ISSN: 2005-4238 IJAST 129
Copyright ⓒ 2019 SERSC
Statistical Process Control-Based Inventory Policy
T. Chinna Pamulety1
and V. Madhusudanan Pillai2
Associate Professor, Department of Mechanical Engineering, Sreenivasa Institute of Technology and management studies, Chittoor – 517127, India
Professor, Department of Mechanical Engineering, National Institute of Technology Calicut, Calicut - 673601, India,
Supply chain is a network of business entities like supplier, wholesaler, distributor, retailer etc. to perform various business functions to meet the needs of an end customer. An effective inventory policy maximizes the customer service level and keeps the total inventory at minimum. Improper inventory policy used generates the bullwhip effect which degrades the performance of a supply chain. In the present work, Statistical Process Control (SPC) based inventory policy is proposed. It’s performance is evaluated in terms of variance of orders, fill rate and total inventory at each stage of a serial supply chain and compared with the performance of order up-to level and moving average demand policies by simulation. Three sets of inventory Decision Rules namely DR1, DR2 & DR3 were developed under SPC policy to optimize future orders and inventory levels. It is found that performance of DR3 is better than other inventory policies.
Keywords: supply chain management, inventory policies, statistical process control, performance measures
Supply chain is a network of organizations that work together and performs various business functions such as procurement of raw materials, converting the raw material into semi-finished or finished goods and distributing the same to their ultimate customers (Simchi-Levi et al., 2008). The objectives of supply chain management are to maximize the customer service level and reduce the supply chain cost. One of the problems in supply chains is bullwhip effect and it is defined as the increase in order variability as we move from downstream stage to upstream stage in a supply chain.
Downstream means the direction towards the external demand, whereas the direction towards the end or ultimate supplier in the supply chain is upstream. Its presence in a supply chain creates excessive inventories or shortages, poor customer service levels because of unavailability of products or long backorders, insufficient or excessive capacities, or unstable or uncertain production planning (Lee et al., 1997). Thus, the bullwhip effect is costly, harmful, increases uncertainty in the supply chain and reduces the efficiency of the supply chain. Bullwhip effect is an important performance indicator of supply chains (Shi and Bian, 2010) and reduction in bullwhip effect increases the profitability of the whole supply chain (Caloiero et al., 2008, Bottani et al., 2010).
Inventory policy used in an organization is one of the causes of the bullwhip effect and the performance of the supply chain depends on the inventory policy used (Dejonckheere et al., 2003, Disney and Towill, 2006). Inventory policy which reduces the bullwhip effect and maximizes the supply chain fill rate is essential for the survival of the supply chain in this competitive world. A SPC based policy adjusts dynamically with the variation in inventory and may perform well. Pfohl et al.
(1999) developed a Statistical Process Control (SPC) based inventory control system which determines replenishment orders by adjusting dynamically with the variation in inventory and demand data. Le and Wu (2006) modified the SPC policy of Pfohl et al. (1999) and evaluated the performance of a two stage supply chain. Various demand and inventory rules are used for determining the replenishment orders in their studies. Actually, Watts et al. (1994) used the control charts to monitor and diagnose the performance of a reorder point inventory system. The present work suggests some decision rules under statistical control of inventory levels for inventory management and applies to every stage of a four-stage serial supply chain to evaluate the performance.
In the present research, SPC based inventory policy with three decision rules such as DR1, DR2, and DR3 is developed and their performance is analyzed by using the same policy at all stages
ISSN: 2005-4238 IJAST 130
Copyright ⓒ 2019 SERSC
in a four-stage serial supply chain. Simulation is the tool used to analyze the performance. Various performance measures used for valuation are variance of orders placed by each stage, fill rate of each stage, and total inventory at each stage. It is observed that the performance of the SPC with DR3 is better than with DR1 and DR2. The performance of the SPC with DR3 is compared with the commonly used inventory policies such as order up-to level and moving average demand policy.
Result shows that the performance of SPC based inventory policy is better than the other policies studied.
2. Supply Chain model
In this research, a serial supply chain of four stages is considered. The four stages are retailer, distributor, manufacturer and supplier. Customer places orders to retailer, retailer to distributor and so on. Each stage in a supply chain can act as either supplier or customer to the other. Each stage member takes two decisions such as quantity to be shipped and size of the order to be placed to its supplier. The order placed reach the supplier after a fixed time period called Order Lead Time (OLT) and the shipment quantity reaches the downstream stage after a fixed amount of time called Delivery Lead Time (DLT). The shipment quantity is equal to the size of the order placed if sufficient inventory is available otherwise it is equal to the available inventory at that time period. The size of the order is determined based on the inventory policies. The performance of the supply chain is evaluated by using the same policy at every stage by simulation. The details of the inventory policies used, simulation parameters and the performance measures used for valuation are explained in Section 3, 4 and 5, respectively.
The assumptions in the present study are: (i) Initial inventory is 75 units for first three stages and is 50 for the supplier, (ii) Replenishment occurs at the beginning of the period (iii) ,Order placed to the higher stage is at the beginning of the period, (iv) Shipment for the demand raised is done at the beginning of the period but after the order placement, (v) Back orders are not allowed, (vi) Lead time is two periods for retailer, distributor & manufacturer and one period for supplier, (vii) Review is done at each period, (viii) Customer demand is faced by the retailer and it follows normal distribution with mean 25 and standard deviation of 5.
3. Inventory polices
The performance of the supply chain is evaluated under the following inventory policies.
3.1. Proposed SPC policy
SPC is one of the tools used in quality control. In SPC, past data are collected from a process and control charts are prepared to check that the process is in statistical control or not. The control chart technique involves the calculation of mean, standard deviation, Upper Control Limit (UCL) and Lower Control Limit (LCL). When the process is in control, the control parameter is within the UCL and LCL. Sometimes the process may be out of control; in such cases the special causes that affects the process has to be found and eliminated. By eliminating the special causes we can bring the process in statistical control.
The plotted data on a control chart can be interpreted by various rules such as, whether the data points lies outside of the control limits, trend followed by the data points is either up or down, too many data points on one side of central line and points near to control limit. When such characteristics appear it shows that process is out of control, then we need to investigate the causes for abnormal variations and by eliminating those causes we can bring back the process to controlled condition.
The SPC based inventory control uses the control chart concepts for developing replenishment strategy. As we rely on the historical data, SPC inventory management does not rely on demand forecast. In this policy the control of inventory level is checked and control parameters for the inventory level is determined.
At the beginning, a database has to be filled with historical inventory and demand data. In the past period, the order up-to level policy was used, and the inventory and demand data generated are used to start the SPC based inventory policy. The control chart parameters such as mean, UCL and LCL are calculated for historical inventory data based on the 3σ limits. If the LCL is negative, fix it as 3% of mean value in order to reduce the stock outs. There are three set of decision rules developed, namely, DR1, DR2 and DR3 for deciding the ordering strategy. Actually, the first rule is developed
ISSN: 2005-4238 IJAST 131
Copyright ⓒ 2019 SERSC
and tested its performance. The performance was not satisfactory and hence the rules are modified to get new rules.
3.1.1 Decision rules in DR1:
(1) If the inventory run of four points in a row is in the range of mean inventory and 75%
UCL, then the order quantity is equal to the previous 4-period demand average minus the difference of overall inventory mean and mean of the 4-period inventory. (2) If the inventory run of four points in a row is in the range of mean inventory and 25% mean inventory, then the order quantity is equal to the previous 4-period demand average plus the difference of overall inventory mean and mean of the 4-period inventory. (3) If the current inventory is above UCL, then the order quantity placed is zero.
(4) If the current inventory level is in the range of UCL and 75% UCL, then the order quantity is half of the average of 4-period demand. (5) If the current inventory level is in the range of LCL and 25%
mean inventory, then the order quantity is one and half times the average of 4-period demand. (6) If the current inventory level is less than LCL, then the order quantity is twice the average of 4-period demand. (7) The order quantity is the average 4-period demand for all other cases.
3.1.2 Decision rules in DR2:
In this, rules 1, 2, 3 and 7 are as in DR1 and remaining rules are different from DR1. They are: (4) If the current inventory level is in the range of UCL and 75% UCL, then the order quantity is the average of 4-period demand. (5) If the current inventory level is in the range of LCL and 25%
mean inventory, then the order quantity is twice the average of 4-period demand. (6) If the current inventory level is less than LCL, then the order quantity is thrice the average of 4-period demand.
3.1.3 Decision rules in DR3:
(1) If the inventory run of four points in a row is in the range of UCL and 75% UCL, then the order quantity is equal to the previous 4-period demand average minus the difference of overall inventory mean and mean of the 4-period inventory. (2) If the inventory run of four points in a row is in the range of mean inventory and 25% mean inventory, then order quantity is equal to the previous 4-period demand average plus the difference of overall inventory mean and mean of the 4-period inventory. (3) If the current inventory is above UCL, then the order quantity is equal to the previous 4-period demand average minus the difference of current inventory level and 75% UCL. (4) If the current inventory level is below 25% mean inventory, then the order quantity is one and half times the average of 4-period demand. (5) The order quantity is the average of 4-period demand for all other cases.
3.2. Order up-to level
In this policy an order is placed at each review period and its size is equal to the difference between the maximum inventory level and inventory position at that period. Thus, the order size varies from time to time and it is depending on the inventory position. Inventory position at a period is equal to the sum of the on-hand inventory and the orders yet to be received. The maximum inventory level S = (R + L) × mean demand per period. In the present study, the mean demand per period has been forecasted based on the simple moving average of demands. This policy is considered under simple moving average with two periods (2MA) and four periods (4MA).
3.3. Moving average demand policy
In this policy the order quantity is equal to 52-period moving average demand. If 52 periods are not available, the average value of the available number of periods is considered as order quantity.
4. Performance measures
The followings are the performance measures used for evaluation.
4.1 Variance of orders placed by each stage: This is used to know and measure the bullwhip effect in a supply chain. If the variance of orders placed by each stage is increasing from downstream to upstream then, there is bullwhip effect in the supply chain.
4.2 Fill rate: It is defined as the fraction of demand met from the shelf. An effective inventory policy maximizes the customer satisfaction or fill rate of each stage.
4.3 Total inventory at each stage: By properly managing inventory at each supply chain stage the customer satisfaction can be increased and supply chain costs can be reduced.
ISSN: 2005-4238 IJAST 132
Copyright ⓒ 2019 SERSC
5. Simulation parameters
The simulation parameters such as warm-up period, run length and number of replications are calculated based on the total inventory of the supply chain. The warm-up period is identified by using Welch`s procedure (Law and Kelton, 2000) and it is fixed as 43 periods. The simulation run length is fixed as 104 periods which is greater than twice the warm-up period (Law and Kelton, 2000). The number of replications (Banks et al., 2005) required is calculated at 5% error and it is fixed as 38. The performance measures of the supply chain are calculated under each inventory policy by collecting the data after warm-up period. The average value of each performance measure over 38 replications is recorded and is used for establishing conclusions.
6. Results and discussion
The performance of the supply chain under SPC with DR1, DR2 and DR3 rules is shown in Table 1 and it is found that the performance of SPC with DR3 is better than others. The performance of this policy is compared with the commonly used inventory policies such as the order up-to level and the moving average demand policy and the results are shown in Table 2. In the order up-to level policy, the mean demand is forecasted using 2-period moving average and 4-period moving average method.
From Table 2, it is clear that the performance of SPC with DR3 is better than the other polices studied with respect to the fill rate and the variance of orders. Increase in magnitude of variance of orders from downstream stage to upstream stage represents the presence of bullwhip effect in the supply chain. The magnitude of variance of orders is increased from the retailer to the supplier under order up-to level policy but it is not so under SPC inventory policy (see Table 2). So, there is no bullwhip effect when SPC inventory policy is used. Previous research also shows that order up-to level policy exhibits the bullwhip effect (Dejonckheere et al., 2003). The present result is also confirming the same. The total inventory under SPC policy is higher than the moving average demand policy and lesser than the order up-to level policies.
Table1. Performance of the supply chain under SPC inventory policy Policy Retailer Wholesaler Distributor Factory
DR1 60 88 94 96
DR2 68 91 93 96
DR3 83 93 94 96
Variance of orders
DR1 26 115 37 38
DR2 24 121 47 49
DR3 26 34 24 20
DR1 63 744 1195 1298
DR2 111 994 1332 1388
DR3 133 677 771 764
Table2. Performance of the supply chain under inventory policies
Policy Retailer Wholesaler Distributor Factory
SPC-DR3 83 93 94 96
Order up-to level (2MA) 84 89 94 95
Order up-to level (4MA) 81 81 83 90
Moving average demand 83 84 78 85
Variance of orders
SPC-DR3 26 34 24 20
ISSN: 2005-4238 IJAST 133
Copyright ⓒ 2019 SERSC
Order up-to level (2MA) 25 212 851 1952
Order up-to level (4MA) 25 151 457 873
Moving average demand 24 91 181 185
SPC-DR3 133 677 771 764
Order up-to level (2MA) 456 1346 3478 8558
Order up-to level (4MA) 317 527 1169 3520
Moving average demand 219 278 220 584
The performance of a four-stage serial supply chain is analyzed by using proposed SPC (with DR1, DR2, and DR3 rules), order up-to level and moving average demand inventory policies. The performance of SPC with DR3 is better with respect to the performance measures such as customer service level and variance of orders placed at every stage of the supply chain. It is also found that there is no bullwhip effect in the supply chain under SPC inventory policy. The present study suggests the use of SPC based inventory control system in supply chains to meet the objectives of the supply chain management.
1. Banks, J., Carson, J.S., Nelson, B.L. and Nicol, D.M., 2005. Discrete-Event System Similation, 4th Ed. Pearson Education.
2. Bottani, E., Montanari, R. and Volpi, A., 2010. The impact of RFID and EPC network on the bullwhip effect in the Italian FMCG supply chain, International Journal of Production Economics 124, 426-432.
3. Caloiero, G., Strozzi, F., Comenges, J.Z., 2008. A supply chain as a series of filters or amplifiers of the bullwhip effect, International Journal of Production Economics 114, 631-645.
4. Dejonckheere, J., Disney, S.M., Lambrecht M.R. and Towill D.R., 2003. Measuring and avoiding the bullwhip effect: A control theoretic approach, European Journal of Operational Research 147, 567-590.
5. Disney, S.M. and Towill, D.R., 2006. A methodology for benchmarking replenishment-induced bullwhip, Supply Chain Management: An International 11(2), 160-168.
6. Law, A.M. and Kelton, W.D., 2000. Simulation modeling and analysis, 3rd ed. McGraw Hill.
7. Lee, H.L, Padmanabhan, V. and Whang, S., 1997. The bullwhip effect in supply chains, Sloan Management Review 38 (3), 93-102.
8. Lee, H. T. and Wu, J. C., 2006. A study on inventory replenishment policies in a two-echelon supply chain system, Computer and Industrial Engineering 51, 257-263.
9. Pfohl, H. C., Cullmann, O. and Stolzle, W., 1999. Inventory management with statistical process control: Simulation and evaluation, Journal of Bussiness Logistics 20, 101-120.Shi, C. and Bian, D., 2010. On impact of information sharing in the supply chain bullwhip effect, IEEE transactions, 329 – 333.
10. Simchi-Levi, D., Kaminsky, P., Simchi-Levi, E. and Shankar, R., 2008. Designing and Managing the Supply Chain - concepts, strategies and case studies, 3rd ed. Tata McGraw-Hill.
11. Watts, C. A., Hahn, C. K. and Sohn, B. K., 1994. Monitoring the performance of a reorder point system: a control chart approach, International Journal of Operations & Production Management 14, 51-61.