346

3 derived from the interview with the manager, which equal to 5 Baht per unit per week. C. Performance Measure The key performance measures are average total cost per week and the fill rate. Average total cost per week measures the cost effectiveness of the policy, while fill rate represents customer service level. The better and more effective inventory policy will contribute to lower average total cost per week and higher fill rate. The average total cost per week consists of three major costs which are average ordering cost per week, average inventory carrying cost per week, and average stockout cost per week. Detailed formulas can be found in [9]. The other performance measure is fill rate which is a fraction of the demand that can be satisfied from on-hand inventory. This measure represents the ability to satisfy customer. The higher the fill rate, the better the customer service level. In this study, we will focus on the unit fill rate which is calculated as follow: For each simulation run, the model will automatically calculate the average total cost per week and the fill rate. This will make it easier for performance comparison of different inventory policy. D. Model Verification and Validation Several verification techniques suggested by [5] including structure walkthrough, running the model under simplify assumptions and under a variety of the input parameter, and output traces were used to verify the model. In addition, the result from analytical model is also used to compare with the simulation result to ensure that the model performs correctly. Animation was not considered in this case since it is irrelevant to the nature of the problem. For model validation, face validity was evaluated. In addition, the author also compares the results of the model against reference behavior pattern (real world performance). It was found that the model result is consistent with the real world data. (1) III. CASE STUDY RESULTS PERFORMANCE COMPARISON The case study company would like to examine the performance of continuous review policy or (Q, r) policy and periodic review policy or (s, S) policy before making decision whether to change its inventory policy to continuous review policy. Therefore, the two simulation models were used to simulate the performance of each policy. The replication length is 52 weeks which is approximately equal to one year. The number of replications was set to 30 replications. OptQuest was used to find the best inventory policy that will minimize the average total cost while maintaining 90% service level. Therefore, the objective of the optimization problem is to minimize the average total cost. The constraint is that the fill rate should be equal to or more than 0.9. For continuous review policy, the control variables are the reorder point (r) and the quantity ordered (Q). For periodic review policy, the reorder point (s) and the order-up-to level (S) are control variables. The review interval is set to 1 week as in practice. The parameters obtained from optimization for each policy are shown in Table 1. The average total costs from periodic review policy and from continuous review policy are not statistically significant different at 0.05 level. Thus, one can conclude that both policies lead to approximately the same total costs. The case study company can still use periodic review policy and do not need to invest in implementing continuous review system. Table 1 shows the results from these two policies. To further examine the effectiveness of the two policies under different conditions, the experimentation on the effect of the variability in demand is performed. As mentioned before, The weekly customer demand is normally distribution with a mean of 157,812 units per week and the standard deviation of 38,566, which means that the coefficient of demand variation is approximately Therefore, the standard deviation of customer demand is changed to 15,781 to represents situation with low variability in demand (coefficient of demand variation is 0.1). For the case of high variability in demand, the standard deviation of customer demand is changed to 63,124 (coefficient of demand variation is 0.4). The simulation model for each policy is used to simulate the performance. The number of replications is set to 30 replications. Note that simulation optimization is also conducted to identify optimal parameters TABLE 1: RESULT COMPARISON OF PERIODIC AND CONTINUOUS POLICIES Policy Average Total Reorder Point Order-Up-To Quantity Cost per Week (s or r) Level (S) Ordered (Q) (Baht) Unit Fill Rate Periordic Review 251, , , % Continuous Review 241, , , % Differe nce -1.85%* 2.51%* * not significant different at 0.05 level 2347

4 TABLE 2: LOW VARIABILITY IN DEMAND (0.1) AND RESULT COMPARISON Policy Average Total Reorder Point Order-Up-To Quantity Cost per Week (s or r) Level (S) Ordered (Q) (Baht) Unit Fill Rate Periordic Review 234, , , % Continuous Review 194, , , % Difference -5.73% 1.93% TABLE 3: HIGH VARIABILITY IN DEMAND (0.4) AND RESULT COMPARISON Policy Average Total Reorder Point Order-Up-To Quantity Cost per Week (s or r) Level (S) Ordered (Q) (Baht) Unit Fill Rate Periordic Review 277, , , % Continuous Review 184, , , % Difference -5.63%* 1.98%* * not significant different at 0.05 level in each case before running the simulation. Table 2 and 3 shows the result comparison of these two policies under different variability in demand condition. The effect of demand variation in general is similar to the result from previous study [9] such that high variability in demand contributes to high average total cost per week. One can see that the average total cost per week of both periodic and continuous review policies increase to 361,640 Baht and 382,010 Baht, compared to 304,320 Baht and 298,700 Baht consecutively when coefficient of demand variation increases from 0.25 to 0.4. However, when comparing the result from each policy when demand variability is high, average total cost per week from both policies are not statistically significant different at 0.05 level. Although, in low variability in demand situation, the average total cost per week of continuous review policy is lower than that of periodic review policy (259,750 Baht vs. 275,530 Baht), the cost reduction is relatively small. Therefore, it is not worthwhile for the company to invest in the new system in order to gain the benefit of continuous review policy. Based on the finding discussed above, the case study company decides to continue using periodic review policy since the performance is relatively similar to the continuous review policy. To further understand the impact of factors/conditions on the performance of the periodic review policy, design of experimentation (DOE) is conducted and shown in the next section. This finding from DOE can help manager configure the policy to gain even better performance. IV. DESIGN OF EXPERIMENT (DOE) The focus of the experimentation is to find out which parameters or factors have the greatest impact on the total cost (average total cost per week). In order to efficiently and effectively answer the above question, a systematic approach for analyzing model results is needed. Design of Experiments (DOE) is a statistical technique for organizing and analyzing experiments. DOE is often used with simulation models to examine the impacts of changes in parameter values on the outcome measures of interest. Subtle interactions in a complex system can also be revealed by performing DOE [11]. In DOE, the factors are the parameters that are varied (independent variables) which are under experimenter s control, while the responses are dependent variables or the variables of interest, which is average total cost per week in this case. Factors may be model parameters that could be modified to represent different policies such as review interval or different conditions/environments such as variability in demand and lead time. The 2 k factorial design is one of very useful form of DOE techniques. Each of the k factors is allowed to take on two values (high and low). It has been proved to be economical and effective in revealing interaction effects [5, 11]. Therefore, this study will use 2 k factorial design to evaluate the effect of several parameters on the performance of periodic review policy. More information about design of experiment can be found in [5]. A. Factorial Design Based on the literatures and discussion with manager at the case study company, three factors believed to impact the performance of the periodic review policy are identified. These factors includes variability in demand (coefficient of demand variation CODVAR), lead time (time required for factory to send products to DC once order is placed - LT), and review interval (INT). Therefore, a 2 3 factorial design with 10 replications for each design point (a modest sample size from a statistical viewpoint [5]) for a total of 80 runs. The response (dependent) variable is the average total cost per week. Note that service level (fill rate) is not considered since the policy of the company is controlled to keep fill rate at approximately 90% in all case. Table 4 shows the factors and their levels. 2348

5 TABLE 4: EFFECT OF VARIABILITY IN DEMAND Factors Levels Parameters Descriptions Coefficient of Demand Variation (CODVAR) Lead time (LT) Review Interval (INT) Low 0.1 Variability in demand High 0.4 Low UNIF (1.5,2) High UNIF (3.5,4) Low 1 High 4 Time required for factory to send products to DC once order is placed (week) Regular interval an inventory level is reviewed (week) Figure 1: Main effect for average total cost per week A. Results from Factorial Design The main effects of all three factors are statistically significant. Fig. 1 shows the main effect plot of the three factors on the average total cost per week. As expected, an increase in demand variability results in an increase in the average total cost per week. Longer lead time also contributes to higher average total cost per week. This finding has been often mentioned in the literature and research. Increasing review interval from 1 week to 4 weeks results in a reduction in average total cost per week. The reason may be that the ordering cost is relatively high. Thus, reviewing the inventory level and place order every 4 weeks results in lower number of order placed, which contribute to lower ordering cost. Nevertheless, this situation warrant further examination, which will be discussed in the next section. To evaluate the magnitude of the effect of each factor, Pareto chart for standardized effects is created. Figure 2 shows the Pareto chart for standardized effects of the factors and their interactions on average total cost per week. The Pareto chart indicates that main effects of lead time and review interval have strong impact on average total cost per week. In addition, interaction effect between lead time and review interval is also very significant. To understand the behavior of the interaction, the interaction effect plot is created as shown in Fig. 3. Figure 2: Pareto chart on average total cost per week The interaction effect plot reveals that an increase in review interval does not always result in a reduction in average total cost per week. The direction of the effect depends on the lead time. If the lead time is short (uniformly distributed with minimum of 1.5 weeks and maximum of 2 weeks), increasing review interval from 1 week to 4 weeks contributes to higher total cost (Solid line). On the other hand, when lead time is long (uniformly distributed with minimum of 3.5 weeks and maximum of 4 weeks), increasing review interval leads to a reduction in total costs (Dash line). This finding implies that it is very important to select review 2349

6 Figure 3: Interaction effect plot between lead time and review interval interval that is appropriate to the lead time. When lead time is short, one should review inventory more often. To examine the relationship between lead time and review interval in more detail, the author decides to perform further experimentation by varying the review interval from 1 to 4 under different lead time. B. Experimentation on Interaction of Lead Time and Review Interval To experiment on the interaction of lead time and review interval, the simulation model is run under 2 lead time conditions, which are short lead time (uniformly distributed with minimum of 1.5 weeks and maximum of 2 weeks) and long lead time (uniformly distributed with minimum of 3.5 weeks and maximum of 4 weeks). In each condition, 4 different review intervals are set, which are 1, 2, 3, and 4 weeks. Fig. 4 shows the average total cost per week with different review intervals. For short lead time where maximum lead time is equal to 2 weeks, the review interval of 2 weeks yields the lowest average total cost per week. Increasing the review interval beyond 2 weeks leads to higher costs. For long lead time where maximum lead time is equal to 4 weeks, increasing review interval contributes to a reduction in total costs. If the review interval match the lead time (4 weeks in this case), the average total cost per week will be the lowest. Therefore, one can conclude that review interval should be set to match the lead time in order to be cost-effective. If the review interval is shorter or longer than the lead time, the total costs tend to be higher than the optimal ones. This also illustrate how useful a simulation is in assisting manager to determine the appropriate review interval that will yield the lowest total costs. Nevertheless, this finding seems to be counterintuitive especially for long lead time situation. In general, one would expect that costs will increase as the review interval increases. Therefore, the author further investigates the cause of this interesting relationship. It is found that the way the company calculates order quantity does not take into account the quantity previously ordered. As a result, when lead time is long (4 weeks) but the review interval is only 1 week, company tends to order every week without taking to account that the previous quantity ordered will arrive in the near future. In short, the company orders more than it need. This action, therefore, contributes to high inventory level and results in extremely high average total cost per week. The situation warrants further investigation and probably results in the change in the way company calculate its order quantity, which is unfortunately out of scope of this paper. 1,500,000 Average Total Cost per Week 1,300,000 1,100, , , , ,000 Short LT Long LT 100, Review Interval (Weeks) Figure 4: Average total cost per week with different review intervals 2350

7 V. CONCLUSION This paper shows how simulation optimization approach and design of experiment can be used to determine the most suitable inventory policy under different circumstance. First, the case study company uses simulation model to evaluate the effectiveness of periodic and continuous review policy given the same service level. It was found that both inventory policies perform approximately the same in terms of total costs. Therefore, the case study company does not have to invest in implementing new inventory control system. It can still use the current system which is the periodic review policy or (s, S) policy. Then, design of experiment (DOE) is performed in order to help company better understand the effect of three important factors including variation in demand, lead time, and review interval. The 2 k factorial design is selected to evaluate the impact. It is found that all three factors impact the performance in terms of costs. In general, higher variation in demand and longer lead time contributes to higher average total cost per week. In addition, the interaction between lead time and review interval is also significant. When the lead time is short, increasing review interval contributes to higher total cost. On the other hand, when lead time is long, increasing review interval leads to a reduction in total costs. This emphasizes the important of choosing the review interval that match the lead time. Thus, the results of the experimentation can be used to gain better understanding of different inventory policies and be able to select the configuration that best suit the company s objective. ACKNOWLEDGMENTS This work was supported by Chulalongkorn University for the project titled Chulalongkorn University Centenary Academic Development Project. REFERENCES [1] Al-Harkan, I. and Hariga, M., "A Simulation Optimization Solution to The Inventory Continuous Review Problem With Lot Size Dependent Lead Time," The Arabian Journal for Science and Engineering, vol. 32, pp , October [2] Cerda, C. and Monteros, A., "Evaluation of A (R,s,Q,c) Multi-Item Inventory Replenishment Policy Through Simulation," in 1997 Winter Simulation Conference, [3] Heizer, J. and Render, B., Operations Management, 9th ed.: Pearson Education, [4] Larson, L., "Investigation of Inventory and Production Policies Using Simulation," in Simulation in Inventory and Production Control, H. Bekiroglu, Ed.: Society for Computer Simulation Proceedings, 1984, pp [5] Law A.M and Kelton, W. D., Simulation Modeling and Analysis, 2nd ed. New York: McGraw-Hill, [6] Lipman, B., How to Control to Reduce Inventory. Englewood Cliffs, NJ: Prentice-Hall, [7] Merkuryeva, G. and Vecherinska, O., "Simulation-Based Approach for Comparison of (s, Q) and (R, S) Replenishment Policies Utilization Efficiency in Multi-echelon Supply Chains," in Tenth International Conference on Computer Modeling and Simulation, 2008, pp [8] Morrice, D., Valdez, R., Chida, J., J., and Eido, M., "Discrete Event Simulation in Supply Chain Planning and Inventory Control at Freescale Semiconductor, Inc.," in 2005 Winter Simulation Conference, [9] Setamanit, S., "Using Simulation to Explore the Impact of Inventory Policies on Supply Chain Performance," in Portland International Conference on Management of Engineering and Technology (PICMET), Phuket, Thailand, [10] Simchi-Levi, D., Kaminski, P., and Simchi-Levi, E., Designing and Managing the Supply Chain: Concepts, Strategies, Case Studies: McGraw-Hill, [11] Wakeland, W., Martin, R., and Raffo, D., "Using Design of Experiments, Sensitivity Analysis, and Hybrid Simulation to Evaluate Changes to a Software Development Process: A Case Study," Software Process Improvement and Practice, pp , [12] Xudong, X., Kumar, A., and Wee Kwan Tan, A., "A simulation-based approach for evaluating diverse inventory policies in a supply chain," Int. J. Simulation and Process Modelling, vol. 4, pp ,