6 Inventory Systems Rules to manage inventory, specifically: timing (when to order) sizing (how much to order) Continuous Review or Fixed-Order Quantity Models (Q) Event triggered (Example: running out of stock) Periodic Review or Fixed-Time Period Models (P) Time triggered (Example: Monthly sales call by sales representative)
7 Comparison of Periodic and Continuous Review Systems Periodic Review Fixed order intervals Variable order sizes Convenient to administer Inventory position only required at review Continuous Review Varying order intervals Fixed order sizes (Q) Allows individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks
8 Inventory costs C = Unit cost or production cost: the additional cost for each unit purchased or produced. H = Holding costs: cost of keeping items in inventory(cost of lost capital, taxes and insurance for storage, breakage, etc., handling and storing) S = Setup or ordering costs: a fixed cost incurred every time you place an order or a batch is produced.
9 Total costs of carrying inventory Assumptions demand is constant and uniform throughout the period for your products (5 cases per day) Price per unit is constant for the period ($16/case) Inventory holding cost is based on an average cost. Total Inventory Policy Cost annually = annual purchase cost + annual order cost + annual holding cost
11 Total cost of Inventory Policy = annual purchase cost (annual demand * Cost/item) + annual order cost (annual # orders * Cost to order) + annual holding cost (average units held*cost to carry one unit)
12 D = yearly demand of units C = cost of each unit Q = quantity ordered S = cost to place order H = average yearly holding cost for each unit = storage+interest*C D/Q = number of orders per year Q/2 = average inventory held during a given period assuming with start with Q and drop to zero before next order arrives (cycle inventory). Total Inventory Cost Equation
13 Deriving the EOQ : Economic Order Quantity Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero
14 EOQ Model--Basic Fixed-Order Quantity Model (Q) R = Reorder point Q = Economic order quantity L = Lead time L L QQQ R Time Number of units on hand
15 The Reorder Point Reorder point = (average period demand)*Lead Time periods =d * L
16 Another EOQ Example Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15 Determine the economic order quantity & reorder point.
17 Minor Deviations Here What causes minor deviations from the ideal order size? Assumptions behind the regular EOQ Model?
18 Variations in lead time If we have variations in lead time, how should we change the reorder point so we rarely run out? Reorder Point = Average demand during lead time(d*L) + safety stock (Z* L ) where: d= average daily (or weekly) demand L = Lead time (matching days or weeks) L = standard deviation of demand during lead time. D = standard deviation of demand (days or weeks).
19 Service Level or % of time inventory will meet demand during lead time Z ValueResulting Service Level 1.2890% 1.6595% 2.3399% 3.0899.9%
20 Example Annual Demand = 1000 units 250 work days in the year d=1000/250 = 4 units/day Q= 200 units L=9 days L = 3 units z=2 (97.7% likelihood that we wont run out during lead time) Reorder point= d*L +z* L = (4*9) + (2*3) = 42 units
21 P Method (periodic review) You have a predetermined time (P) between orders (sales rep comes by every 10 days) or the average time between orders from EOQ = Q/D How much should you order to bring inventory level up to some predetermined level, R where: R = restocking level Current Inventory position = IP Order Quantity= R-IP
22 Restocking Level Needs to meet most demand situations R= Restocking level = Average demand during lead time & review period+ safety stock = P+L + z* P+L where: P+L = average demand during lead time and review period z = # of standard dev from mean above the average demand (higher z is lower probability of running out). RP+L = standard deviation of demand during lead time + review period
23 ABC Inventory Management Based on Pareto concept (80/20 rule) and total usage in dollars of each item. Classification of items as A, B, or C based on usage. Purpose is to set priorities on effort used to manage different SKUs, i.e. to allocate scarce management resources. SKU: Stock Keeping Unit
24 ABC Inventory Management A items: 20% of SKUs, 80% of dollars B items: 30 % of SKUs, 15% of dollars C items: 50 % of SKUs, 5% of dollars Three classes is arbitrary; could be any number. Percents are approximate. Danger: dollar use may not reflect importance of any given SKU!
25 Item Annual Usage in UnitsUnit CostDollar Usage Percentage of Total Dollar Usage 1 5,000 $ 1.50 $ 7,5002.9% 2 1,500 8.00 12,0004.7% 3 10,000 10.50 105,00041.2% 4 6,000 2.00 12,0004.7% 5 7,500 0.50 3,7501.5% 6 6,000 13.60 81,60032.0% 7 5,000 0.75 3,7501.5% 8 4,500 1.25 5,6252.2% 9 7,000 2.50 17,5006.9% 10 3,000 2.00 6,0002.4% Total $ 254,725100.0% Example of SKU list for 10 items