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Notes. Quiz This Friday Covers 13 March through today. MGTSC 352. Lecture 21: Inventory Management A&E Noise example Methods for finding good inventory policies: 1) simulation 2) EOQ + LTD models Using EOQ for the Distribution Game: Multi-Echelon Systems. Why Keep Inventory?.

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  1. Notes • Quiz This Friday • Covers 13 March through today

  2. MGTSC 352 Lecture 21: Inventory Management A&E Noise exampleMethods for finding good inventory policies: 1) simulation2) EOQ + LTD models Using EOQ for the Distribution Game: Multi-Echelon Systems

  3. Why Keep Inventory? • Seasonality (anticipated variation) • Provide flexibility (unanticipated variation) a.k.a.: • Economies of scale • Price speculation (not an ops reason) • Something to work on • NDR,JP

  4. Inventory By Where it IS • Raw Materials • Finished Goods • Work in Process • Or, with apologies to PS, “One man’s ceiling is another man’s floor.”

  5. Approximation 1: constant demand Therefore: We let inventory drop to zero just before an order arrives Inventory Time

  6. Acquisition Costs (pg. 142) No matter what the inventory policy, acquisition costs = Demand X Cost They don’t change, So they don’t go in the model (Unless you get quantity discounts, then it matters.)

  7. Order Costs • Number of orders per year  (3695 VCRs / year)/(80 VCRs / order) = 46.2 orders / year • Total order cost per year  (46.2 orders / year)($30 / order) = $1385.63 / year • Total Order Costs = S * D/Q

  8. Holding Costs (pg. 143) • Minimum inventory  0 for now Later = Safety Stock • Maximum inventory = Q (+SS) • Average inventory  Q/2 = (80)/2 = 40 VCRs • Total holding cost per year  (40 VCR-years)($37.5 / VCR / year) = $1500 / year • Total Holding Costs = H*Q/2

  9. Acquisition costs don’t depend on Q No shortages, by assumption pg. 144 EOQ = Economic Order Quantity Model • Given demand is constant • Find the Q that minimizes total cost Total cost = acquisition cost + order cost + carrying cost + shortage cost • Total relevant cost = order cost + carrying cost

  10. S = order cost ($/order) H = carrying cost ($/item/year) D = demand (units/year) Q = order quantity N = number of orders per year Iavg = average inventory pg. 147 EOQ Derivation Relevant cost = order cost + carrying cost RC = S  N + H  Iavg RC(Q) = S  D / Q + H  Q / 2 Note: you can change year to day, week, or any other time unit, as long as you are consistent Common mistake: inconsistent time units To Excel

  11. pg. 147 EOQ Formula Relevant cost = ordering cost + carrying cost RC = S  N + H  Iavg RC(Q) = S  D / Q + H  Q / 2

  12. The magic part (optional)

  13. pg. 147 Using EOQ for A&E Noise YNOS XD D = 10.12 VCRs/day, S = $30/order, H = $0.10/VCR/day  Q* = SQRT(210.1230/0.10) = 77.9  round to Q* = 78 N* = 10.12/78 = 0.13 orders/day = 47.4 orders/year Order every 365/47.4 = 8 days Relevant cost: RC(Q*) = S  (D/Q*) + H (Q*/2) = 30  (10.12/78) + 0.10 (78/2) = 3.90 + 3.90 = $7.80 / day = $2,847 / year

  14. Common mistake: using inconsistent time units D = 10.12 VCRs/day, S = $30/order, H = $37.5/VCR/year  Q* = SQRT(210.1230/37.5) = 4 • Off by (77.9 – 4)/77.9 = 95% • Will not be worth a lot of part marks

  15. Pg. 149 More on EOQ: Economies of Scale The Capital Health Region* operates four hospitals. Presently each hospital orders its own supplies and manages its inventory. A common item used is a sterile intravenous (IV) kit, with a weekly demand of 600 per week at each hospital. Each IV kit costs $5 and incurs a holding cost of 30% per year. Each order incurs a fixed cost of $150 regardless of order size. The supplier takes one week to deliver an order. Currently, each hospital orders 6,000 kits at a time. Question 1: Could costs be decreased by ordering more often? Question 2: Would it make sense to centralize inventory management for the four hospitals? * Fictional data

  16. Analysis for one Hospital • D = 600 / week = (600 / week) (52 weeks/year)= 31,200 / year • S = $150 / order • H = 0.3  5 = $1.50 / kit / year • Q = SQRT(2  D  S / H) = 2,498 ≈ 2,500 • Costs: • Q = 6,000: S  D / Q + H  Q / 2 = $780 + $4,500 = $5,280 • Q = 2,500: S  D / Q + H  Q / 2 = $1,872 + $1,875 = $3,747 • 29% savings

  17. Analysis for one Hospital • D = 600 / week = (600 / week) (52 weeks/year) = 31,200 / year • S = $150 / order • H = 0.3  5 = $1.50 / kit / year • Q = SQRT(2  D  S / H) = 2,498 ≈ 2,500 • Close your course pack • Active Learning: How do we change the analysis if inventory management were centralized for the four hospitals?

  18. Analysis for four hospitals managed together • D = 4  31,200 / year = 124,800 / year • S = $150 / order • H = $1.50 / kit / year • Q = SQRT(2  124,800  150 / 1.5) = 4,996 ≈ 5,000 • Costs: • Each hospital operated independently: 4  $3,747 = $14,988 / year • All four together: S  D / Q + H  Q / 2 = $3,744 + $3,750 = $7,494 / year • 50% savings • Quadrupling demand doubles the optimal order quantity and doubles the total relevant cost

  19. Four hospitals managed together • Costs: • Each hospital operated independently: 4  $3,747 = $14,988 / year • All four together: S  D / Q + H  Q / 2 = $3,744 + $3,750 = $7,494 / year • 50% savings • Quadrupling demand doubles the optimal order quantity and doubles the total relevant cost

  20. Inventory ROP demand during lead time lead time Time Determining ROP with EOQ model Lead time = 5 days Demand during lead time = (5 days) (10.12 VCRs / day)  51 VCRs  Set ROP = 51 VCRs Problem: this calculation assumes constant demand. May lead to shortages too frequently

  21. Pg. 149 What happens to Holding Cost when we Increase ROP? • EOQ: constant demand, zero safety stock • ROP = avg. demand during lead time • Iavg = (min + max)/2 = (0+Q)/2 = Q/2 • Holding cost = H  Q / 2 • If we add safety stock = SS, then: • ROP = avg. demand during lead time + SS • Iavg = Q/2 + min = SS + Q/2 • Holding cost = H  (SS + Q / 2)

  22. Pg. 152 ROP Demand during leadtime Demand that was not met Leadtime How Shortages Happen Inventory Active learning:How could we have avoided the shortage? Time

  23. ROP Inventory The demand during the lead time is uncertain. Here are 4 possibilities. We’ll see how to pick ROP so as to provide a specified fill rate … to Excel Time

  24. LTD Recap • “LTD” worksheet in A&E Noise workbook • Purpose: vary ROP (and Q, if desired) and see what happens to the fill rate • “LTD-exotic version”: can vary the lead time • Useful for comparing suppliers that provide different lead times

  25. pg. 151 Simulation versus EOQ

  26. Pg. 158 Back to the Distribution Game: Can we use EOQ here? Retailer A “multi-echelon” system Retailer Supplier Warehouse Retailer

  27. Using EOQ for a two-echelon system • Upper echelon: • Use warehouse holding cost rate • Ignore higher cost of holding inventory at retailers • Lead time = 15 (supplier  warehouse) + 5 (warehouse  retailer) = 20 days • Lower echelon: • Use incremental retailer holding cost rate • Lead time = 5 days • Coordination: warehouse order size should be a multiple of the sum of the retailer order sizes

  28. Data Assume open 250 days / year • Supplier to warehouse transit time: 15 days • Warehouse to retailer transit time: 5 days • Demand per retailer: 500 per year • Selling price: $100/unit • Purchase price: $70/unit • Supplier to warehouse order cost: $200 • Warehouse to retailer order cost: $2.75 • Warehouse holding cost: $10/unit/year • Retailer holding cost: $12/unit/year … To Excel

  29. Upper echelon: • Use warehouse holding cost rate • (Ignore higher cost of holding inventory at retailers) • Lead time = 15 (supplier  warehouse) + 5 (warehouse  retailer) = 20 days Upper echelon Retailer Retailer Supplier Warehouse Retailer

  30. Lower echelon: • Use incremental retailer holding cost rate • = retailer holding cost rate – warehouse holding cost rate • Lead time = 5 days Lower echelon Retailer Retailer Supplier Warehouse Retailer

  31. Coordination • Suppose each retailer uses QLower = 20. If all retailers order at once, the total is 60. • Active learning: you are the warehouse manager. Knowing the retailer order sizes, how would you pick the warehouse order size?

  32. Using EOQ for a 2-echelon system: the details • Upper echelon: • DUpper = 3  DRetailer • SUpper = SWarehouse • HUpper = HWarehouse • LTUpper = LTSupplier  Warehouse + LTWarehouse  Retailer • ROPUpper = DUpper  LTUpper • Lower echelon • DLower = DRetailer • SLower = SRetailer • HLower = HRetailer - HWarehouse • LTLower = LTWarehouse  Retailer • ROPLower = DLower  LTLower • Coordination: QUpper = n  SUM(QLower) • Choose n (an integer) and QLower to minimize total cost for the whole system

  33. Data Assume open 250 days / year • Supplier to warehouse transit time: 15 days • Warehouse to retailer transit time: 5 days • Demand per retailer: 500 per year • Selling price: $100/unit • Purchase price: $70/unit • Supplier to warehouse order cost: $200 • Warehouse to retailer order cost: $2.75 • Warehouse holding cost: $10/unit/year • Retailer holding cost: $12/unit/year … To Excel

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