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Assignment Ch12a.1 Problem 1: A toy manufacturer uses approximately silicon chips annually. The Chips are used at a steady rate during the 240 days a year that the plant operates. Annual holding cost is 60 cents per chip, and ordering cost is $24. Determine a) How much should we order each time to minimize our total cost b) How many times should we order c) what is the length of an order cycle d) What is the total cost

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**What is the Optimal Order Quantity**

D = 32000, H = .6, S = 24

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**How many times should we order**

Annual demand for a product is 32000 D = 32000 Economic Order Quantity is 1600 EOQ = 1600 Each time we order EOQ How many times should we order ? D/EOQ 32000/1600 = 20

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**what is the length of an order cycle**

working days = 240/year 32000 is required for 240 days 1600 is enough for how many days? (1600/32000)(240) = 12 days

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**What is the Optimal Total Cost**

The total cost of any policy is computed as The economic order quantity is 1600 This is the total cost of the optimal policy

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Assignment Ch12a.2 Victor sells a line of upscale evening dresses in his boutique. He charges $300 per dress, and sales average 30 dresses per week. Currently, Vector orders 10 week supply at a time from the manufacturer. He pays $150 per dress, and it takes two weeks to receive each delivery. Victor estimates his administrative cost of placing each order at 225. His inventory charring cost including cost of capital, storage, and obsolescence is 20% of the purchasing cost. Assume 52 weeks per year.

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Assignment Ch12a.2 Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the current ordering policy? Without any EOQ computation, is this the optimal policy? Why? Compute Vector’s total annual cost of inventory system (carrying plus ordering but excluding purchasing) under the optimal ordering policy? What is the ordering interval under optimal ordering policy? What is average inventory and inventory turns under optimal ordering policy? Inventory turn = Demand divided by average inventory. Average inventory = Max Inventory divided by 2. Average inventory is the same as cycle inventory.

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**Number of orders/yr = D/Q = 1560/300 = 5.2 **

Current Policy Problem 6.3 flow unit = one dress flow rate d = 30 units/wk purchase cost C = $150/unit fixed order cost S = $225 H = 20% of unit cost. order lead time L = 2 weeks Orders ten weeks supply Q = 10(30) = 300 units. 52 weeks per year Annual demand = 30(52) = 1560 Number of orders/yr = D/Q = 1560/300 = 5.2 (D/Q) S = 5.2(225) = 1,170/yr. Average inventory = Q/2 = 300/2 = 150 H = rC = .2*150 = 30 Annual holding cost = H (Q/2) = 30(150) = 4,500 /yr. Without any computation, is this the optimal policy? Why? Without any computation, is EOQ larger than 300 or smaller Why Total annual costs = = 5670

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Optimal Policy Q* = EOQ = = 153 units. An order for 153 units two weeks before he expects to run out. That is, whenever current inventory drops to 30 units/wk * 2 wks = 60 units which is the re-order point. His annual cost will be 4,589

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Inventory Turns Inventory turns = yearly demand / Average inventory Average inventory = cycle inventory = I = Q/2 Current policy inventory turns = D/(Q/2)= 1560/(300/2) Current policy Inventory turns = 10.4 times per year. Optimal policy inventory turns = D/(Q/2)= 1560/(153/2) Optimal policy inventory turns = = 20.4 turns roughly double

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Assignment Ch12a.3 Complete Computer (CC) is a retailer of computer equipment in Minneapolis with four retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 per week. Each unit of product costs $200, and CC has a holding cost of 20% per annum. The fixed cost of each order (administrative plus transportation) is $900. Assume 50 weeks per year. The holding cost will be the same in both decentralized and centralized ordering systems. The ordering cost in the centralized ordering is twice of the decentralized ordering system.

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Assignment Ch12a.3 Decentralized ordering: If each outlet orders individually. Centralized ordering: If all outlets order together as a single order. Compute EOQ in decentralized ordering Compute the cycle inventory for one outlet and for all outlets. Compute EOQ in the centralized ordering Compute the cycle inventory for all outlets and for one outlet Compute the total holding cost + ordering cost (not including purchasing cost) for the decentralized policy Compute the total holding cost plus ordering cost for the centralized policy

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**With a cycle inventory of 1500 units for each outlet. **

Decentralized Policy Four outlets Each outlet demand D = 4000(50) = 200,000 S= 900 C = 200 H = .2(200) = 40 If all outlets order together in a centralized ordering, then S= 1800 =3000 With a cycle inventory of 1500 units for each outlet. The total cycle inventory across all four outlets equals 6000 units. With centralization of purchasing the fixed order cost is S = $1800. =8485 and a cycle inventory of units.

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**Total holding and ordering costs under the two policies**

Decentralized Decentralized: TC for all four warehouses = 4(120000)=480000 Centralized compared to about 30% improvement

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