Inventory Management Chapter 13

Learning Objectives You should be able to: Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management Explain periodic and perpetual review systems Explain the objectives of inventory management Describe the A-B-C approach and explain how it is useful Describe the basic EOQ model and its assumptions and solve typical problems Describe the economic production quantity model and solve typical problems Describe the quantity discount model Describe reorder point models Describe situations in which the single-period model would be appropriate, and solve typical problems Instructor Slides

Inventory Inventory A stock or store of goods Independent demand items Items that are ready to be sold or used A “typical” firm (on “typical” times) has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory 13-3

Types of Inventory Raw materials and purchased parts Work-in-process (WIP) = partially completed goods Finished goods inventories (manufacturing) or merchandise (retail) Maintenance and repairs (MRO) inventory Goods-in-transit to warehouses or customers (pipeline inventory) 13-4

Inventory Inventories are a vital part of business: necessary for operations contribute to customer satisfaction But Costly May have limited shelf-life Carrier may have limited space 13-5

Functions of Inventory To meet anticipated demand “anticipation stock” To smooth production requirements seasonal demand To permit operations Work-In-Process To decouple operations buffer between successive operations in case of a breakdown To protect against stock-outs Delayed deliveries or increase in demand To take advantage of order cycles minimize purchasing and holding costs or economies of producing in large quantities To help hedge against price increases To take advantage of quantity discounts

Inventory Costs Purchase cost Holding (carrying) costs Ordering costs The amount paid to buy the inventory Holding (carrying) costs Cost to carry an item in inventory for a length of time, usually a year (rent, equipment, materials, labor, insurance, security, interest and other direct expenses). Ordering costs Costs of ordering and receiving inventory Setup costs (Analogous to ordering costs) The costs involved in preparing equipment for a job Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit Lead time Time interval between ordering and receiving the order 13-7

Objectives of Inventory Control The overall objective of inventory management is to achieve: Satisfactory levels of customer service Having the right goods available in the right quantity in the right place at the right time Focus on size and timing While keeping inventory costs (ordering and carrying) within reasonable bounds (minimize) 13-8

Objectives of Inventory Control Measures of performance: Customer satisfaction Number and quantity of backorders Customer complaints Inventory turnover = (average) cost of goods sold (average) inventory investment during a period 13-9

Inventory Management Management has two basic functions concerning inventory: Establish a system for tracking items in inventory Make decisions about When to order How much to order 13-10

ABC Classification System A-B-C approach Classifying inventory according to some measure of importance, and allocating control efforts accordingly A items (very important) 10 to 20 percent of the number of items in inventory about 60 to 70 percent of the annual dollar value B items (moderately important) C items (least important) 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value 13-11

ABC Classification System How to classify? For each item, multiply annual volume by unit price to get the annual dollar value. Arrange annual values in descending order. A items: the few with the highest annual dollar value C items: the most with the lowest dollar value. B items: those in between # Annual demand Unit price Annual value Clss % of items % of value 8 1,000 4,000 4,000,000 A 5.3 52.7 3 2,400 500 1,200,000 B 6 1,000,000 31.4 40.8 1 2,500 360 900,000 4 1,500 100 150,000 C 10 200 100,000 9 8,000 80,000 2 70 70,000 63.3 6.5 5 700 49,000 7 210 42,000 18,800 7,591,000 13-12

Inventory Counting Systems Periodic System (e.g. small retailer) Physical count of items in inventory made at periodic intervals Many items ordered at the same time. Savings in processing and shipping of orders. vs. Lack of control between reviews. Having to keep extra stock to protects against shortages. Perpetual Inventory System (e.g. bank transactions) 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 (can optimize Q) Vs. Added cost of record keeping. Usually has to be accompanied by a periodic physical count. Note: RFID technology is used by inventory counting systems 13-13

Inventory Ordering Models Economic Order Quantity models: identify the optimal order quantity by minimizing total annual costs that vary with order size and frequency The basic Economic Order Quantity model (EOQ) The Economic Production Quantity model (EPQ) The Quantity Discount model* Other Models Reorder Point Ordering* (uncertainty, when to order) Fixed-Order-Interval Model* Single Period model (perishable items) 13-14

Basic Economic Order Quantity Model The basic EOQ model: used to find a fixed order quantity that will minimize total annual inventory costs Purchase price is not included (cost is unaffected by it) Assumptions: Only one product is involved Annual demand requirements are known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts 13-15

The Inventory Cycle (EOQ) Profile of Inventory Level Over Time Quantity on hand Q Receive order Place Lead time Reorder point Usage rate Time 13-16

Total Annual Cost 13-17 Average number of units in inventory Number of orders 13-17

Goal: Total Cost Minimization Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QO Annual Cost (optimal order quantity) Holding Costs 13-18

Deriving EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. Length of order cycle = Q/D Number of orders = D/Q The total cost curve reaches its minimum where the carrying and ordering costs are equal. 13-19

Example Tire distributer D (Demand)=9,600 tires per year H (Holding cost)=$16 per unit per year S (Ordering cost) = $75 per order

Example Tire distributer D (Demand)=9,600 tires per year H (Holding cost)=$16 per unit per year S (Ordering cost) = $75 per order Q0=300 tires TCmin = 4,800 TC curve relatively flat at optimum

Economic Production Quantity (EPQ) The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate) Assumptions Only one item is involved Annual demand requirements are known Usage rate is constant Usage occurs continually, but production occurs periodically The production rate is constant Lead time does not vary There are no quantity discounts Instructor Slides

EPQ: Inventory Profile Qp Imax Production and usage Usage only Cumulative production Amount on hand Time Instructor Slides

EPQ – Total Cost Solution: Instructor Slides

Example Toy manufacturer makes rubber wheels for dump truck toys. D=48,000 wheels per year S=$45 H=$1 per wheel per year P=800 wheels per day u=200 wheels per day Instructor Slides

Quantity Discount Model Take into account quantity discount offered by supplier (add purchase cost to model) Quantity discount Price reduction for larger orders offered to customers to induce them to buy in large quantities Instructor Slides

Quantity Discounts* The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price Adding PD does not change EOQ Instructor Slides

Reorder Point Ordering When the quantity on hand of an item drops to this amount (quantity-trigger), the item is reordered. Determinants of the Reorder-Point The rate of demand The lead time The extent of demand and/or lead time variability The degree of stockout risk acceptable to management 13-28

Safety Stock* Instructor 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 Instructor Slides

Fixed-Quantity (ROP) vs. Fixed-Interval Ordering* Instructor Slides

Single-Period Model Single-period model Model for ordering of perishables and other items with limited useful lives Period = life of the good. Items are not carried over to the next period The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs Two categories of problems: Demand can be characterized by a continuous distribution Demand can be characterized by a discrete distribution 13-32

Single-Period Model Shortage cost Generally, the unrealized profit per unit Cshortage = Cs = Revenue per unit – Cost per unit Excess cost Different between purchase cost and salvage value of items left over at the end of the period Cexcess = Ce = Cost per unit – Salvage value per unit 13-33

Continuous Stocking Levels Uniform Demand Service Level = probability that demand will not exceed the stocking level (S). Shortage: Demand > S0 Excess: Demand < S0 Service level So Balance Point Quantity Ce Cs So =Optimum Stocking Quantity Like a Seesaw, leverage If demand is not uniformly distributed, consider cumulative probability of demand So=min+SL*(max-min) 13-34

Continuous Stocking Levels Uniform Demand Sweet cider delivered to bar Demand uniformly distributed between 300 and 500 liters/week. Cost=20 cent/liter Revenue = 80 cent/liter. Ce= cost-salvage =.2 $/liter Cs= revenue-cost =.8-.2=.6 $/liter SL= Cs/(Cs+Ce) =.6/(.6+.2)=.75 So= min+SL*(max-min) =300+.75*(500-300)=450 liter Stockout risk = 1-SL = 1- .75=.25 Service level=75% So =450 Balance Point Ce=.2 $/liter Cs=.6 $/liter 300 500 13-35

Discrete Stocking Levels Cs/(Cs+Ce) may not coincide with a feasible stocking level. Solution: Stock at the next higher level so that the desired service level is equaled or exceeded. 13-36

Discrete Stocking Levels p = $5.5 v= $0 c= $2 SL= Cs/(Cs+Ce)= (p-c)/[(p-c)+(c-v)] = (5.5-2)/[(5.5-2)+(2-0)] = 3.5/(3.5+2)= .636 Q=13 Q P(R≤Q) Expected profit 1 0.05 3.5 2 0.1 6.725 3 0.15 9.675 4 0.2 12.35 5 0.25 14.75 6 0.3 16.875 7 0.35 18.725 8 0.4 20.3 9 0.45 21.6 10 0.5 22.625 11 0.55 23.375 12 0.6 23.85 13 0.65 24.05 14 0.7 23.975 15 0.75 23.625 16 0.8 23 17 0.85 22.1 18 0.9 20.925 19 0.95 19.475 20 17.75

Discrete Stocking Levels Shortage (downtime) cost = $4,200 Excess (spare part) cost = $200 SL = = 4200/(4200+200) = .84 Next level - > 2 spare parts 90% will not run out of spare parts Spares used Relative frequency Cumulative frequency .2 1 .4 .6 2 .3 .9 3 .1 4 or more 13-38

Operations Strategy* Too much inventory: Costly to maintain Tends to hide problems (easier to live with problems than to eliminate them) Wise strategy = find ways to Improve demand forecasts = reduce safety stock Improve inventory management Reduce Ordering costs Reduce inventory Holding costs Reduce variation (e.g., lead-time) Lean Operations Supply-Chain Management