2. Notes Quiz This Friday Covers 13 March through today

3. 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

4. Why Keep Inventory? 1.Seasonality (anticipated variation) 2.Provide flexibility (unanticipated variation) a.k.a.: 3.Economies of scale 4.Price speculation (not an ops reason) 5.Something to work on 6.NDR,JP

5. 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.”

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

7. 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.)

8. 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

9. 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

10. 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 pg. 144 Total relevant cost = order cost + carrying cost No shortages, by assumption Acquisition costs don’t depend on Q

11. EOQ Derivation S = order cost ($/order) H = carrying cost ($/item/year) D = demand (units/year) Q = order quantity N = number of orders per year I avg = average inventory Relevant cost=order cost+carrying cost RC=S  N+H  I avg 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 pg. 147 To Excel

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

13. The magic part (optional)

14. 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 pg. 147

15. 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

16. 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? Pg. 149 * Fictional data

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 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

18. 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?

19. 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

20. 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

21. 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 Time Inventory lead time demand during lead time ROP Problem: this calculation assumes constant demand. May lead to shortages too frequently

22. What happens to Holding Cost when we Increase ROP? EOQ: constant demand, zero safety stock –ROP = avg. demand during lead time –I avg = (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 –I avg = Q/2 + min = SS + Q/2 –Holding cost = H  (SS + Q / 2) Pg. 149

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

24. Time Inventory ROP 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

25. 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

26. Simulation versus EOQ DimensionSimulationEOQ + LTD Ease of evaluating a policy Need to build model – time consuming Simple formula for RC – back of an envelope Finding the optimumTrial and error / data table Plug into formula for Q* Random demand fluctuations Taken into accountIgnored in EOQ Seasonal demand fluctuations Can be taken into account Ignored ShortagesTaken into accountIgnored in EOQ Likely errors (common mistakes) Errors in formulasInconsistent units pg. 151

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

28. 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

29. Data 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 Assume open 250 days / year … To Excel

30. Upper echelon SupplierWarehouse Retailer 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

31. Lower echelon SupplierWarehouse Retailer Lower echelon: Use incremental retailer holding cost rate = retailer holding cost rate – warehouse holding cost rate Lead time = 5 days

32. Coordination Suppose each retailer uses Q Lower = 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?

33. Using EOQ for a 2-echelon system: the details Upper echelon: –D Upper = 3  D Retailer –S Upper = S Warehouse –H Upper = H Warehouse –LT Upper = LT Supplier  Warehouse + LT Warehouse  Retailer –ROP Upper = D Upper  LT Upper Lower echelon –D Lower = D Retailer –S Lower = S Retailer –H Lower = H Retailer - H Warehouse –LT Lower = LT Warehouse  Retailer –ROP Lower = D Lower  LT Lower Coordination: Q Upper = n  SUM(Q Lower ) Choose n (an integer) and Q Lower to minimize total cost for the whole system

34. Data 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 Assume open 250 days / year … To Excel