Homework 6 Môn Inventory Management | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

lOMoAR cPSD| 58605085 INVENTORY MANAGEMENT HOMEWORK 6 Problem 1:
Consider a two-stage serial process where the second stage is a rather minor
operation adding little extra value to the product. To be more specific, suppose we
have an item with these characteristics (borrowing the notation of “W” for
warehouse, or primary stage and “R” for retailer, or finishing stage).
● 𝐷 = 1,000 units/year ● 𝑣 = $5/unit 𝑊 ● 𝑣 = $6/unit 𝑅 ● 𝑟 = 0.24 $/$/year ● 𝐴 = $20 𝑊 ● 𝐴 = $10 𝑅 Find 𝑄 , 𝑄 , and 𝑛. 𝑊 𝑅 Solution: ● 𝑣' = 𝑣 = $5/𝑢𝑛𝑖𝑡 𝑊 𝑊 ● ' 𝑣 = 𝑣 𝑅 𝑅 − 𝑣 𝑊 =6−5=$1 /𝑢𝑛𝑖𝑡 ' 𝐴 ● 𝑛 * = 𝑊 𝑣 𝑅 =0.63<1 →𝑛 ' = (20)(1) 𝐴 (10)(5) =1 𝑅 𝑣 𝑊 2 𝐴 𝐷 ● 𝑅 ( + 𝐴 𝑊𝑛 ) 2(10+ 20 𝑄 = 1 )(1,000) 𝑅 = ' ' 𝑛𝑣 𝑣 + ( )𝑟
[(1)(5)+1](0.24) =204 𝑢𝑛𝑖𝑡𝑠 𝑊 𝑅
● 𝑄 𝑊 = 𝑛𝑄 𝑅 =(1)(204)=204 𝑢𝑛𝑖𝑡𝑠 Conclusion: ● 𝑄 = 204 𝑢𝑛𝑖𝑡𝑠 𝑅 lOMoAR cPSD| 58605085 ● 𝑄 = 204 𝑢𝑛𝑖𝑡𝑠 𝑊 ● 𝑛 = 1 Problem 2:
A warehouse supplies a single retailer with a product. The warehouse’s purchasing
lead time is 3 weeks and the lead time for the retailer (from the warehouse) is 1 week.
Assume that forecast errors are normally distributed with the σ for 1 week being 70
units, and that σ =𝑡σ . The annual demand rate is 12,000 units, and the 𝑡1
following data have been gathered: 𝑣
= $32/unit, 𝑣 = $38/unit, 𝑟 = 0.22 $/$/year, 𝑛 = 2, or the warehouse orders two 𝑊 𝑅
batches of the retailer’s order quantity at one time. The retailer’s order quantity is 𝑄
= 500 units. Finally, suppose that the fractional charge per unit short, 𝐵 , is set 𝑅
2 at 0.65. Find the reorder point for both locations. SOLUTION 𝐿 = 3 𝑤𝑒𝑒𝑘𝑠 𝑊 𝐿 = 𝐿 = 1 𝑤𝑒𝑒𝑘 𝑅𝐸 𝑅 σ = 70 𝑢𝑛𝑖𝑡𝑠
𝐷 = 12, 000 𝑢𝑛𝑖𝑡𝑠 𝑣 = $32/𝑢𝑛𝑖𝑡 𝑊 𝑣 = $38/𝑢𝑛𝑖𝑡 𝑅
𝑟 = 0. 22 $/$/𝑦𝑒𝑎𝑟 𝑛 = 2 𝑄 = 500 units 𝑅 𝐵 = 0. 65 lOMoAR cPSD| 58605085 2 Retailer: ● 𝑝 ( ) 𝑢≥ 2 𝑅 ● 𝑘 = 2. 84 𝑅 ● 𝑠 = 𝑥^ + 𝑘 σ = (12,
000)() + (2. 84)( 1)(70) = 430 𝑢𝑛𝑖𝑡𝑠 𝑅 𝐿𝑅 𝑅 𝐿𝑅 Warehouse:
𝑄𝑅(𝑣𝑅+(𝑛−1)𝑣𝑊)𝑟 (500)[38+(2−1)(32)](0.22) ● 𝑝𝑢≥( )𝑘𝑊 = 𝐵2𝑣𝑅𝐷 = (0.65)(38)(12,000) = 0. 025978 ● 𝑘 = 1. 94 𝑊 ● 𝑠 = 𝑥^ + 𝑘 σ =
(12, 000)() + (1. 94)( 3 + 1)(70) = 1, 195 𝑢𝑛𝑖𝑡𝑠 𝑊 𝐿 +𝐿 𝑊 𝐿 +𝐿 𝑊 𝑊 𝑅 𝑅 Conclusion: ● 𝑠 = 1, 195 𝑢𝑛𝑖𝑡𝑠 𝑊 ● 𝑠 = 430 𝑢𝑛𝑖𝑡𝑠 𝑅 Problem 3:
A retailer supplies a small storefront outlet with a unique product. In a sense, the
retailer serves as the warehouse for this outlet. The retailers’ purchasing lead time is
2 weeks and the lead time for the outlet from the retailer is also 2 weeks, primarily
due to order handling time. Assume that forecast errors are normally distributed with
the σ for 1 week being 10 units, and that σ =𝑡σ . The annual 𝑡1
demand rate is 2,000 units, and the following data have been gathered: 𝑣 = 𝑊 lOMoAR cPSD| 58605085
$6/unit, 𝑣 = $8/unit, 𝑟 = 0.24 $/$/year, 𝑛 = 2, or the retailer orders two batches of 𝑅
the outlets order quantity at one time. The outlet’s order quantity is 𝑄 = 200 units. 𝑅
Finally, suppose that the fractional charge per unit short, 𝐵 , is set at 0.4. Find the 2
reorder point for both locations. SOLUTION 𝐿 = 2 𝑤𝑒𝑒𝑘𝑠
𝐷 = 2, 000 𝑢𝑛𝑖𝑡𝑠
𝑟 = 0. 24 $/$/𝑦𝑒𝑎𝑟 𝑊 𝐿
= 𝐿 = 2 𝑤𝑒𝑒𝑘𝑠
𝑣𝑊 = $6/𝑢𝑛𝑖𝑡 𝑛 = 2 𝑅𝐸 𝑅 σ = 10 𝑢𝑛𝑖𝑡𝑠
𝑣𝑅 = $8/𝑢𝑛𝑖𝑡 𝑄𝑅 = 200 units 𝐵 = 0. 4 2 lOMoAR cPSD| 58605085
International University, HCMC
School of IEM – LSCM Program Student Full name: Student ID: Retailer: ● 𝑝 = 0. 015 2 𝑅 ● 𝑘 = 2. 17 𝑅
● 𝑠 = 𝑥^ + 𝑘 σ = (2,
000)() + (2. 17)( 2)(10) = 108 𝑢𝑛𝑖𝑡𝑠 𝑅 𝐿𝑅 𝑅 𝐿𝑅 Warehouse: 𝑅( 𝑅 )𝑟 (200)[8+(2−1)(6)](0.24) ● 𝑝 ( ) = = 0. 105 2 𝑅 ● 𝑘 = 1. 25 𝑊 ● 𝑠 = 𝑥^ + 𝑘 σ = (2,
000)() + (1. 25)( 2 + 2)(10) = 179 𝑢𝑛𝑖𝑡𝑠 𝑊 𝐿 +𝐿 𝑊 𝐿 +𝐿 𝑊 𝑊 𝑅 𝑅 Conclusion: ● 𝑠 = 179 𝑢𝑛𝑖𝑡𝑠 𝑊 ● 𝑠 = 108 𝑢𝑛𝑖𝑡𝑠 𝑅