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3 session 3a risk_pooling

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3 session 3a risk_pooling

  1. 1. Dr. RAVI SHANKAR Professor Department of Management Studies Indian Institute of Technology Delhi Hauz Khas, New Delhi 110 016, India Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m) Fax: (+91)-(11) 26862620 Email: r.s.research@gmail.com http://web.iitd.ac.in/~ravi1 SESSION#3: TUTORIAL ON RISK POOLING (CFVG: 2012) A TUTORIAL ON RISK POOLING
  2. 2. RISK POOLING Risk pooling is an important concept in supply chain management. The idea of risk pooling is executed by a centralized distribution system which caters to the requirements of all the markets in a given region instead of separate warehouse allocated for different markets.
  3. 3. Market Two Risk Pooling • Consider these two systems: Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One
  4. 4. Supplier Warehouse Retailers Centralized Systems
  5. 5. Decentralized System Supplier Warehouses Retailers
  6. 6. Demand Forecasts • The three principles of all forecasting techniques: – Forecasting is always wrong – The longer the forecast horizon the worst is the forecast – Aggregate forecasts are more accurate
  7. 7. The Effect of Demand Uncertainty • Most companies treat the world as if it were predictable: – Production and inventory planning are based on forecasts of demand made far in advance of the selling season – Companies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents reality • Recent technological advances have increased the level of demand uncertainty: – Short product life cycles – Increasing product variety
  8. 8. Market one Market two Factory Central warehouse
  9. 9. Warehouse 1 Warehouse 2 Factory Decentralized Warehouses
  10. 10. Market one Market two Factory Centralised warehouse at Ayutthaya
  11. 11. Market Two ABC Chiang Pai Market One Market Two ABC Chiang Pai Market One Prachin Buri Warehouse Pathumthani Warehouse Central warehouse: Ayutthaya Market Pathumthani Market Prachin Buri Factory: ABC Central warehouse
  12. 12. Market Two ABC company Market One Market Two ABC company Market One Prachin Buri Warehouse Pathumthani Warehouse Central warehouse (Ayutthaya) Market one Market two Market one Market two
  13. 13. WEEK 1 2 3 4 5 6 7 8 Pathumthani 68(-17) 37(+14) 45(+6) 58(-7) 16(+35) 32(+19) 72(-21) 80(-29) Prachin Buri 87(-27) 62(-3) 55(+4) 67(-8) 12(+47) 42(+17) 69(-10) 81(-22) TOTAL 155(-45) 99(+11) 100(+10) 125(-15) 28(+82) 74(+36) 141(-31) 161(-51) PRODUCT A 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 WEEK AVERAGEWEEKLYDEMAND DEMAND Pathumthani DEMAND Prachin Buri HISTORICAL DEMAND DATA 51 59 110 Average
  14. 14. Theoretical Approach • Consider two markets – Risk Polling by Aggregating Demand by Centralized procurement, centralized warehousing, centralized distribution like super stores etc – Risk Polling by Aggregating time horizon by combining orders as discussed in previous slide
  15. 15. A Detail Analysis of RISK POOLING Case
  16. 16. The Basic EOQ Model We assumed that, we will only keep half the inventory over a year then The total carry cost/yr = Cc x (Q/2). Total order cost = Co x (D/Q) Then , Total cost = 2 QC Q DCTC co += Finding optimal Q*
  17. 17. Cost Relationships for Basic EOQ (Constant Demand, No Shortages) TC–AnnualCost Total Cost Carrying Cost Ordering Cost EOQ balances carrying costs and ordering costs in this model. Q* Order Quantity (how much)
  18. 18. The Basic EOQ Model • EOQ occurs where total cost curve is at minimum value and carrying cost equals ordering cost: •Where is Q* located in our model? c o c o C DCQ QC Q DCTC 2 2 * min = += (How to obtain this?)Then, * c o c o C DCQ QC Q DCTC 2 2 * min = +=
  19. 19. A Revision of model discussed in Sesion-3: Model with “re-order points” • The reorder point is the inventory level at which a new order is placed. • Order must be made while there is enough stock in place to cover demand during lead time. • Formulation: R = dL, where d = demand rate per time period, L = lead time Then R = dL = (10,000/311)(10) = 321.54 Working days/yr
  20. 20. Reorder Point • Inventory level might be depleted at slower or faster rate during lead time. • When demand is uncertain, safety stock is added as a hedge against stockout. Two possible scenarios Safety stock! No Safety stocks! We should then ensure Safety stock is secured!
  21. 21. Determining Safety Stocks Using Service Levels • We apply the Z test to secure its safety level, )( LZLdR dσ+= Reorder point Safety stock Average sample demand How these values are represented in the diagram of normal distribution?
  22. 22. Reorder Point with Variable Demand stocksafety yprobabilitlevelservicetoingcorresponddeviationsstandardofnumber demanddailyofdeviationstandardthe timelead demanddailyaverage pointreorder where = = = = = = += LZ Z L d R LZLdR d d d σ σ σ
  23. 23. Reorder Point with Variable Demand Example Example: determine reorder point and safety stock for service level of 95%. 26.1.:formulapointreorderintermsecondisstockSafety yd1.3261.26300)10)(5)(65.1()10(30 1.65Zlevel,service95%For dayperyd5days,10Lday,peryd30 d =+=+=+= = === LZLdR d dσ σ
  24. 24. A detail treatment of this case study
  25. 25. TERMINOLOGY • AVG: Average daily demand faced by the distributor. • STD: standard deviation of the daily demand faced by the distributor. • L: Replenishment lead time from the supplier to the distributor in days • K: Fixed cost (set up cost) incurred every time the warehouse places an order, it includes transportation cost. • h: Cost of holding one unit of the product in the inventory for one day at the warehouse. • α: Service level -the probability of not stocking out during lead time.
  26. 26. • Average demand during lead time=L×AVG. This ensures that if a distributor places an order the system has enough inventory to cover expected demand during lead time. • Safety stock= z×STD× this is the amount of inventory distributor needs to keep to meet deviations from average demand during lead time. • z: Safety factor which is chosen from statistical table to ensure that probability of stock out is exactly 1-α • Reorder level (s) = average demand during lead time + safety stock =L×AVG + z×STD× Whenever the inventory level drops below reorder level the distributor should place new order to raise its inventory. L L
  27. 27. • . Order quantity (Q): It is the number of items ordered each time places an order that minimizes the average total cost per unit of time distributor. Q= • Order-up-to level (S): Since there is variability in demand the distributor places an order for Q items whenever inventory is below reorder level (s). S= Q + s 2K AVG h ×
  28. 28. • Average inventory = Q/2 + z STD • Coefficient of variation = ×× L STD AVG L×
  29. 29. A View of (s, S) Policy Time InventoryLevel S s 0 Lead Time Lead Time Inventory Position
  30. 30. EXAMPLE OF RISK POOLING Let us illustrate this with an example of a Chiang Pai based company ABC that produces certain type of products and distributes them in the South Thailand region .The current distribution system partitions S- Thailand region into two markets each of which has a warehouse. 1. One warehouse is located in Prachin Buri 2. Another one located in Pathumthani. alternative strategy of centralized distribution system replaces two warehouses by a single warehouse located between the two cities in Ayutthaya that will serve all customer orders in both markets
  31. 31. Market Two Consider these two systems: ABC company Pathumthani Warehouse Prachin Buri. Warehouse Market One Market Two ABC company Central warehouse Market OneMarket one Market two Market two Market one Chiang Rai Chiang Rai
  32. 32. ASSUMPTIONS • Manufacturing facility has sufficient capacity to satisfy any warehouse demand • Lead time for delivery to each warehouse is about one week and is assumed to be constant. • Delivery time does not change significantly if we adopt a centralized distribution system. • Service level of 95% that is the probability of stocking out is 5% is maintained.
  33. 33. DATA ANALYSIS Now with analysis of weekly demand for two different products, product A and product B produced by ABC company for last 8 weeks in both market zones we will be able to decide which distribution strategy will be more efficient and cost effective.
  34. 34. WEEK 1 2 3 4 5 6 7 8 Pathum 68 37 45 58 16 32 72 80 Prachine 87 62 55 67 12 42 69 81 TOTAL 155 99 100 125 28 74 141 161 PRODUCT A 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 WEEK AVERAGEWEEKLYDEMAND DEMAND Pathum DEMAND Prachine HISTORICAL DEMAND DATA FOR PRODUCT A
  35. 35. WEEK 1 2 3 4 5 6 7 8 Pathum 0 0 1 3 2 4 0 1 Prachine 1 0 2 0 0 3 1 1 TOTAL 1 0 3 3 2 7 1 2 PRODUCT B 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 1 2 3 4 5 6 7 8 WEEK AVERAGEDEMAND DEMAND Pathum DEMAND Prachine HISTORICAL DEMAND DATA FOR PRODUCT B
  36. 36. ANALYSIS OF HISTORICAL DATA PRODUCT AVERAGE DEMAND STANDARD DEVIATION COEFFICIENT OF VARIATION Pathum A 51 20.70 0.41 Prachin B 1.38 1.41 1.02 Pathum A 59.38 22.23 0.32 Prachin B 1 1 1 CENTRAL A 110.38 39.14 0.35 CENTRAL B 2.38 1.99 0.84
  37. 37. SAMPLE CALCULATIONS FOR PRODUCT A IN Pathumthani WAREHOUSE 1. Average demand = (68+37+45+58+16+32+72+80)/8=51 2. Standard deviation of demand = = 20.7 3. Coefficient of variation = 20.7/51 = 0.41 2 2 2 (68 51) (51 37) .............. (80 51) 8 − + − + −
  38. 38. GENERALIZATIONS • average demand for product A is much higher than product B which is a slow moving product. • Both standard deviation (absolute) and coefficient of variation (relative to average demand) are measure of variability of demand but we find that STD for product A is higher but coefficient of variation of product B is higher. • For centralized distribution average demand is simply the sum of the demand faced by each of existing warehouse • However the variability of demand as measured by STD or COV faced by central warehouse is lower than that faced by the two existing ones.
  39. 39. NUMERICAL VALUES • Safety factor (Z) =1.65 • Fixed cost for both the products (Co) = Rs 3500 • Inventory holding cost (Cc) = Rs 18.5 per unit per week. • Cost of transportation from warehouse to a customer – Current distribution system = Rs 50 per product – Centralized distribution system = Rs 60 per product.
  40. 40. INVENTORY LEVELS PRODUCT AVERAGE DEMAND DURING LEAD TIME SAFETY STOCK (SS) REORDER POINT (s) ORDER QUANTITY (Q) ORDER UPTO LEVEL (S) AVERAGE INVENTORY Pathum A 51 34.16 85 139 224 104 Prachine B 1.38 2.33 4 23 27 14 Pathum A 59.38 36.68 96 150 246 112 Prachine B 1 1.65 3 19 22 11 CENTRAL A 110.38 64.58 175 204 379 167 CENTRAL B 2.38 3.28 6 30 36 18
  41. 41. 4. Safety stock =1.65 20.7 = 34.16 5. Reorder point = 51 + 34.16 = 85.16 6. Order quantity = = 139 7. Order up to level = 139 +85 = 224 8. Average inventory = 139/2 +34.16 = 103.66 × × 1 2 3500 51 18.5 × × SAMPLE CALCULATIONS FOR PRODUCT A IN Pathumthani WAREHOUSE
  42. 42. % REDUCTION IN INVENTORY REDUCTION IN AVERAGE INVENTORY PRODUCT A = = 22.7% PRODUCT B = = 28% (104 112 167) 100 (104 112) + − × + (14 11 18) 100 (14 11) + − × +
  43. 43. NORMAL DISTRIBUTION Average mean = 0 Standard deviation = 1 X axis- safety factor Shaded area under curve= service level Z=1.65 P(z)=.95 Z=0
  44. 44. Demand Variability: Example 1 Product Demand 150 75 225 100 150 50 125 61 48 53 104 45 0 50 100 150 200 250 Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Month Demand (000's)
  45. 45. Reminder: The Normal Distribution 0 10 20 30 40 50 60 Average = 30 Standard Deviation = 5 Standard Deviation = 10
  46. 46. ANALYSIS AT DIFFERENT SERVICE LEVELS When average inventory for different level of service is calculated corresponding to varying value of z it was found that there exists a trade- off between service level and reduction in inventory through risk pooling. SERVICE LEVEL (%) 90 91 92 93 94 95 96 97 98 99 99.9 Z 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08
  47. 47. PERCENTAGE REDUCTION IN AVERAGE INVENTORY VS SERVICE LEVEL 0 5 10 15 20 25 30 90 93 96 99 SERVICE LEVEL %REDUCTIONINAVG INVENTORY PRODUCT A PRODUCT B SERVICE LEVEL (%) 90 91 92 93 94 95 96 97 98 99 99.9 PRODUCT A 24 23.7 23.4 23.1 23 22.7 22.3 21.8 21.7 21.2 19.5 PRODUCT B 27.12 27.07 27.0 26.94 26.89 26.82 26.72 26.59 26.44 26.2 25.65 % REDUCTION IN AVERAGE INVENTORY
  48. 48. Following generalizations are made • If a company goes for higher level of service it has to compromise with the % of reduction in the inventory level and vice versa. • To provide high service level company has to maintain high inventory too. • % reduction in inventory decreases with increase in service level.
  49. 49. IDEAL SITUATION This works best for – High coefficient of variation, which reduces required safety stock. – Negatively correlated demand as in such a case the high demand from one customer will be offset by low demand from another

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