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order Production Delay Wholesaler Inventory Shipping Delay Shipping Delay Distributor Inventory Retailer Inventory Item Withdrawn
Discuss the role of information technology in managing inventories.
Describe the functions and costs of an inventory system.
Determine the order quantity.
Determine the reorder point and safety stock for inventory systems with uncertain demand.
Design a continuous or periodic review inventory-control system.
Conduct an ABC analysis of inventory items.
Determine the order quantity for the single-period inventory case.
Describe the rationale behind the retail discounting model.
Role of Inventory in Services
Considerations in Inventory Systems
Type of customer demand
Planning time horizon
Replenishment lead time
Constraints and relevant costs
Relevant Inventory Costs
Receiving and inspections costs
Holding or carrying costs
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?
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 0 Units on Hand Q Q D Time
Annual Costs For EOQ Model
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
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 Q Q-K 0 -K T1 T2 TIME T
Formulas for Special Models
Quantity Discount Total Cost Model
Model with Planned Shortages
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 + + + = u=3 u=3 u=3 u=3 ROP s s Four Days Lead Time Demand During Lead time
Safety Stock (SS)
Demand During Lead Time (LT) has Normal Distribution with - -
SS with r% service level
Continuous Review System (Q,r) Average lead time usage, d L Reorder point, ROP Safety stock, SS Inventory on hand Order quantity, EOQ EOQ EOQ d 1 d 2 d 3 Amount used during first lead time First lead time, LT 1 Order 1 placed LT 2 LT 3 Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received Time
Periodic Review System (order-up-to) RP RP RP Review period First order quantity, Q1 d 1 Q 2 Q 3 d 2 d 3 Target inventory level, TIL Amount used during first lead time Safety stock, SS First lead time, LT 1 LT 2 LT 3 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
Continuous Review System
Periodic Review System
ABC Classification of Inventory Items A B C
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 Model Newsvendor Problem Example
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: C u = unit contribution from newspaper sale ( opportunity cost of under estimating demand) C o = unit loss from not selling newspaper (cost of over estimating demand) D = demand Q = newspaper stocked
Critical fractile for the newsvendor problem P(D<Q) (C o applies) P(D>Q) (C u applies ) 0.722
Retail Discounting Model
S = current selling price
D = discount price
P = profit margin on cost (% markup as decimal)
Y = average number of years to sell entire stock of “dogs” at current price (total years to clear stock divided by 2)
N = inventory turns (number of times stock turns in one year)
Loss per item = Gain from revenue S – D = D(PNY)
Topics for Discussion
Discuss the functions of inventory for different organizations in the supply chain.
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?
The class engages in an estimation of the cost of a 12-ounce serving of Coke in various situations (e.g., supermarket, convenience store, fast-food restaurant, sit-down restaurant, and ballpark). What explains the differences?