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unit5-dq1-reading.docxSystems Based on the Q System
Two systems based on the Q system are the two-bin system and the base-stock system.
Two-Bin System
The concept of a Q system can be incorporated in a visual system, that is, a system that allows employees to place orders when inventory visibly reaches a certain marker. Visual systems are easy to administer because records are not kept on the current inventory position. The historical usage rate can simply be reconstructed from past purchase orders. Visual systems are intended for use with low-value SKUs that have a steady demand, such as nuts and bolts or office supplies. Overstocking is common, but the extra inventory holding cost is minimal because the items have relatively little value.
visual system
A system that allows employees to place orders when inventory visibly reaches a certain marker.
A visual system version of the Q system is the two-bin system in which a SKU’s inventory is stored at two different locations. Inventory is first withdrawn from one bin. If the first bin is empty, the second bin provides backup to cover demand until a replenishment order arrives. An empty first bin signals the need to place a new order. Premade order forms placed near the bins let workers send one to purchasing or even directly to the supplier. When the new order arrives, the second bin is restored to its normal level and the rest is put in the first bin. The two-bin system operates like a Q system, with the normal level in the second bin being the reorder point R. The system also may be implemented with just one bin by marking the bin at the reorder point level.
two-bin system
A visual system version of the Q system in which a SKU’s inventory is stored at two different locations.
Base-Stock System
In its simplest form, the base-stock system issues a replenishment order, Q, each time a withdrawal is made, for the same amount as the withdrawal. This one-for-one replacement policy maintains the inventory position at a base-stock level equal to expected demand during the lead time plus safety stock. The base-stock level, therefore, is equivalent to the reorder point in a Q system. However, order quantities now vary to keep the inventory position at R at all times. Because this position is the lowest IP possible that will maintain a specified service level, the base-stock system may be used to minimize cycle inventory. More orders are placed, but each order is smaller. This system is appropriate for expensive items, such as replacement engines for jet airplanes. No more inventory is held than the maximum demand expected until a replacement order can be received.
base-stock system
An inventory control system that issues a replenishment order, Q, each time a withdrawal is made, for the same amount of the withdrawal.
Calculating Total Q System Costs
Total costs for the continuous review (Q) system is the sum of three cost components:
Total cost = Annual cycle inventory holding cost + annual ordering cost + annual safety stock holding cost C = Q 2 ( H ) + D Q ( S ) + ( H ) ( Safety stock )
The annual cycle-inventory holding cost and annual ordering cost are the same equations we used for computing the total annual cycle-inventory cost in Example 9.2. The annual cost of holding the safety stock is computed under the assumption that the safety stock is on hand at all times. Referring to Figure 9.10 in each order cycle, we will sometimes experience a demand greater than the average demand during lead time, and sometimes we will experience less. On average over the year, we can assume the safety stock will be on hand. See Solved Problems 4 and 6 at the end of this chapter for an example of calculating the total costs for a Q system.
Advantages of the Q System
The primary advantages of Q systems are the following:
1. The review frequency of each SKU may be individualized. Tailoring the review frequency to the SKU can reduce total ordering and holding costs.
2. Fixed lot sizes, if large enough, can result in quantity discounts. The firm’s physical limitations, such as its truckload capacities, materials handling methods, and shelf space might also necessitate a fixed lot size.
3. The system requires low levels of safety stock for the amount of uncertainty in demands during the lead time.
Periodic Review System
An alternative inventory control system is the periodic review (P) system, sometimes called a fixed interval reorder system or periodic reorder system, in which an item’s inventory position is reviewed periodically rather than continuously. Such a system can simplify delivery scheduling because it establishes a routine. A new order is always placed at the end of each review, and the time between orders (TBO) is fixed at P. Demand is a random variable, so total demand between reviews varies. In a P system, the lot size, Q, may change from one order to the next, but the time between orders is fixed. An example of a periodic review system is that of a soft-drink supplier making weekly rounds of grocery stores. Each week, the supplier reviews the store’s inventory of soft drinks and restocks the store with enough items to meet demand and safety stock requirements until the next week.
periodic review ( P ) system
A system in which an item’s inventory position is reviewed periodically rather than continuously.
Under a P system, four of the original EOQ assumptions are maintained: (1) no constraints are placed on the size of the lot, (2) the relevant costs are holding and ordering costs, (3) decisions for one SKU are independent of decisions for other SKUs, and (4) lead times are certain and supply is known. However, demand uncertainty is again allowed for. Figure 9.13 shows the periodic review system under these assumptions. The downward-sloping line again represents on-hand inventory. When the predetermined time, P, has elapsed since the last review, an order is placed to bring the inventory position, represented by the dashed line, up to the target inventory level, T. The lot size for the first review is Q1, or the difference between inventory position IP1 and T. As with the continuous review system, IP and OH differ only during the lead time. When the order arrives at the end of the lead time, OH and IP again are identical. Figure 9.13 shows that lot sizes vary from one order cycle to the next. Because the inventory position is lower at the second review, a greater quantity is needed to achieve an inventory level of T.
FIGURE 9.13 P System When Demand Is Uncertain
MyOMLab Animation
EXAMPLE 9.8 Determining How Much to Order in a P System
Return to the distribution center (DC) in Example 9.5. Suppose that management wants to use a periodic review system for the Sony TV sets. The first review of the inventory is scheduled for the end of Day 2. Assume that all demands and receipts occur at the end of the day. On the scheduled review day, inventory replenishment orders are placed after the demands and receipts have been accounted for. The lead time is 5 days, and management has set T = 620 and P = 6 days. Given the demand schedule in the table below, determine how much to order (Q) using a P system.
SOLUTION
We use the following equations:
Inventory Position ( IP ) = OH + SR − BO Order Quantity ( Q ) = T − IP
Day
Demand
OH
SR
BO
IP
Q
1
50
400
400
2
60
340
280 after ordering
340 before ordering
340 + 280 = 620 after ordering
620 − 340 = 280 (due Day 7)
3
80
260
280
260 + 280 = 540
4
40
220
280
220 + 280 = 500
5
75
145
280
145 + 280 = 425
6
55
90
280
90 + 280 = 370
7
95
90 + 280 − 95 = 275
275 + 0 = 275
8
50
225
395 after ordering
225 + 0 = 225 before ordering
225 + 395 = 620 after ordering
620 − 225 = 395 (due Day 13)
9
45
180
395
180 + 395 = 575
10
30
150
395
150 + 395 = 545
11
50
100
395
100 + 395 = 495
12
60
40
395
40 + 395 = 435
13
40
40 + 395 − 40 = 395
395 + 0 = 395
14
50
345
275 after ordering
345 + 0 = 345 before ordering
345 + 275 = 620 after ordering
620 − 345 = 275 (due Day 19)
DECISION POINT
The figure to the right shows the relationship between on-hand inventory and the inventory position. The DC did not experience any backorders because on Day 7 the replenishment order arrived in the nick of time. Notice that the order quantities vary in size while the time between orders remains a constant. Compare the operation of the P system in this example to the Q system in Example 9.5. The Q system requires constant monitoring to determine when the order point is reached. However, the average daily inventory is only 188 sets, compared to 226 sets for the P system. Granted, the Q system experienced backorders because of some unexpectedly large orders. Nonetheless, it is a general rule that to gain the benefits of periodic ordering, the P system requires more inventory for the same level of protection against stock-outs or backorders. We will see why this is the case as we develop the parameters for the P system.
Selecting the Time between Reviews
To run a P system, managers must make two decisions: the length of time between reviews, P, and the target inventory level, T. Let us first consider the time between reviews, P. It can be any convenient interval, such as each Friday or every other Friday. Another option is to base P on the cost trade-offs of the EOQ. In other words, P can be set equal to the average time between orders for the economic order quantity, or TBOEOQ. Because demand is variable, some orders will be larger than the EOQ and some will be smaller. However, over an extended period of time, the average lot size should be close to the EOQ. If other models are used to determine the lot size (e.g., those described in Supplement C, “Special Inventory Models”), we divide the lot size chosen by the annual demand, D, and use this ratio as P. It will be expressed as the fraction of a year between orders, which can be converted into months, weeks, or days as needed.
Large, fixed capacity modes of transportation require defined schedules of operation. Such a situation supports the use of periodic review systems. Here ocean vessels await loads of petro-chemicals at the Vopak terminal in the Port of Rotterdam.
Selecting the Target Inventory Level When Demand Is Variable and Lead Time Is Constant
