You should be able to: 1. Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management 2. Discuss the nature and importance of service inventories 3. Explain periodic and perpetual review systems 4. Explain the objectives of inventory management 5. Describe the A-B-C approach and explain how it is useful 6. Describe the basic EOQ model and its assumptions and solve typical problems 7. Describe the economic production quantity model and solve typical problems 8. Describe the quantity discount model and solve typical problems 9. Describe reorder point models and solve typical problems 10. Describe situations in which the single-period model would be appropriate, and solve typical problems 13-2 Student Slides
Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used Inventories are a vital part of business: (1) necessary for operations and (2) contribute to customer satisfaction A “typical” firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory 13-3 Student Slides
Management has two basic functions concerning inventory: 1. Establish a system for tracking items in inventory 2. Make decisions about When to order How much to order Student Slides 13-4
Periodic System Physical count of items in inventory made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item An order is placed when inventory drops to a predetermined minimum level Two-bin system Two containers of inventory; reorder when the first is empty Student Slides 13-5
Purchase cost The amount paid to buy the inventory Holding (carrying) costs (H) Cost to carry an item in inventory for a length of time, usually a year Ordering costs (S) Costs of ordering and receiving inventory Setup costs (S) The costs involved in preparing equipment for a job Analogous to ordering costs Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit 13-6 Student Slides
Annual Demand (D) Order Quantity (Q) Holding (carrying) costs (H or C) Cost to carry an item in inventory for a length of time, usually a year Ordering costs (S) Costs of ordering and receiving inventory Total Annual Cost (TC) TC = (Q/2)(H) + (D/Q)(S) 13-7 Student Slides
Annual Cost ($) Order Quantity Minimum Total Annual Stocking Costs Annual Carrying Costs Annual Ordering Costs Total Annual Stocking Costs SmallerLarger Lower Higher EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. 13-9 Student Slides
Zartex Co. produces fertilizer to sell to wholesalers. One raw material – calcium nitrate – is purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year. The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595. a) What is the most economical order quantity? b) How many orders will be placed per year? c) How much time will elapse between orders?
Economical Order Quantity (EOQ) D = 5,750,000 tons/year H =.40(22.50) = $9.00/ton/year S = $595/order = 27,573.135 tons per order
Total Annual Stocking Cost (TSC) TSC = (Q/2)H + (D/Q)S = (27,573.135/2)(9.00) + (5,750,000/27,573.135)(595) = 124,079.11 + 124,079.11 = $248,158.22 Note: Total Carrying Cost equals Total Ordering Cost
Number of Orders Per Year = D/Q = 5,750,000/27,573.135 = 208.5 orders/year Time Between Orders = Q/D = 1/208.5 =.004796 years/order =.004796(365 days/year) = 1.75 days/order Note: This is the inverse of the formula above.
Setup costs (S) The costs involved in preparing equipment for a job Analogous to ordering costs Daily production rate: p Daily usage rate: u Assuming p > u TC = (Q/2p) (p-u) (H) + (D/Q) (S) 13-14 Student Slides
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. 13-15 Student Slides
Highland Electric Co. buys coal from Cedar Creek Coal Co. to generate electricity. CCCC can supply coal at the rate of 3,500 tons per day for $10.50 per ton. HEC uses the coal at a rate of 800 tons per day and operates 365 days per year. HEC’s annual carrying cost for coal is 20% of the acquisition cost, and the ordering cost is $5,000. a) What is the economical production lot size? b) What is HEC’s maximum inventory level for coal?
Economical Production Lot Size d = 800 tons/day; D = 365(800) = 292,000 tons/year p = 3,500 tons/day S = $5,000/order H =.20(10.50) = $2.10/ton/year = 42,455.5 tons per order
Total Annual Stocking Cost (TSC) TSC = (Q/2)((p-d)/p)H + (D/Q)S = (42,455.5/2)((3,500-800)/3,500)(2.10) + (292,000/42,455.5)(5,000) = 34,388.95 + 34,388.95 = $68,777.90 Note: Total Carrying Cost equals Total Ordering Cost
Maximum Inventory Level = Q(p-d)/p = 42,455.5(3,500 – 800)/3,500 = 42,455.5(.771429) = 32,751.4 tons Note: HEC will use 23% of the production lot by the time it receives the full lot.
Reorder point When the quantity on hand of an item drops to this amount, the item is reordered. Determinants of the reorder point 1. The rate of demand 2. The lead time 3. The extent of demand and/or lead time variability 4. The degree of stockout risk acceptable to management Student Slides 13-20
Demand or lead time uncertainty creates the possibility that demand will be greater than available supply To reduce the likelihood of a stockout, it becomes necessary to carry safety stock Safety stock Stock that is held in excess of expected demand due to variable demand and/or lead time Student Slides 13-22
The amount of safety stock that is appropriate for a given situation depends upon: 1. The average demand rate and average lead time 2. Demand and lead time variability 3. The desired service level Student Slides 13-23
Note: If only demand is variable, then 13-24 Student Slides
Fixed-order-interval (FOI) model Orders are placed at fixed time intervals Reasons for using the FOI model Supplier’s policy may encourage its use Grouping orders from the same supplier can produce savings in shipping costs Some circumstances do not lend themselves to continuously monitoring inventory position Student Slides 13-26
OI = Order Interval D = Annual Demand H = Ordering Cost Optimal order interval 13-27 Student Slides
D = 29,385 jars per year S = $10.90 per order AC: acquisition cost = $0.29 per jar H = @30% of the ac = $0.29*0.3 Optimal order interval 13-28 Student Slides
Class A 20% of the materials in inventory 75% of the inventory value Class B 30% of the materials in inventory 20% of the inventory value Class A 50% of the materials in inventory 5% of the inventory value Student Slides 13-30
Inventory management can offer significant cost reduction and customer satisfaction by: Good record keeping Records and data must be accurate and up-to-date Variation reduction Lead variation Forecast errors Reduced stockout Lean operations Low inventory level Low inventory cost Low operation cost Higher inventory turnover Supply chain management Student Slides 13-31