The replenishment lead time (L) = 1week.

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Presentation transcript:

The replenishment lead time (L) = 1week. Problem 7.8 # of warehouses = 4 R/week at each warehouse = 10,000/wk or 500,000 yr R = N(10,000, 2,000) H=.25(10) = 2.5 /yr S = 1000 L = 1 week SL = .95 Decentralized Policy =20000 The replenishment lead time (L) = 1week. Standard deviation of demand during lead time at each store σ = 2,000. Safety stock at each store for 95% level of service Is= 1.65 x 2,000 = 3,300. ROP = LTD + Is = 10,000 + 3,300 = 13,300. =13300 =4(13300) = 53200 Average time unit spends in store (T) = Id / (4R) = 53,200/40,000 = 1.33 weeks.

Total Cost We do not consider RC because it does not depend on the inventory policy. But you can always add it. Inventory system cost for one warehouse Inventory system cost for four warehouses = 4(58,250) Inventory system cost for four warehouses = 233,000

b. Centralized Policy R/week in each warehouse follows Normal distribution with mean of 10,000, and Standard deviation of 2,000 When combining all in a central warehouse Mean (central) = 4(10000) = 40000 =40000 Variance (central) = 4(variance at each warehouse) Variance at each warehouse = (2000)2 = 4,000,000 Variance (central) = 4(4,000,000) = 16,000,000 Standard deviation (central) = 4,000 R (central) = Normal(40,000, 4000)

Centralized Policy The replenishment lead time (L) = 1week. Standard deviation of demand during lead time in the centralized system is σ (central) = 4,000. Safety stock at each store for 95% level of service Is (central) = 1.65 x 4,000 = 6,600. =26600 =26600 53200 Average time unit spends in store (T) = 26600 / 40000 = = .67 weeks.

Total Cost We do not consider RC because it does not depend on the inventory policy. But you can always add it. Inventory system cost for four warehouse in centralized system Inventory system cost for four warehouses in decentralized system