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- 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. 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. Market Two Risk Pooling • Consider these two systems: Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One
- 4. Supplier Warehouse Retailers Centralized Systems
- 5. Decentralized System Supplier Warehouses Retailers
- 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. 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. Market one Market two Factory Central warehouse
- 9. Warehouse 1 Warehouse 2 Factory Decentralized Warehouses
- 10. Market one Market two Factory Centralised warehouse at Ayutthaya
- 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. 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. 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. 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. A Detail Analysis of RISK POOLING Case
- 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. 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. 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. 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. 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. 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. 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. 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. A detail treatment of this case study
- 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. • 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. • . 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. • Average inventory = Q/2 + z STD • Coefficient of variation = ×× L STD AVG L×
- 29. A View of (s, S) Policy Time InventoryLevel S s 0 Lead Time Lead Time Inventory Position
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. % 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. 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. 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. Reminder: The Normal Distribution 0 10 20 30 40 50 60 Average = 30 Standard Deviation = 5 Standard Deviation = 10
- 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. 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. 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. 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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