IEOR150F10_hw03_sol

# 2 a since t r t 0 1 years and ? 2000 the order

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lower, and a lower setup cost results in a smaller order quantity and a shorter order cycle. 2. (a) Since T R = T = 0 . 1 years and λ = 2000, the order quantity of the retail store is Q R = λT R = 200 units . The inventory level of the retail store is the dashed line depicted below. - 6 S S S S S S S S S S S S S S S S Time (years) 0.1 Inventory level (units) 200 The order quantity of the warehouse is the same, i.e., Q W = 200 units . The inventory level of the warehouse is the thick line depicted below. Note that it is always zero: Whenever the warehouse get replenished, it ships all it receives to the retail store immediately. 1

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- 6 Time (years) Inventory level (units) (b) The annual setup cost of the warehouse is K W T = \$500. The annual setup cost of the retail store is K R T R = \$100. The annual holding cost of the warehouse is \$0 since there is no inventory in the warehouse. The annual holding cost of the retail store is h R Q R 2 = \$1000. The annual total cost of the system is thus \$1600 . (c) k = 2 implies T 0 R = T 2 = 0 . 05 years, which further implies Q 0 R = λT R = 100 units . The inventory level of the retail store is the dotted line depicted below. - 6 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·
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• Fall '09
• Trigraph, retail store, annual holding cost

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