OM&PM/Class 5b1 1Operations Strategy 2Process Analysis 3Lean Operations 4Supply Chain Management –Class 5a: Inventories & Economies of Scale –Class 5b: Dealing with Uncertainty & role of Centralization »The impact of uncertainty: safety stocks »Centralization: pooling benefits 5Capacity Management in Services 6Total Quality Management 7Business Process Reengineering Operations Management & Performance Modeling
OM&PM/Class 5b2 South Face: warehouses Service levels & inventory management The South Face has 4 warehouses which experience a demand that is not steady from one week to the next. Weekly demand is in fact normally distributed with a mean of 5,000 and a standard deviation of 1,500. SF’s order lead time is two weeks. Fixed order costs are $2,000/order and it costs $50 to hold one jacket in inventory during one year. –If SF uses the ordering policy discussed last class, what will the probability of running out of stock in a given cycle be? SF would like this probability to be no higher than 5% for customer satisfaction. What ordering policy would you recommend for SF?
OM&PM/Class 5b3 Safety Stocks Q Time t ROP L R L order mean demand during supply lead time: = R L safety stock ss Inventory on hand I(t) Q ss 0
OM&PM/Class 5b4 Hedge against demand uncertainty with safety stocks L= Supply lead time, D=N(R R )=Demand per unit time is normally distributed with mean R and standard deviation R, Cycle service level = P(no stock out) = P(demand during lead time < ROP) = P(N(0,1) < z* = (ROP- )/ LTD ) = F(z*)[use tables to find z*] Safety stock ss = z* LTD Reorder pointROP = RL + ss
OM&PM/Class 5b5 The standard normal distribution F(z) F(z) z 0 Transform X = N( ) to z = N(0,1) z = (X - ) / . F(z) = Prob( N(0,1) < z) Transform back, knowing z*: X* = + z* .
OM&PM/Class 5b6 Determining the required Safety Stock: at each warehouse of the South Face DATA: R = 5,000 jackets/ week R = 1,500 jackets/ week H = $ 50 / jacket, year S = $ 2,000 / orderL = 2 weeks QUESTION: What should safety stock be to insure a desired cycle service level of 95%? ANSWER: 1. Determine lead time demand = 2. Required # of standard deviations z*= 3. Answer: Safety stock =
OM&PM/Class 5b7 Comprehensive Financial Evaluation: Warehouse Inventory Costs of the South Face 1. Cycle Stock (Economies of Scale) 1.1 Optimal order quantity = 1.2 # of orders/year= 1.3 Annual ordering cost per warehouse = $114,017. 1.4 Annual cycle stock holding cost/w.h.= $114,017. 2. Safety Stock (Uncertainty hedge) 2.1 Safety stock per warehouse= 3,500 2.2 Annual safety stock holding cost/w.h.= $174,982. 3. Total Costs for 4 warehouses= 4 (114,017 + 114,017 + 174,982) = $1,612,069.
OM&PM/Class 5b8 Learning Objectives: safety stocks Safety stock increases (decreases) with an increase (decrease) in: demand variability or forecast error, delivery lead time for the same level of service, delivery lead time variability for the same level of service.
OM&PM/Class 5b9 The Effect of Centralization Weekly demand per warehouse = 5,000 jackets/ week with standard deviation = 1,500 / week H = $ 50 / jacket, year S = $ 20,000 / order Supply lead time L = 2 weeks Desired cycle service level F(z*) = 95%. The South Face decides to merge all of its warehouses. = =
OM&PM/Class 5b10 The Effect of Pooling pairs of warehouses R = 10,000 widgets/week = Sqrt(2) 4,000 = 5,657 widgets/week Optimal order quantity Q per 2-warehouse = 20,396 widgets/order. Annual ordering cost per 2-warehouse = $50,990. lead time demand = 6,928 widgets. Safety stock per 2-warehouse = 11,432 widgets. Reorder point = 26,432 widgets. Average inventory 2-warehouse = 21,630 widgets. Average cycle time = 2.16 weeks. Annual holding cost per 2-warehouse = $108,150. Total average inventory across two 2-warehouses = 43,260 widgets. Total annual cost across two 2-warehouses = $318,280.
OM&PM/Class 5b11 Comprehensive Financial Evaluation of centralizing Four Warehouses into One R = 20,000 jackets/week R = Sqrt(4) 1,500 = 3,000 jackets/week 1. Cycle Stock Optimal order quantity Q consolidated warehouse = jackets/order. Annual ordering cost = $228,035. 2. Safety Stock lead time demand = 4,242 jackets. Safety stock consolidated warehouse = 7,000 jackets. Reorder point = 47,000 jackets. Average inventory consolidated warehouse = 11,560 jackets. Average flow time = 0.578 weeks. Annual holding cost = $578,000. Total annual cost consolidated warehouse = $806,034.
OM&PM/Class 5b12 Supply Chain of IBM PC Europe Build to Plan (BTP) vs. Late Customization (LC) vs. Build to Order (BTO) vs. Exploiting component commonality(FLEX) Physical Pooling of transhipment points Source: Feigin, An, Connors and Crawford, ORMS Today April 96
OM&PM/Class 5b13 Learning Objectives: centralization/pooling è Different methods to achieve pooling efficiencies: –Physical centralization –Information centralization –Specialization –Raw material commonality (postponement/late customization) è Cost savings are sqrt(# of locations pooled).
OM&PM/Class 5b14 Postponement & Commonality: HP Laserjet Generic Power Production Unique Power Production Process I: Unique Power Supply Europe N. America Europe N. America Transportation Process II: Universal Power Supply Make-to-StockPush-Pull BoundaryMake-to-Order
OM&PM/Class 5b15 MidTerm Results Median = 85%, Stdev = 10%, Max =99% 0 5 10 15 20 25 6069798999 Frequency