Managing Facilitating Goods. Considerations in Inventory Systems

Transcription

1 Managing Facilitating Goods Dr. Shuguang Liu Managing Facilitating Goods Replenishment Replenishment Replenishment Customer Factory Wholesaler Distributor Retailer Customer Production Shipping Shipping Item Withdrawn Wholesaler Distributor Retailer Learning Objectives Describe the functions and costs of an inventory system. Determine the quantity. Conduct an ABC analysis of inventory items. Determine the quantity for the singleperiod inventory case. Describe the rationale behind the retail discounting model. Role of in Services Decoupling inventories Seasonal inventories Speculative inventories Cyclical inventories In-transit inventories Safety stocks Considerations in Systems Type of customer demand Planning time horizon Replenishment lead time Constraints and relevant costs Relevant Costs Ordering costs Receiving and inspections costs olding or carrying costs Shortage costs 1

2 Management uestions What should be the quantity ()? When should an be placed, called a re point (ROP)? ow much safety stock (SS) should be maintained? Models Economic Order uantity () Special Models! With uantity Discounts! Planned Shortages Demand Uncertainty - Safety Stocks Control Systems! Continuous-Review (,r)! Periodic-Review (-up-to) Single Period Model Levels For Model Units on and D Annual Costs For Model Annual Cost, $ Order uantity, olding Cost Ordering Cost Total Cost Formula Notation D = demand in units per year = holding cost in dollars/unit/year S = cost of placing an in dollars = quantity in units Total Annual Cost for Purchase Lots TCp = S( D / ) + ( / 2) DS Annual Costs for uantity Discount Model = Order quantity, Annual Cost, $ 22, C = $2. C = $19.5 C = $

3 Levels For Planned Shortages Model -K -K T1 T T2 TIME Formulas for Special Models uantity Discount Total Cost Model TC = CD + S ( qd D / ) + I ( C / 2) Model with Planned Shortages 2 2 D ( K ) K TC b = S + + B 2 2 * = + B B * * K = + B Values for * and K* as A Function of Back Cost B B < B < B * K* Levels + B B undefined * + B * Demand During Lead Example σ = 15. u=3 σ = 15. σ = u=3 u=3 u=3 Four Days Lead σ =15. = d L =12 σ L =3 s s ROP Demand During Lead time Safety Stock (SS) Demand During Lead (LT) has Normal Distribution with - Mean( d ) = µ ( LT) L - Std. Dev.( σ L ) = σ LT SS with r% service level SS = zrσ LT Re Point ROP = SS + d L Continuous Review System (,r) Re point, ROP on hand Average lead time usage, d L Safety stock, SS Amount used during first lead time d 1 First lead time, LT 1 Order quantity, d 2 d 3 LT 2 LT 3 Order 1 placed Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received 3

4 Periodic Review System (-up-to) Control Systems ABC Classification of Items on and Target inventory level, TIL Review period RP RP RP Amount used during first lead time First quantity, 1 d Safety stock, SS First lead time, LT 1 LT2 LT 3 Order 1 placed Order 2 placed Order 3 placed Shipment 1 received Shipment 2 received Shipment 3 received d 2 d 3 Continuous Review System = ROP = SS + µ LT SS = z σ LT r Periodic Review System RP = / µ TIL = SS + µ ( RP + LT) SS = z σ RP + LT r Percentage of dollar volume A B C Percentage of inventory items (SKUs) 1 Items Listed in Dollar Volume Monthly Percent of Unit cost Sales Dollar Dollar Percent of Item ($) (units) Volume ($) Volume SKUs Class Computers , 74 2 A Entertainment center , Television sets , Refrigerators , 16 3 B Monitors 2 5 1, Stereos , Cameras 2 4 8, Software 5 1 5, 1 5 C Computer disks 5 1 5, CDs 2 2 4, Totals 35, 1 1 Single Period Model Newsvendor Problem Example D = newspapers demanded p(d) = probability of demand = newspapers stocked P = selling price of newspaper, $1 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 Model Expected Value Analysis Stock p(d) D Expected Profit $31.54 $34.43 $35.77 $35.99 $

5 Single Period Model Incremental Analysis Critical fractile for the Newsvendor Problem Retail Discounting Model E (revenue on last sale) E (loss on last sale) P ( revenue) (unit revenue) P (loss) (unit loss) PD ( C ) PD ( < C ) [ ] u 1 P( D < ) C P( D < ) C u Cu PD ( < ) (Critical Fractile) Cu+ Co C u = unit contribution from newspaper sale (opportunity cost of underestimating demand) C o = unit loss from not selling newspaper (cost of overestimating demand) D = demand = newspaper stocked o o Probability P(D<) (C o applies).722 P(D>) (C u applies) Newspaper demand, 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) S D = ( 1+ PNY ) 5