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Slide 2

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Slide 4 Demand Distribution

Slide 5 Ideal depletion

Slide 6 Without Safety Stock

Slide 7 With Safety Stock

Slide 8 Inventory/Time with ROP

Slide 9 Lead Time Variability

Slide 10 Reorder Point With Variable Demand R = dL + z  d L where d=average daily demand L=lead time  d =the standard deviation of daily demand z=number of standard deviations corresponding to the service level probability z  d L=safety stock

Slide 11 Reorder Point for a Service Level Probability of meeting demand during lead time = service level Probability of a stockout R Safety stock dL Demand z  d L

Slide 12 Economic Order Quantity (EOQ) Model

Slide Demand = 20 units/day

Slide Demand = 20 units/day

Slide Demand = 20 units/day

Slide 16 Size of order Annual cost (dollars) Lowest total cost (EOQ) Total cost Inventory carrying cost Ordering cost Cost Trade-offs Required to Determine the Most Economic Order Quantity 4 8

Inventory Carrying Costing: based on % of Product Value Cost Percentage of Product Value Opportunity 12 % Shrinkage8 Tax/Insurance3 Storage/Handling2 Total 25 %

Slide 18 EOQ Cost Model C o - cost of placing orderD - annual demand C c - annual per-unit carrying costQ - order quantity Annual ordering cost = CoDCoDQQCoDCoDQQQ Annual carrying cost = CcQCcQ22CcQCcQ222 Total cost = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222

Slide 19 EOQ Cost Model TC = + CoDQCoDQ CcQ2CcQ2 = + CoDQ2CoDQ2 Cc2Cc2  TC  Q 0 = + C0DQ2C0DQ2 Cc2Cc2 Q opt = 2CoDCc2CoDCc Deriving Q opt Proving equality of costs at optimal point = CoDQCoDQ CcQ2CcQ2 Q 2 = 2CoDCc2CoDCc Q opt = 2CoDCc2CoDCc

Slide 20 EOQ Example C c = $0.75 per yardC o = $150D = 10,000 yards Q opt = 2CoD2CoDCcCc2CoD2CoDCcCc 2(150)(10,000)(0.75) Q opt = 2,000 yards TC min = + CoDCoDQQCoDCoDQQQ CcQCcQ22CcQCcQ222 (150)(10,000)2,000(0.75)(2,000)2 TC min = $750 + $750 = $1,500 Orders per year =D/Q opt =10,000/2,000 =5 orders/year Order cycle time =311 days/(D/Q opt ) =311/5 =62.2 store days

Economic Order Quantity (EOQ) Models  Orders arrive in a single shipment  No quantity discounts (i.e., single price)  Demand rate is constant  No constraints on order size  relevant costs include only holding and ordering/setup  Ordering decisions for items are independent from other items.  No uncertainty in lead time or supply  Basic EOQ Model: assumptions

Slide 22 Order Quantity Number of Orders (D/Q) Ordering Cost P*(D/Q) Inventory Carrying Cost 1/2 (Q*C*V) Total Cost $ 4,800 3,200 2,400 1,920 1,600 1,400 1, $ ,000 1,250 1,500 1,750 2,000 2,500 3,750 5,000 $ 5,300 3,950 3,400 3,170 3,100 3,150 3,200 4,460 4,470 5,480 Cost Trade-offs Required to Determine the Most Economic Order Quantity 4 9

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Slide 24 Inventory Control Systems  Continuous system (fixed- order-quantity)  constant amount ordered when inventory declines to predetermined level  Periodic system (fixed-time- period)  order placed for variable amount after fixed passage of time

Slide 25 Objednávání fixního množství k proměnlivému okamžiku Continuous system - označení (B,Q) nebo (s,Q) s q0q0 q0q0 q0q0 S1S1 S2S2 s S3S3 Čas Stav t 1 t 2 t 3

Slide 26 Objednávání variabilního množství k pevně stanovenému okamžiku označení Periodic system - (s,S) nebo (R,S) S q1q1 q2q2 q3q3 Stav Čas t 0 t 0 t 0

Slide 27 Two Forms of Demand  Dependent  Demand for items used to produce final products  Tires stored at a Goodyear plant are an example of a dependent demand item  Independent  Demand for items used by external customers  Cars, appliances, computers, and houses are examples of independent demand inventory