INVENTORY AND ECONOMIC ORDER QUANTITY MODELS Types of Demand Retailers and distributors must manage independent demand items-that is, items for which demand is influenced by market conditions and isn t related to the inventory decisions for any other item held in stock. Independent demand inventory includes: 1. wholesale and retail merchandise 2. service industry inventory 3. end-item and replacement part distribution inventories 4. maintenance, repair and operating (MRO) supplies Manufacturers and service providers must manage dependent demand items-that is, items that are required as components or inputs to a product or service. Accounting Categories of Inventory Inventory exists in three aggregate categories, which are useful for accounting purposes. Raw materials are inventories needed for the production of good or services. While they have arrived from the supplier, no processing has yet been applied to them. Work-inprocess consists of components or sub assemblies used in the manufacture of final products. WIP is also present in service industries. In both cases, one or more phases of processing have been completed. Finished goods in manufacturing plants, warehouses, and retail outlets are items sold to the firm s customers. Types of Inventory Another way to look at inventory is to consider how or why it comes into being. Cycle inventory. The portion of total inventory that varies directly with the lot size is called cycle inventory. Determining how much to order and how often is called lot sizing. The lot size and therefore the cycle inventory vary directly with the elapsed time between orders. For example, if orders are placed every three weeks, the average lot size must equal 3 weeks of demand and the average cycle inventory will be 1-½ weeks of demand. Safety stock inventory. To provide adequate customer service and avoid costs of unavailable components, companies hold safety stock. Safety stock inventory protects against uncertainties in demand, lead-time and supply. To create safety stock, a firm places an order for an item earlier than when the items is expected to be needed. Anticipation inventory. Inventory used to absorb uneven rates of demand or supply is called anticipation inventory. It is often an attractive alternative to changing the size of the workforce and the use of overtime. A common example is building an inventory for a peak sales season.
Pipeline inventory. Inventory moving from point to point in the materials flow system is called pipeline inventory. Pipeline inventory between two points is determined by the corresponding lead-time. Decoupling inventory. Inventory that s serves as a buffer between stages in a production process that have significantly different operating characteristics (e.g., set up times, lot sizes, run lengths, product flexibility, etc.). It also is used to buffer production from distribution. ABC Inventory Classification Inventories are often classified in order to allocate the appropriate extent of management review. A typical approach is the ABC classification. Class A items typically represent 10% to 20% of the items types or stock keeping units (SKU) and as much as 80% of the dollar value of the inventory. These items are identified for top management attention. Class B items typically represent about 30% of the items types or SKU s and 10% to 20% of the dollar value of the inventory. These items receive management attention by exception and typically are handled by computer systems. Class C items typically represent about 50% of the items types or SKU s and as little as 5% of the dollar value of the inventory. These items are handled by crude systems and seldom receive management attention. Inventory Placement A critical decision in the design of supply chains is where to locate the inventories of finished goods. Backward placement refers to the strategy of placing inventory back in the supply chain. The extreme case is to hold no finished goods inventory and to assemble to order or build to order. Another somewhat less extreme case is to hold inventory in a single centralized facility. Backwards placement provides the benefits of pooling which reduces risk and the levels of safety stock required. Forward placement is the opposite strategy of placing inventory backward in the supply chain, i.e., nearer the customer. The advantages include faster response time to customers and, sometimes, reduced transportation costs, both of which can lead to enhanced sales. Inventory Review Systems Inventory levels are reviewed or measured either continuously or periodically.
Continuous Review (Q) Systems, sometimes called reorder point (ROP) systems, track the inventory level each time a withdrawal is made to determine if it is time to reorder. Whenever the inventory level falls to or below a reorder point (R), an order for a fixed quantity (Q) is made. Although the order size is fixed, the time between orders (TBO) will change. Periodic Review (P) Systems, review the inventory level at fixed periods (e.g., weekly, monthly) in order to determine how large an order to place. An order is placed to take the inventory position (on hand inventory + schedules receipts backorders) up to a predetermined target level (T). Thus in a P system the TBO is constant but the order quantity will change. ECONOMIC ORDER QUANTITY In a continuous review system, ordering too often (in quantities too small) increases the annual cost of placing orders. Ordering too infrequently (in quantities too large) increases the annual cost of holding inventory. The economic order quantity (EOQ) is the quantity that minimizes the sum of these two costs. It is based on the following assumptions: 1. The demand for the item is constant and known with certainty. 2. There are no upper or lower limits on the order quantity (lot size). 3. Stockouts are not permitted. 4. There are no quantity discounts. 5. Lead time and supply are known with certainty; lead time is constant. 6. Order quantities for individual items are made independently. The classic saw tooth diagram of inventory level over time is illustrated in Figure 1. Figure 1. Inventory levels over time.
Cost If we define C - total annual (period) cost S - fixed cost of placing an order D - annual (period) demand H - annual (period) unit cost of holding inventory Q order quantity (to be determined) then SD HQ C. Q 2 The Figure 2 displays the cost relationships involved in the model: Cost Versus Order Quantity 1200 1000 800 600 400 200 0 100 200 300 400 500 600 700 800 900 1000 Q Order Cost = (S*D)/Q Holding Cost = (H*Q)/2 Total Cost Figure 2. Inventory cost versus order size Q. The economic order quantity is calculated by EOQ 2SD H. MINIMUM ORDER SIZES AND ORDER BLOCK SIZES Dealing with minimum order sizes and order block sizes (a number which all order sizes must be a multiple of) is quite easy. We Round EOQ to AOQ (allowable order quantity) by choosing the multiple of the order block size that is closest to EOQ and at least equal to minimum order size
QUANTITY DISCOUNTS In many instances, a vendor offers an item at a unit price, which we will call the normal cost and denote by P n, but will make the item available at a reduced unit cost, which we will call the discount cost and denote by P d, as long as the order size is at least equal to the discount volume (DV). In such a case we begin by calculating EOQ and rounding to AOQ. The cost relationships for the quantity discount problem are illustrated in Figure 3. Figure 3. Cost relationships for quantity discounts. Therefore, we must compare the total cost per period for AOQ and DV and use whichever produces the smaller cost. This total cost adds the purchase cost per period to the order plus holding cost specified previously. Thus we calculate (1) Daily Cost ataoq SD H * AOQ D * Pn, AOQ 2 IF AOQ DV OR
Daily Cost ataoq SD H * AOQ D * Pd, AOQ 2 IF AOQ DV AND SD H * DV ( 2) Daily Costat DV D * DV 2 However, it can be noted that whenever AOQ DV, the cost comparison will always select AOQ. EXAMPLES Suppose demand for final product is as follows: F001: 98 F002: 244 F003: 198 Consider P037 Spokes 20 Order cost (S): $ 10 Holding Cost Per Day (H): $0.00009 Normal Cost (P n ): $ 0.050 Discount Cost (P d ): $ 0.045 Discount Volume (DV): 200,000 Minimum Order: 20,000 Order block: 2,000 Since there are 72 P037 s in each F001 and 0 in each F002 and F003, we estimate daily volume for P037 as D = Daily Volume = 98(72)+244(0)+198(0) = 7056 P d Q 2SD H 2(10)(7056).00009 39,598 Above minimum order so round to AOQ = 40,000 Since AOQ is below DV we calculate by (1) by using the first equation
DailyCost ataoq 10(7,056) 40,000.00009(40,000) 7,056(.050) 1.76 1.80 352.80 356.36 2 and by (2) DailyCost atdv 10(7,056) 200,000.00009(200,000) 7,056(.045) 0.35 9.00 317.52 326.87 2 Then since Daily Cost at DV < Daily Cost at AOQ order quantity is set to discount volume = 200,000. Order cycle = DV/ D = 200,000/(7,056) = 28.3 days Consider P043 Steel Tubing Order cost(s): $ 45 Holding Cost Per Day(H): $0.00035 Normal Cost (P n ): $ 0.20 Discount Cost (P d ): $ 0.18 Discount Volume (DV): 10,000 Minimum order: 5,000 Order block: 1000 Since there are 21 P043 s in each F001, 23 in each F002 and 24 in each F003, we estimate daily volume for P043 as D = Daily Volume = 98 (21) + 244(23) + 198(24) = 12,422 Q 2SD H 2(45)(12,422).00035 56,517,51 Above minimum order so round to 57,000 Since AOQ is above DV we calculate by (1) by using the second equation DailyCost ataoq 45(12,422) 57,000.00035(57,000) 12,422(.18) 9.81 9.97 2,235.96 2,255.74 2 and by (2) DailyCost atdv 45(12,422) 10,000.00035(10,000) 12,422(.18) 55.90 1.75 2,235.96 2,293.61 2
Then since Daily Cost at AOQ < Daily Cost at DV order quantity is set to AOQ = 57,000. This could have been anticipated since AOQ > DV. Order cycle =AOQ/D = 57,000/12,422 = 4.6 days