1 Operations Strategy 2 Process Analysis 3 Lean Operations 4 Supply Chain Management

1. Operations Management & Performance Modeling 1 OperationsStrategy 2 Process Analysis 3 Lean Operations 4 Supply 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 5 Capacity Management in Services 6 Total Quality Management 7 Business Process Reengineering OM&PM/Class 5b

2. South Face: warehousesService 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 5b

3. R L Safety Stocks Inventory on hand I(t) Q Q order order order ROP mean demand during supply lead time: m = R L ss safety stock ss 0 Time t L OM&PM/Class 5b

4. Hedge against demand uncertainty with safety stocks • L = Supply lead time, • D=N(R, sR) =Demand per unit time is normally distributed with mean R and standard deviation sR , • Cycle service level = P(no stock out) = P(demand during lead time <ROP) = P(N(0,1) <z* = (ROP- m)/sLTD) = F(z*) [use tables to find z*] Safety stock ss = z*sLTD Reorder point ROP = RL + ss OM&PM/Class 5b

5. F(z) z 0 The standard normal distribution F(z) • Transform X = N(m,s) to z = N(0,1) • z = (X - m) / s. • F(z) = Prob( N(0,1) <z) • Transform back, knowing z*: • X* = m + z*s. OM&PM/Class 5b

6. Determining the required Safety Stock: at each warehouse of the South Face DATA: R= 5,000 jackets/ week sR = 1,500 jackets/ week H = $ 50 / jacket, year S = $ 2,000 / order L = 2 weeks QUESTION: What should safety stock be to insure a desired cycle service level of 95%? ANSWER: 1. Determine slead time demand = 2. Required # of standard deviations z* = 3. Answer: Safety stock = OM&PM/Class 5b

7. 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) 2.1Safety 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 5b

8. 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 5b

9. 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. m= s = OM&PM/Class 5b

10. The Effect of Pooling pairs of warehouses R= 10,000 widgets/week s = 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. slead 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 5b

11. Comprehensive Financial Evaluation of centralizing Four Warehouses into One R = 20,000 jackets/week sR = Sqrt(4) 1,500 = 3,000 jackets/week 1. Cycle Stock Optimal order quantity Q consolidated warehouse = 9,121 jackets/order. Annual ordering cost = $228,035. 2. Safety Stock slead time demand = 4,242jackets. Safety stock consolidated warehouse = 7,000jackets. Reorder point = 47,000 jackets. Average inventory consolidated warehouse = 11,560jackets. Average flow time = 0.578 weeks. Annual holding cost = $578,000. Total annual cost consolidated warehouse = $806,034. OM&PM/Class 5b

12. 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 5b

13. Learning Objectives: centralization/pooling • Different methods to achieve pooling efficiencies: • Physical centralization • Information centralization • Specialization • Raw material commonality (postponement/late customization) • Cost savings are sqrt(# of locations pooled). OM&PM/Class 5b