Lect17

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Lect17

  1. 1. Inventory Management Multi-Items and Multi-Echelon Chris CapliceESD.260/15.770/1.260 Logistics Systems Nov 2006
  2. 2. Advanced Topics So far, we have studied single-item single location inventory policies. What about . . . Multiple Items How do I set aggregate policies? What if I have to meet a system wide objective? Multiple Locations – Multi-echelon Deterministic demand Stochastic demandMIT Center for Transportation & Logistics – ESD.260 2 © Chris Caplice, MIT
  3. 3. Inventory Planning Hierarchy Inputs Plan Results Strategic Annual/Quarterly • Transportation costs • Inventory flow • Facility fixed and variable costs Network • Network configuration • Inventory costs Design • Capacity • Service levels • Item-level flow • Forecast • Item classifications • Lead times • Inventory locations Quarterly/Monthly • Variable and Deployment Operational Tactical inventory costs • Target Service levels • Business policies • Target Reorder points • Target Safety stock • Forecasts/Orders • How much and when • Lead times to replenish • Handling costs • Reorder Points Replenishment • Vendor/volume Reorder Quantities discounts • Review Periods Weekly/Daily/Hourly • Customer orders • Demand prioritization • On-hand and • Assign inventory to in-routeinventories Allocation orders • Real transit costs • Production schedules Jeff Metersky, Vice President Chainalytics, LLC Rosa Birjandi, Asst. Professor Air Force Institute of TechnologyMIT Center for Transportation & Logistics – ESD.260 3 © Chris Caplice, MIT
  4. 4. Inventory Policies for Multiple Items Aggregate constraints are placed on total inventory Avg total inventory cannot exceed a certain budget ($ or Volume) Total number of replenishments per unit time must be less than a certain number Inventory as a portfolio of stocks – which ones will yield the highest return? Cost parameters can be treated as management policy variables There is no single correct value for holding cost, r. Best r results in a system where inventory investment and service level are in agreement with overall strategy. Cost per order, A, is also not typically known with any precision. Safety factor, k, is set by management. Exchange Curves Cycle Stock - Trade-off between total cycle stock and number of replenishments for different A/r values Safety Stock – Trade-off between total safety stock and some performance metric for different k valuesMIT Center for Transportation & Logistics – ESD.260 4 © Chris Caplice, MIT
  5. 5. Exchange Curves Set notation for each item: A = Order cost common for all items r = Carrying cost common for all items Di = Demand for item i vi = Purchase cost of item i Qi = Order quantity for item i Need to find: Total average cycle stock (TACS) and Number of replenishments (N) ⎛ 2 ADi ⎞ N = ∑ i =1 n Di = ∑ i =1 n Di ⎜ ⎜ rv ⎟ v i ⎟ Qi 2 ADi n Qi v i n ⎝ ⎠ TACS = ∑ i =1 = ∑ i =1 i rv i 2 2 rDi v i r 1 N = ∑ i =1 ∑ Di v i n n ADi v i A 1 = TACS = ∑ i =1 ∑ Di v i n n = 2A A 2 i =1 2r r 2 i =1MIT Center for Transportation & Logistics – ESD.260 5 © Chris Caplice, MIT
  6. 6. Exchange Curves Exchange Curve $160,000 A/r = 10000 Total Average Cycle Stock Value $140,000 $120,000 $100,000 Current Operations $80,000 $60,000 A/r = 10 $40,000 $20,000 $- - 100 200 300 400 500 Number of Replenishments Exchange curve for 65 items from a hospital ward. Current operations calculated from actual orders. Allows for management to set A/r to meet goals or budget, Suppose TACS set to $20,000 – we would set A/r to be ~100MIT Center for Transportation & Logistics – ESD.260 6 © Chris Caplice, MIT
  7. 7. Exchange Curves Now consider safety stock, where we are trading off SS inventory with some service metric Different k values dictate where we are on the curve Suppose that we only have budget for $2000 in SS – what is our CSL? Single Item Exchange Curve 7000 6000 5000 Safety Stock ($) 4000 3000 2000 1000 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1000 -2000 -3000 Cycle Service LevelMIT Center for Transportation & Logistics – ESD.260 7 © Chris Caplice, MIT
  8. 8. Exchange Curves Set notation for each item: σLi = RMSE for item i ki = Safety factor for item i Di = Demand for item i vi = Purchase cost of item i Qi = Order quantity for item i Need to find: Total safety stock (TSS) and Some service level metric Expected total stockout occasions per year (ETSOPY) Expected total value short per year (ETVSPY) TSS = ∑ i =1 k i σ Li v i n Di Di ETSOPY = ∑ i =1 ETVSPY = ∑ i =1 σ Li v i G(ki ) n n P [SOi ] Qi QiMIT Center for Transportation & Logistics – ESD.260 8 © Chris Caplice, MIT
  9. 9. Exchange Curves $3,500 $3,000 k=3 Total Safety Stock ($) $2,500 k=1.6 $2,000 $1,500 $1,000 $500 $- - 100 200 300 400 500 600 700 800 Expected Total Stockout Occasions per Year Exchange curve for same 65 items from a hospital ward. Allows for management to set aggregate k to meet goals or budget, Suppose TSS set to $1,500 – we would expect ~100 stockout events per year and would set k= 1.6MIT Center for Transportation & Logistics – ESD.260 9 © Chris Caplice, MIT
  10. 10. Replenishment in a Multi-Echelon System Plant RDC1 RDC2 LDC1 LDC2 LDC3 LDC4 R1 R2 R3 R4 R5 R6 R7 R8MIT Center for Transportation & Logistics – ESD.260 10 © Chris Caplice, MIT
  11. 11. What if I Use Traditional Techniques? In multi-echelon inventory systems with decentralized control, lot size / reorder point logic will: Create and amplify "lumpy" demand Lead to the mal-distribution of available stock, hoarding of stock, and unnecessary stock outs Force reliance on large safety stocks, expediting, and re-distribution.MIT Center for Transportation & Logistics – ESD.260 11 © Chris Caplice, MIT
  12. 12. Impact of Multi-Echelons CDC Demand Pattern RDC Ordering Patterns RDC Inventory Cycles Customer Demand Patterns Layers of Inventory Create Lumpy DemandMIT Center for Transportation & Logistics – ESD.260 12 © Chris Caplice, MIT
  13. 13. What does a DRP do? Premises Inventory control in a distribution environment Many products, many stockage locations Multi-echelon distribution network Layers of inventory create "lumpy" demand Concepts Dependent demand versus independent demand Requirements calculation versus demand forecasting Schedule flow versus stockpile assets Information replaces inventory "DRP is simply the application of the MRP principles and techniques to distribution inventories“ Andre MartinMIT Center for Transportation & Logistics – ESD.260 13 © Chris Caplice, MIT
  14. 14. DRP Requirements Information Requirements: Base Level Usage Forecasts Distribution Network Design Inventory Status Ordering Data DRP Process: Requirements Implosion Net from Gross Requirements Requirements Time Phasing Planned Order ReleaseMIT Center for Transportation & Logistics – ESD.260 14 © Chris Caplice, MIT
  15. 15. A Distribution Network Example Plant Central Warehouse Regional Warehouse 1 Regional Warehouse 2 Regional Warehouse 3 Retailer A Retailer D Retailer G Retailer B Retailer E Retailer H Retailer C Retailer E Retailer IMIT Center for Transportation & Logistics – ESD.260 15 © Chris Caplice, MIT
  16. 16. Central Warehouse Facility The DRP Plan Q=200, SS=0, LT=2 NOW 1 2 3 4 5 6 7 8 Period Usage 100 20 50 30 100 0 100 0 Gross Rqmt 100 20 50 30 100 0 100 0 Begin Inv 150 50 30 180 150 50 50 150 Sched Recpt 0 0 0 0 0 0 0 0 Net Rqmt - - 20 - - - 50 - Planned Recpt 0 200 0 0 0 200 0 End Inv 150 50 30 180 150 50 50 150 150 Planned Order 200 200 Regional Warehouse One Q=50, SS=15, LT=1 NOW 1 2 3 4 5 6 7 8 Period Usage 25 25 25 25 25 25 25 25 Gross Rqmt 40 40 40 40 40 40 40 40 Plant Begin Inv 50 25 50 25 50 25 50 25 Sched Recpt 0 0 0 0 0 0 0 0 Net Rqmt - 15 - 15 - 15 - 15 Central Warehouse Planned Recpt 0 50 0 50 0 50 0 50 End Inv 50 25 50 25 50 25 50 25 50 Planned Order 50 50 50 50 Regional Warehouse 1 Regional Warehouse 2 Regional Warehouse 3 Regional Warehouse Two Q=30, SS=10, LT=1 NOW 1 2 3 4 5 6 7 8 Period Usage 10 10 10 10 20 20 20 20 Retailer A Retailer D Retailer G Gross Rqmt 20 20 20 20 30 30 30 30 Retailer B Retailer E Retailer H Begin Inv 20 10 30 20 10 20 30 10 Retailer C Retailer E Retailer I Sched Recpt 0 0 0 0 0 0 0 0 Net Rqmt - 10 - - 20 10 - 20 Planned Recpt 30 0 0 30 30 0 30 End Inv 20 10 30 20 10 20 30 10 20 Planned Order 30 30 30 30 Regional Warehouse Three Q=20, SS=10, LT=1 NOW 1 2 3 4 5 6 7 8 Note: Period Usage Gross Rqmt 5 15 15 25 10 20 10 20 0 10 15 25 0 10 15 25 Gross Rqmt = Period Usage + SS Begin Inv 15 10 15 25 15 15 20 20 Sched Recpt 0 0 0 0 0 0 0 0 Net Rqmt - 15 5 - - 10 - 5 Planned Recpt 0 20 20 0 0 20 0 20 End Inv 15 10 15 25 15 15 20 20 25MIT Center for Transportation & Logistics – ESD.260 16 © Chris Caplice, MIT
  17. 17. Example: The DRP Plan Regional Warehouse One Forecast Q=50 , SS=15 , LT=1 NOW 1 2 3 4 5 6 7 8 Period Usage 25 25 25 25 25 25 25 25 Gross Rqmt 40 40 40 40 40 40 40 40 Begin Inv 50 25 50 25 50 25 50 25 Sched Rcpt 0 0 0 0 0 0 0 0 Net Rqmt 15 15 15 15 Plan Rcpt 0 50 0 50 0 50 0 50 End Inv 50 25 50 25 50 25 50 25 50 POR 50 50 50 50MIT Center for Transportation & Logistics – ESD.260 17 © Chris Caplice, MIT
  18. 18. Example: The DRP Plan Regional Warehouse Two Q=30 , SS=10 , LT=1 NOW 1 2 3 4 5 6 7 8 Period Usage 10 10 10 10 20 20 20 20 Gross Rqmt 20 20 20 20 30 30 30 30 Begin Inv 20 10 30 20 10 20 30 10 Sched Rcpt 0 0 0 0 0 0 0 0 Net Rqmt 10 20 10 20 Plan Rcpt 0 30 0 0 30 30 0 30 End Inv 20 10 30 20 10 20 30 10 20 POR 30 30 30 30MIT Center for Transportation & Logistics – ESD.260 18 © Chris Caplice, MIT
  19. 19. Example: The DRP Plan Regional Warehouse Three Q=20 , SS=10 , LT=1 NOW 1 2 3 4 5 6 7 8 Period Usage 5 15 10 10 0 15 0 15 Gross Rqmt 15 25 20 20 10 25 10 25 Begin Inv 15 10 15 25 15 15 20 20 Sched Rcpt 0 0 0 0 0 0 0 0 Net Rqmt 15 5 10 5 Plan Rcpt 0 20 20 0 0 20 0 20 End Inv 15 10 15 25 15 15 20 20 25 POR 20 20 20 20MIT Center for Transportation & Logistics – ESD.260 19 © Chris Caplice, MIT
  20. 20. The DRP Plan for All Locations Rolling Up Orders NOW 1 2 3 4 5 6 7 8 CENTRAL Period Usage 100 20 50 30 100 0 100 0 POR 200 200 REGION ONE Period Usage 25 25 25 25 25 25 25 25 POR 50 50 50 50 REGION TWO Period Usage 10 10 10 10 20 20 20 20 POR 30 30 30 30 REGION THREE Period Usage 5 15 10 10 0 15 0 15 POR 20 20 20 20MIT Center for Transportation & Logistics – ESD.260 20 © Chris Caplice, MIT
  21. 21. Example: The DRP Plan Central Warehouse Q=200 , SS=0 , LT=2 NOW 1 2 3 4 5 6 7 8 Period Usage 100 20 50 30 100 0 100 0 Gross Rqmt 100 20 50 30 100 0 100 0 Begin Inv 150 50 30 180 150 50 50 150 Sched Rcpt 0 0 0 0 0 0 0 0 Net Rqmt 20 50 Plan Rcpt 0 0 200 0 0 0 200 0 End Inv 150 50 30 180 150 50 50 150 150 POR 200 200MIT Center for Transportation & Logistics – ESD.260 21 © Chris Caplice, MIT
  22. 22. Results and Insights DRP is a scheduling and stockage algorithm -- it replaces the forecasting mechanism above the base inventory level DRP does not determine lot size or safety stock -- but these decisions must be made as inputs to the process DRP does not explicitly consider any costs -- but these costs are still relevant and the user must evaluate trade-offs DRP systems can deal with uncertainty somewhat -- using "safety time" and "safety stock"MIT Center for Transportation & Logistics – ESD.260 22 © Chris Caplice, MIT
  23. 23. MRP / DRP Integration Purchase Orders C C C C C C C C SA SA SA SA MRP A A MPS Product CDC DRP RDC RDC Retail Retail Retail Retail Sales/Marketing PlanMIT Center for Transportation & Logistics – ESD.260 23 © Chris Caplice, MIT
  24. 24. Evolution of Inventory Management Traditional Replenishment Inventory: Lot Size/ Order Point Logic Single item focus Emphasis on cost optimization Long run, steady state approach The MRP / DRP Approach: Scheduling emphasis Focus on quantities and times, not cost Multiple, inter-related items and locations Simple heuristic rulesMIT Center for Transportation & Logistics – ESD.260 24 © Chris Caplice, MIT
  25. 25. Evolution of Inventory Management MRP / DRP have limited ability to deal with: Capacity restrictions in production and distribution “set-up” costs fixed and variable shipping costs alternative sources of supply network transshipment alternatives expediting opportunities Next Steps in MRP/DRP Establish a time-phased MRP/MPS/DRP network Apply optimization tools to the network Consider cost trade-offs across items, locations, and time periods Deal with shortcomings listed aboveMIT Center for Transportation & Logistics – ESD.260 25 © Chris Caplice, MIT
  26. 26. A DRP Network Plan What happens when actual demand in the short term doesn’t follow the forecast exactly….. How should I re-deploy my inventory to take the maximum advantage of what I do have? Plant RDC1 RDC2 LDC1 LDC2 LDC3 LDC4 R1 R2 R3 R4 R5 R6 R7 R8MIT Center for Transportation & Logistics – ESD.260 26 © Chris Caplice, MIT
  27. 27. A DRP Network Reality Plant RDC1 RDC2 SHORTAGES EXCESS LDC1 LDC2 LDC3 LDC4 R1 R2 R3 R4 R5 R6 R7 R8 Higher than expected demand Lower than expected demandMIT Center for Transportation & Logistics – ESD.260 27 © Chris Caplice, MIT
  28. 28. Optimal Network Utilization Plant RDC1 RDC2 SHORTAGES EXCESS LDC1 LDC2 LDC3 LDC4 R1 R2 R3 R4 R5 R6 R7 R8MIT Center for Transportation & Logistics – ESD.260 28 © Chris Caplice, MIT
  29. 29. Information and Control Impacts Centralized Decentralized Control Control Global Vendor Managed DRP (most cases) Information Inventory (VMI) Base Stock Control DRP (some cases) Extended Base Stock Control Systems Local Standard Inventory Information N/A Policies: (R,Q), (s,S) etc.MIT Center for Transportation & Logistics – ESD.260 29 © Chris Caplice, MIT
  30. 30. Questions?

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