Published on January 23, 2008
Managing Facilitating Goods: Managing Facilitating Goods Factory Wholesaler Distributor Retailer Customer Replenishment order Replenishment order Replenishment order Customer order Production Delay Wholesaler Inventory Shipping Delay Shipping Delay Distributor Inventory Retailer Inventory Item Withdrawn Learning Objectives : Learning Objectives Discuss the role of information technology in managing inventories. Describe the functions and costs of an inventory system. Determine the order quantity. Calculate the reorder point and safety stock for an inventory system. Design a continuous or periodic review inventory-control system. Conduct an ABC analysis of inventory items. Determine the order size for the single-period inventory case. Describe the rationale behind the retail discounting model. Role of Inventory in Services: Role of Inventory in Services Decoupling inventories Seasonal inventories Speculative inventories Cyclical inventories In-transit inventories Safety stocks Considerations in Inventory Systems: Considerations in Inventory Systems Type of customer demand Planning time horizon Replenishment lead time Constraints Relevant Inventory Costs: Relevant Inventory Costs Ordering costs Receiving and inspections costs Holding or carrying costs Shortage costs Inventory Management Questions: Inventory Management Questions What should be the order quantity (Q)? When should an order be placed, called a reorder point (ROP)? How much safety stock (SS) should be maintained? Inventory Models: Inventory Models Economic Order Quantity (EOQ) Special Inventory Models With Quantity Discounts Planned Shortages Demand Uncertainty - Safety Stocks Inventory Control Systems Continuous-Review (Q,r) Periodic-Review (order-up-to) Single Period Inventory Model Inventory Levels For EOQ Model: Inventory Levels For EOQ Model 0 Units on Hand Q Q D Time Annual Costs For EOQ Model: Annual Costs For EOQ Model EOQ Formula: EOQ Formula Notation D = demand in units per year H = holding cost in dollars/unit/year S = cost of placing an order in dollars Q = order quantity in units Total Annual Cost for Purchase Lots EOQ Annual Costs for Quantity Discount Model: Annual Costs for Quantity Discount Model 0 100 200 300 400 500 600 700 22,000 21000 20000 2000 1000 C = $20.00 C = $19.50 C = $18.75 Order quantity, Q Annual Cost, $ Inventory Levels For Planned Shortages Model: Inventory Levels For Planned Shortages Model Q Q-K 0 -K T1 T2 TIME T Formulas for Special Models: Formulas for Special Models Quantity Discount Total Cost Model Model with Planned Shortages Values for Q* and K* as AFunction of Backorder Cost: Values for Q* and K* as A Function of Backorder Cost B Q* K* Inventory Levels undefined Q* 0 0 0 0 Demand During Lead Time Example: Demand During Lead Time Example + + + = u=3 u=3 u=3 u=3 ROP s s Four Days Lead Time Demand During Lead time Safety Stock (SS): Safety Stock (SS) Demand During Lead Time (LT) has Normal Distribution with - - SS with r% service level Reorder Point Continuous Review System (Q,r): Continuous Review System (Q,r) Average lead time usage, dL Reorder point, ROP Safety stock, SS Inventory on hand Order quantity, EOQ EOQ EOQ d1 d2 d3 Amount used during first lead time First lead time, LT1 Order 1 placed LT2 LT3 Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received Time Periodic Review System(order-up-to): Periodic Review System (order-up-to) RP RP RP Review period First order quantity, Q1 d1 Q2 Q3 d2 d3 Target inventory level, TIL Amount used during first lead time Safety stock, SS First lead time, LT1 LT2 LT3 Order 1 placed Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received Time Inventory on Hand Inventory Control Systems: Inventory Control Systems Continuous Review System Periodic Review System ABC Classification of Inventory Items: ABC Classification of Inventory Items A B C Inventory Items Listed in Descending Order of Dollar Volume: Inventory Items Listed in Descending Order of Dollar Volume Monthly Percent of Unit cost Sales Dollar Dollar Percent of Inventory Item ($) (units) Volume ($) Volume SKUs Class Computers 3000 50 150,000 74 20 A Entertainment center 2500 30 75,000 Television sets 400 60 24,000 Refrigerators 1000 15 15,000 16 30 B Monitors 200 50 10,000 Stereos 150 60 9,000 Cameras 200 40 8,000 Software 50 100 5,000 10 50 C Computer disks 5 1000 5,000 CDs 20 200 4,000 Totals 305,000 100 100 Single Period Inventory ModelNewsvendor Problem Example: Single Period Inventory Model Newsvendor Problem Example D = newspapers demanded p(D) = probability of demand Q = newspapers stocked P = selling price of newspaper, $10 C = cost of newspaper, $4 S = salvage value of newspaper, $2 Cu = unit contribution: P-C = $6 Co = unit loss: C-S = $2 Single Period Inventory Model Expected Value Analysis: Single Period Inventory Model Expected Value Analysis Stock Q p(D) D 6 7 8 9 10 .028 2 4 2 0 -2 -4 .055 3 12 10 8 6 4 .083 4 20 18 16 14 12 .111 5 28 26 24 22 20 .139 6 36 34 32 30 28 .167 7 36 42 40 38 36 .139 8 36 42 48 46 44 .111 9 36 42 48 54 52 .083 10 36 42 48 54 60 .055 11 36 42 48 54 60 .028 12 36 42 48 54 60 Expected Profit $31.54 $34.43 $35.77 $35.99 $35.33 Single Period Inventory Model Incremental Analysis: Single Period Inventory Model Incremental Analysis E (revenue on last sale) E (loss on last sale) P ( revenue) (unit revenue) P (loss) (unit loss) (Critical Fractile) where: Cu = unit contribution from newspaper sale ( opportunity cost of underestimating demand) Co = unit loss from not selling newspaper (cost of overestimating demand) D = demand Q = newspaper stocked Critical fractile for the newsvendor problem: Critical fractile for the newsvendor problem P(D<Q) (Co applies) P(D>Q) (Cu applies) 0.722 Topics for Discussion: Topics for Discussion Discuss the functions of inventory for different organizations in the distribution system. How would one find values for inventory costs? How can information technology create a competitive advantage through inventory management? How valid are the assumptions for the EOQ model? How is a service level determined for inventory items? What inventory model would apply to service capacity such as seats on an aircraft?