Inventory Management

Learning Objectives  Define the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management.  Discuss the nature and importance of service inventories  Discuss periodic and perpetual review systems.  Discuss the objectives of inventory management.  Describe the A-B-C approach and explain how it is useful.

Learning Objectives  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 and solve typical problems.  Describe reorder point models and solve typical problems.  Describe situations in which the single- period model would be appropriate, and solve typical problems.

Independent Demand A B(4) C(2) D(2)E(1) D(3) F(2) Dependent Demand Independent demand is uncertain. Dependent demand is certain. Inventory: a stock or store of goods Inventory

Inventory Models  Independent demand – finished goods, items that are ready to be sold  E.g. a computer  Dependent demand – components of finished products  E.g. parts that make up the computer

Types of Inventories  Raw materials & purchased parts  Partially completed goods called work in progress  Finished-goods inventories  (manufacturing firms) or merchandise (retail stores)

Types of Inventories (Cont’d)  Replacement parts, tools, & supplies  Goods-in-transit to warehouses or customers

Functions of Inventory  To meet anticipated demand  To smooth production requirements  To decouple operations  To protect against stock-outs

Functions of Inventory (Cont’d)  To take advantage of order cycles  To help hedge against price increases  To permit operations  To take advantage of quantity discounts

Objective of Inventory Control  To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds  Level of customer service  Costs of ordering and carrying inventory Inventory turnover is the ratio of average annual cost of goods sold to average inventory investment.

 A system to keep track of inventory  A reliable forecast of demand  Knowledge of lead times  Reasonable estimates of  Holding costs  Ordering costs  Shortage costs  A classification system Effective Inventory Management

Inventory Counting Systems  Periodic System Physical count of items made at periodic intervals  Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

Perpetual Inventory System  Two-Bin System - Two containers of inventory; reorder when the first is empty  Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached

 Lead time: time interval between ordering and receiving the order  Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year  Ordering costs: costs of ordering and receiving inventory  Shortage costs: costs when demand exceeds supply Key Inventory Terms

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A A – 10-20% items, 60-70% value B B – 30-40% items, 20-30% value C C – 50-60% items, 10-15% value Annual Value of items A B C High Low High Percentage of Items

Cycle Counting  A physical count of items in inventory  Cycle counting management  How much accuracy is needed?  When should cycle counting be performed?  Who should do it?

Cycle Counting Example 5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C items Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days) Item ClassQuantityCycle Counting Policy Number of Items Counted per Day A500Each month500/20 = 25/day B1,750Each quarter1,750/60 = 29/day C2,750Every 6 months2,750/120 = 23/day 77/day

 Economic order quantity (EOQ) model  The order size that minimizes total annual cost  Economic production model  Quantity discount model Economic Order Quantity Models

 Only one product is involved  Annual demand requirements 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 Assumptions of EOQ Model

The Inventory Cycle Profile of Inventory Level Over Time Quantity on hand Q Receive order Place order Receive order Place order Receive order Lead time Reorder point Usage rate Time

Total Cost Annual carrying cost Annual ordering cost Total cost =+ TC = Q 2 H D Q S + Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost

Cost Minimization Goal Order Quantity (Q) The Total-Cost Curve is U-Shaped Ordering Costs QOQO Annual Cost ( optimal order quantity)

Deriving the EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D Q S =

Reorder Points  EOQ answers the “how much” question  The reorder point (ROP) tells when to order ROP = Lead time for a new order in days Demand per day = d x L d = D Number of working days in a year

Reorder Point Curve Q* ROP (units) Inventory level (units) Time (days) Lead time = L Slope = units/day = d

 Production done in batches or lots  Capacity to produce a part exceeds the part’s usage or demand rate  Assumptions of EPQ are similar to EOQ except orders are received incrementally during production Economic Production Quantity (EPQ)

 Only one item is involved  Annual demand is known  Usage rate is constant  Usage occurs continually  Production rate is constant  Lead time does not vary  No quantity discounts Economic Production Quantity Assumptions

Production Order Quantity Model Inventory level Time Demand part of cycle with no production Part of inventory cycle during which production (and usage) is taking place t Maximum inventory

Economic Run Size Q = Order quantity H = Holding cost D = Annual demand S = Ordering cost or Setup cost p = Production rate or Delivery rate u = Usage rate

Quantity discount model Annual carrying cost Purchasing cost TC =+ Q 2 H D Q S + + Annual ordering cost PD +

Quantity discount model Unit price 1 Unit price 2 Unit price 3 TC1 TC3 TC2 Cost Quantity

When to Reorder with EOQ Ordering  Reorder Point - When the quantity on hand of an item drops to this amount, the item is reordered  Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.  Service Level - Probability that demand will not exceed supply during lead time.

Determinants of the Reorder Point  The rate of demand  The lead time  Demand and/or lead time variability  Stockout risk (safety stock)

Stock-out Cost can be determined  Used when demand is not constant or certain  Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the {units short x the probability x the stockout cost/unit x the number of orders per year}

Safety Stock Example Demand (Units) Probability of demand level ROP  ROP = 50 unitsStockout cost = $40 per units Orders per year = 6 Carrying cost = $5 per units per year

Safety Stock Example ROP = 50 unitsStockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding CostStockout Cost Total Cost 20(20)($5) = $100$0$100 10(10)($5) = $50(10)(.1)($40)(6)=$240$290 0$0(10)(.2)($40)(6) + (20)(.1)($40)(6)=$960$960 A safety stock of 20 frames gives the lowest total cost ROP = = 70 frames

Safety stock ROP  Place order Probabilistic Demand Inventory level Time Minimum demand during lead time Maximum demand during lead time Mean demand during lead time Normal distribution probability of demand during lead time Expected demand during lead time ROP Receive order Lead time 0 Risk

Probabilistic Demand Safety stock Probability of no stockout 95% of the time Mean demand ROP = ? units Quantity Number of standard deviations 0 z Risk of a stockout (5% of area of normal curve) Z=1.65

Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + Z  dlt whereZ =number of standard deviations  dlt =standard deviation of demand during lead time

Other Probabilistic Models 1.When demand is variable and lead time is constant 2.When lead time is variable and demand is constant 3.When both demand and lead time are variable When data on demand during lead time is not available, there are other models available

Other Probabilistic Models Demand is variable and lead time is constant ROP =(average daily demand x lead time in days) + Z  dlt where  d = standard deviation of demand per day  dlt =  d lead time

Probabilistic Example Average daily demand (normally distributed) = 15 Standard deviation = 5 Lead time is constant at 2 days 90% service level desired Z for 90% = 1.28 ROP= (15 units x 2 days) + Z  dlt = (5)( 2) = = ≈ 39 Safety stock is about 9 units

Other Probabilistic Models Lead time is variable and demand is constant where  lt = standard deviation of lead time in days ROP =(daily demand x average lead time) + Z  dlt Z  dlt Z x (daily demand) x σ lt Z  dlt =Z x (daily demand) x σ lt

Probabilistic Example Daily demand (constant) = 10 Average lead time = 6 days Standard deviation of lead time =  lt = 3 98% service level desired Z for 98% = ROP= (10 units x 6 days) (10 units)(3) = = Reorder point is about 122 units

Other Probabilistic Models Both demand and lead time are variable ROP =(average daily demand x average lead time) + Z  dlt where  d =standard deviation of demand per day  lt =standard deviation of lead time in days  dlt =(average lead time x  d 2 ) + (average daily demand) 2  lt 2

Probabilistic Example Average daily demand (normally distributed) = 150 Standard deviation =  d = 16 Average lead time 5 days (normally distributed) Standard deviation =  lt = 1 days 95% service level desired Z for 95% = 1.65 ROP= (150 packs x 5 days)  dlt = (150 x 5) (5 days x 16 2 ) + (150 2 x 1 2 ) = (154) = 1,004 packs

 Orders are placed at fixed time intervals  Order quantity for next interval?  Suppliers might encourage fixed intervals  May require only periodic checks of inventory levels  Risk of stockout Fixed-Order-Interval Model

On-hand inventory Time Q1Q1Q1Q1 Q2Q2Q2Q2 Target maximum (T) P Q3Q3Q3Q3 Q4Q4Q4Q4 P P Fixed-Order-Interval Model

 Tight control of inventory items  Items from same supplier may yield savings in:  Ordering  Packing  Shipping costs  May be practical when inventories cannot be closely monitored Fixed-Interval Benefits

 Requires a larger safety stock  Increases carrying cost  Costs of periodic reviews Fixed-Interval Disadvantages

 Single period model: model for ordering of perishables and other items with limited useful lives  Shortage cost: generally the unrealized profits per unit = revenue per unit – Cost per unit  Excess cost: difference between purchase cost and salvage value of items left over at the end of a period = Original cost per unit – Salvage value per unit Single Period Model

Optimal Stocking Level Service Level So Quantity CeCs Balance point Service level = Cs Cs + Ce Cs = Shortage cost per unit Ce = Excess cost per unit

Example 15  Ce = $0.20 per unit  Cs = $0.60 per unit  Service level = Cs/(Cs+Ce) =.6/(.6+.2)  Service level =.75 Service Level = 75% Quantity CeCs Stockout risk = 1.00 – 0.75 = 0.25

Supermarket  Items used by many products are held in a common area often called a supermarket  Items are withdrawn as needed  Inventory is maintained using JIT systems and procedures  Common items are not planned by the MRP system

 Too much inventory  Tends to hide problems  Easier to live with problems than to eliminate them  Costly to maintain  Wise strategy  Reduce lot sizes  Reduce safety stock Operations Strategy