35 Inventory Control Systems: Continuous Review System

Vikas Singla

35.1 INTRODUCTION

Previous  chapters  on  Inventory  management  have  discussed  various  inventory  models  such  as Economic Order Quantity, Economic Production Quantity and Quantity discounts. The main purpose of these models was to identify quantity that needs to be ordered per batch so that total cost of inventory should be kept as low as possible. Total cost in these models was function of holding and ordering cost. Thus answer to question of ‘How much to order’ was determined by these models under an assumption that demand of quantity ordered would be constant. But in practice such an assumption is rarely fulfilled. Also these models does not answer the question of ‘When to place an order’ under the conditions of uncertain demand. An inventory control system helps in identifying answer to both the questions of how much and when to place an order. The correctness of such an answer primarily depends on understanding of nature of demand. Categorization of demand of an item into dependent or independent demand is crucial in selection of an inventory control system. Independent demand is defined as demand for items which is influenced only by market conditions and not by demand of any other item kept in stock. For instance, number of flowers a flower shop should keep would be influenced by demand for those flowers, number of books of a bestselling author a book store should keep in stock is influenced by market demand and not by any other book in the store. Thus independent demand is primarily for final products or products stored at retailer level. Dependent demand is for those items which are influenced by production of other items. Demand for such products is influenced by number of units stored of associated items. For instance, number of units of emblems to be used for cars produced is dependent on number of cars being manufactured. Number of tires produced is again a function of number of cars produced. For each unit of car four units of tires has to be manufactured. Thus, demand of tires is dependent on number of cars ordered. It is interesting to know that number of cars ordered is influenced by market forces and thus it falls into independent demand category whereas every other item goes into producing a car falls into dependent demand category.

This chapter discusses inventory control models for independent demand items. Two such models have been discussed: continuous review system called as Q system and periodic review system called as P system.

35.2 CONTINUOUS REVIEW (Q) SYSTEM

Continuous Review System is one of the families of stochastic models which are designed for analyzing inventory systems where there is considerable uncertainty about future demands. In this model the inventory level is being monitored on a continuous basis so that a new order can be placed as soon as the inventory level drops to the reorder point.

The traditional method of implementing a continuous-review inventory system was to use a two-bin system. All the units for a particular product would be held in two bins. The capacity of one bin would equal the reorder point. The units would first be withdrawn from the other bin. Therefore, the emptying of this second bin would trigger placing a new order. During the lead time until this order is received, units would then be withdrawn from the first bin.

In more recent years, two-bin systems have been largely replaced by computerized inventory systems. Each addition to inventory and each sale causing a withdrawal are recorded electronically, so that the current inventory level always is in the computer. (For example, the modern scanning devices at retail store checkout stands may both itemize your purchases and record the sales of stable products for purposes of adjusting the current inventory levels.) Therefore, the computer will trigger a new order as soon as the inventory level has dropped to the reorder point. Several excellent software packages are available from software companies for implementing such a system. Because of the extensive use of computers for modern inventory management, continuous-review inventory systems have become increasingly prevalent for products that are sufficiently important to warrant a formal inventory policy.

A continuous-review inventory system for a particular product normally will be based on two critical numbers:

• R: reorder point.
• Q: order quantity.

For a manufacturer managing its finished products inventory, the order will be for a production run of size Q. For a wholesaler or retailer (or a manufacturer replenishing its raw materials inventory from a supplier), the order will be a purchase order for Q units of the product. An inventory policy based on these two critical numbers is a simple one.

Inventory policy: Whenever the inventory level of the product drops to R units, place an order for Q more units to replenish the inventory.

• 35.2.1 The Assumptions of the Model
  • Each application involves a single product.
  • The inventory level is under continuous review, so its current value always is known.
  • An (R, Q) policy is to be used, so the only decisions to be made are to choose R and Q.
  • There is a lead time between when the order is placed and when the order quantity is received. This lead time can be either fixed or variable.
  • The demand for withdrawing units from inventory to sell them (or for any other purpose) during this lead time is uncertain. However, the probability distribution of demand is known (or at least estimated).
  • If a stockout occurs before the order is received, the excess demand is backlogged, so that the backorders are filled once the order arrives.
  • A fixed setup cost (denoted by K) is incurred each time an order is placed.
  • Except for this setup cost, the cost of the order is proportional to the order quantity Q.
  • A certain holding cost (denoted by h) is incurred for each unit in inventory per unit time.
  • When a stockout occurs, a certain shortage cost (denoted by p) is incurred for each unit backordered per unit time until the backorder is filled.

• 35.2.1 Two scenarios in Q system

  As the title suggests a continuous review system tracks the inventory or remaining stock after every withdrawal. For instance, if from a stock of 50 units first withdrawal takes 10 units and second withdrawal takes 5 units then this system would check for remaining elements at each withdrawal of units. So after first check of stocks the system would indicate that there is stock of 40 units and after second check it would indicate that stock is of 35 units. A perfect illustration of such system is cash withdrawal from ATM. After every cash withdrawal of differing amount ATM gives the receiver a receipt indicating amount of money (stock) left. It is important to note here that every cash withdrawal would not be of same amount. This can be corresponded with number of units withdrawn from inventory which would imply the concept of application of this inventory control system for varying demand.

  This system is also termed as Fixed Order Quantity (FOQ) or Reorder point (ROP) system. FOQ implies how much to order and ROP implies when to order. According to system, tracking of stock is done whenever material is pulled out of stock. So it becomes easy to infer when stock reaches reorder point even in case of varying demand. At reorder point an order of fixed and certain quantity of units is placed with the supplier. Now this scenario provides us with two cases:

• (i) If demand is uncertain before reorder point: as the continuous review system recommends checking of stock level after every withdrawal so consequences of varying demand before reorder point is easily If demand is high then reorder point will be achieved earlier and next order would be placed earlier whereas if demand is weak then reorder point would be achieved at a later date and next order could be placed accordingly. This is easily and effectively tracked because stock is continuously checked.
• (ii) If demand is uncertain after reorder point: after placing an order stock is not checked continuously till next order is made So question is what should happen if demand increases or decreases at abnormal rate during the period which is after reorder level.

These two cases have been discussed in following sections with illustrations

35.2.3 Continuous review system with uncertain demand before reorder point:

Case 1: Suppose batch size i.e. Q = 100 units, daily demand d = 10 units and lead time L = 5 days. Lead time is the time taken by the supplier to replenish stock by Q after order has been placed. If daily demand would have been fixed and certain of 10 units then 100 units would be consumed in 10 days (Table 1) making Time Between Order (TBO) to be of 10 days as shown by Fig.1(a). This TBO would remain same in case of certain daily demand.

Case 2: But if demand before reorder point varies in a manner that on day 1 10 units, on day 2 20 units and on day 3 20 units are consumed (Table 1). This means 50 units are consumed in 3 days instead of 5 days when demand was certain. This could be tracked because of application of continuous review system as it checks remaining stock  after every withdrawal. Thus, next  order of 100 units (Q) is placed i.e. reorder point is achieved after 3 days. As in this illustration demand is certain after reorder point so remaining 50 units would be consumed at rate of 10 units per day making TBO as 8 days as shown by Fig.1(b).

Case 3: In another instance if daily demand before reorder point is weak and varies in following fashion: 5 units on day 1, 10 units on day 2, 5 units on day 3 and 10 units on day 4,5and 6 each then first 50 units would be consumed in 6 days (Table 1). Thus reorder point is reached after 6 days and it is tracked from continuous review system. Next 50 units because of constant daily demand would be consumed in 5 days making TBO as 11 days as shown in Fig.1(c).

These three cases clearly indicates that in Q system

• The batch size ordered remains same of Q = 100 units.
• Time between order varies because of varying demand. TBO was 10 days in case 1, 8 days in case 2 and 11 days in case 3.
• Also, reorder point i.e. time when order is placed also varies. In case 1 order was placed after 5 days, in case 2 it was done after 3 days and in case 3 it was placed after 6 days.
• In Q system as seen from above illustrations estimation of reorder point does not depend on varying demand before lead time as stock level is continuously checked after every removal.

35.2.4 Continuous reviewsystemwithuncertaindemandafter reorderpoint:

As shown in previous section estimation of reorder point in Q system does not depend on variation in demand before lead point. But what happens if demand is varying after lead time? This has been discussed by illustrating following cases.

Suppose a batch size of 100 units is in the stock and for first five days 10 units daily are consumed. Thus after 5 days a stock of 50 units is left. Now as lead time i.e. time between placing and receiving an order is of 5 days so order is placed after 5 days assuming that by the time next batch of 100 units is obtained remaining stock of 50 units would be consumed. This makes reorder point after 5th day when 50 units are left in the stock.

Case 1: Now suppose demand varies in a manner such as: during 6th day 10 units, during 7th and 8th day 5 units each and during 9th and 10th day 10 units each making a total of consumption of 40 units in next five days (Table 2). Thus in first five days daily 10 units have been consumed at constant rate and in next five days a total of 40 units are consumed as shown in Fig. 2(a). As order has been placed after 5th day so it would be received after 10th day operation when in stock 10 units were still there making total inventory of 110 units. These extra 10 units are called as safety stock. Thus,

Stock at ROP level (R = 50) – demand during Lead time (L = 40)                =              Safety stocky (SS = 10) So,          ROP = L + SS

Case 2: After 5 days when ROP is reached and stock is of 50 units suppose demand during lead time varies in a manner such as: during 6th day 10 units, during 7th day 20 units and during 8th and 9th day 10 units each making consumption of last 50 units in next 4 days (Table 2). Thus in first five days daily 10 units have been consumed at constant rate and rest all 50 units are consumed in next four days as shown in Fig. 2(b). It implies that if demand during lead time is strong then stock can get finished before replenishment. This situation is termed as out of stock.

These two cases clearly indicate that:

• As it is fixed order system so every time when ROP is reached an order of fixed batch size of Q is placed with the supplier. So if demand is weak during lead time it would result in creation of safety stock.
• If demand is strong during lead time it would result in out of stock situation and might result in loss of customers.
• This result in uncertainty in estimation of reorder point. In section 35.2.1 it was shown that such uncertainty in estimation of ROP was independent of variation in demand if it happens before lead time. But this uncertainty in estimation of reorder point does happen if demand varies after lead time. Resolution of this uncertainty requires understanding the concept of service level.

35.2.5 Service level: Determination of safety stock

As seen in above illustrations due to uncertainty in demand which is a very practical scenario an organization would always like to have safety stock to buffer against vagaries of demand fluctuation. But keeping a higher safety stock would incur higher holding cost and lower safety stock would result in higher chances of losing customer. Managing this trade off between customer service and inventory holding cost becomes a critical issue in inventory control systems. One way of determining safety stock is to set a service level which is defined as desired probability of serving the customer or not going out of stock per ordering cycle. For instance if company operates under a service level of 95% it would imply that during one ordering cycle chance of demand outstripping supply is only 5%  during lead time  and company would meet customer demand 95% of the time. Higher the service level for instance 99% would make company to employ systems that would result in less loss of service and reduce the level of stock out. But this would on the other hand would ask for keeping higher level of safety stock because even in cases of strong demand company would intend to meet customer demand. However in case of weak demand it would result in higher stock and higher holding costs. Thus a proper estimation of such service level becomes highly critical.

To do so, have a proper understanding of variation in demand during lead time. If variability along average demand is small then safety stock can be small. But if average demand varies greatly from one ordering cycle to other then higher safety stock can be kept. This is gauged by recording past demand data during lead time. This data is plotted by calculating average and deviation values. This variation tends to follow normal distribution implying that central value represents average demand. As these variations follow normal distribution so safety stock is calculated by using following formula:

Safety stock = z (number of deviations deduced from z tables) * (standard deviation in demand during lead time)

Higher service level would imply requirement of creating a higher buffer (safety stock) for higher variation in demand. This variation is represented by higher z value. If z=0, there is no safety stock meaning stock outs will occur during 50% of the order cycles.

Example: Records show that demand data for a product during lead time is normally distributed with an average of 250 units and deviation of 22 units. Estimate safety stock if company intends to maintain a service level of 99%. Also find reorder point.

Solution: At a service level of 99% value of number of deviations from z tables is 2.33

So	Safety stock	= z*standard deviation
		= 2.33*22 = 51 units
	ROP	= average demand during lead time + safety stock
		= 250 + 51 = 301 units

35.2.6 Alternative Measures of Service Level

1. The probability that a stockout will not occur between the time an order is placed and the order quantity is received.
2. The average number of stockouts per year.
3. The average percentage of annual demand that can be satisfied immediately (no stockout).
4. The average delay in filling backorders when a stockout occurs.
5. The overall average delay in filling orders (where the delay without a stockout is 0).

Measures 1 and 2 are closely related. For example, suppose that the order quantity Q has been set at 10 percent of the annual demand, so an average of 10 orders is placed per year. If the probability is 0.2 that a stockout will occur during the lead time until an order is received, then the average number of stockouts per year would be 10(0.2) 2. Measures 2 and 3 also are related. For example, suppose an average of 2 stockouts occur per year and the average length of a stockout is 9 days. Since 2(9) 18 days of stockout per year are essentially 5 percent of the year, the average percentage of annual demand that can be satisfied immediately would be 95 percent. In addition, measures 3, 4, and 5 are related. For example, suppose that the average percentage of annual demand that can be satisfied immediately is 95 percent and the average delay in filling backorders when a stockout occurs is 5 days. Since only 5 percent of the customers incur this delay, the overall average delay in filling orders then would be 0.05(5) 0.25 day per order. A managerial decision needs to be made on the desired value of at least one of these measures of service level. After selecting one of these measures on which to focus primary attention, it is useful to explore the implications of several alternative values of this measure on some of the other measures before choosing the best alternative.

35.3 SUMMARY

Inventory control systems help in determining when to reorder and how much to order of products whose demand is independent from other products. Primarily two inventory control systems are discussed namely Continuous review system (Q) and Periodic review system (P). This chapter has focussed on Q system which tracks the level of stock after every withdrawal making it convenient to judge the reorder point when demand variation is not constant. In this system number of units ordered per batch remains constant whereas time between orders varies with variation in demand patterns. This concept has been illustrated in detail by taking various cases under two sections. In one section variation in time between orders was evaluated when variation in demand is before lead time and in other section it was emphasized when demand variation is after lead time. Variation in demand during lead time can either result in safety stock or stock outs. To resolve these issues concept of service level has been explained.

35.3 GLOSSARY

• Dependent demand: is the demand for those items which are inter-related with each other and need for one item is direct result of need for some other item.
• Independent demand: is the demand for those items which are not related with each other.
• Continuous review system: is an inventory control system wherein stock level is checked after every withdrawal.
• Safety stock: is the excess products that are available during one ordering cycle
• Service level: is identified in terms of probability indicating level of customer service that a company intends to provide..

35.3 REFERENCES/ SUGGESTED READINGS

• Chase, B.R., Shankar, R., Jacobs, F.R. and Aquilano, N.J., Operations & Supply Chain Management, 12thEdition, McGraw Hill.
• Stevenson, W.J., Operations Management, 9thEdition, Tata McGraw Hill.
• Lee J. Krajewski, Operations Management, Prentice-Hall of India, New Delhi, 8th Edition.