Though the average inventory of the centralized distribution system is lower than that of the decentralized distribution system, is it possible that there are disadvantages of a centralized system?
QSO 630 Module 6 1 Module Five presented the formulas used in to calculate safety stock, reorder level, and average inventory level, for a generic product with multiple order/production opportunities. In this module, those formulas are used with a detailed example to compare the average inventory level for a centralized distribution system with that for a decentralized distribution system. In a centralized distribution system, there is a single warehouse distributing products to at least two places; for example, one “central ” warehouse distributes products to both Washington, D.C., and Boston. On the other hand, in a decentralized distribution system, there is a warehouse for EACH place; for example, one warehouse distributes for Washington, D.C., and another warehouse distri butes for Boston. Consider the following example for retailers in Washington, D.C., and Boston in a particular supply chain: Decentralized distribution system: There is one warehouse in Washington, D.C., and one warehouse in Boston The retail stores in each of the above two places receive products from the warehouse in the respective place The two warehouses receive products from a supplier in Atlanta Lead time for delivery to each of the warehouses is two weeks The desired service level is 97 percent; the Module Five lecture presented the definition of service level Centralized distribution system: There is a single “central” warehouse in New York City The retail stores in both Washington, D.C., and Boston prod ucts from the central warehouse in New York City The central warehouse receives products from the supplier in Atlanta Lead time for delivery to the central warehouse is two weeks The desired service level is 97 percent 2 QSO 630 Module 6 2 2 * Average Demand* K h 2 * 27 * 100 0.50 The ordering cost incurred by any warehouse is $100 per order, and the holding cost is $0.50 per unit per week. The following historical demand data is given for the last 7 weeks. Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Washington D.C. 24 34 46 12 18 25 30 Boston 17 45 9 84 12 15 46 Performance of the Decentralized Distribution System Warehouse in Washington D.C Lead Time = 2 weeks (given) K = $100 per order (given) h = $0.50 per unit per week (given) Average Demand (using the AVERAGE function in MS Excel) = 27 units per week Standard Deviation of demand (using the STDEV function in MS Excel) = 11 units per week. Service level = 97%. This means, z = NORMSINV (0.97) = 1.88 Recall from QSO 510 that if area to the left of X under a normal curve is given, X is calculated by first obtaining the value of z by using the NORMSINV function in MS Excel. Safety Stock = z * (Standard Deviation of Demand) * = 1.88 * 11 * = 30 units Reorder Level = (Average Demand * Lead Time) + (Safety Stock) = (27 * 2) + (30) = 84 units Order Quantity, Q = 104 units per order Average inventory level = ( Q/2) + (Safety Stock) = (104 / 2) + (30) = 82 units Warehouse in Boston Lead Time = 2 weeks (given) K = $100 per order (given) h = $0.50 per unit per week (given) LeadTime QSO 630 Module 6 3 2 2 * Average Demand* K h 2 * 33 * 100 0.50 Average Demand (using the AVERAGE function in MS Excel) = 33 units per week Standard Deviation of demand (using the STDEV function in MS Excel) = 28 units per week.
Service level = 97%. This means, z = NORMSINV (0.97) = 1.88 Safety Stock = z * (Standard Deviation of Demand) * = 1.88 * 28 * = 75 units Reor der Level = (Average Demand * Lead Time) + (Safety Stock) = (33 * 2) + (75) = 141 units Order Quantity, Q = 115 units per order Average inventory level = ( Q/2) + (Safety Stock) = (115 / 2) + (75) = 133 units Total of the average inventory levels at the two warehouses in Washington D.C. and Boston = 82 units (Washington D.C.) + 133 units (Boston) = 215 units Performance of the Centralized Distribution System Central Warehouse in New York City Lead Time = 2 weeks (given) K = $100 per order (given) h = $0.50 per unit per week (given) Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Central 24 + 34 + 46 + 9 12 + 84 18 + 12 25 + 15 30 + 46 warehouse 17 = 45 = = 55 = 96 = 30 = 40 = 76 41 79 Average Demand (using the AVERAGE function in MS Excel) = 60 units per week Standard Deviation of demand (using the STDEV function in MS Excel) = 25 units per week.
Service level = 97%. This means, z = NORMSINV (0.97) = 1.88 LeadTime 4 QSO 630 Module 6 2 2 * Average Demand* K h 2 * 60 * 100 0.50 Safety Stock = z * (Standard Deviation of Demand) * = 1.88 * 25 * = 67 units Reorder Level = (Average Demand * Lead Time) + (Safety Stock) = (60 * 2) + (67) = 187 units Order Quantity, Q = 155 units per order Average inventory level = ( Q/2) + (Safety Stock) = (155 / 2) + (67) = 145 units. Evidently, the average inventory level (145 units) for the centralized distribution system is lower than the average inventory level (215 units) for the decentralized distribution system. LeadTime