# OM&PM/Class 5b1 1Operations Strategy 2Process Analysis 3Lean Operations 4Supply Chain Management –Class 5a: Inventories & Economies of Scale –Class 5b:

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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

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