Practical Management Science
5th Edition
ISBN: 9781305250901
Author: Wayne L. Winston, S. Christian Albright
Publisher: Cengage Learning
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Chapter 12.4, Problem 3P
Summary Introduction
To calculate: The optimal order quantity with this assumption.
Inventory and supply chain models:
The functions of inventory and supply chain are one of the most important business decision areas for an organization. The first important aspect of these concepts is to have adequate inventory on hand. The second important aspect is to carry a little amount of inventory as possible.
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A retailer determines that the cost of ordering and storing units of a product can be modelled by C(x)= 3x + 2000 / x, 0 < x < 200. Find the order size that will minimise ordering and storage cost.
Models of inventory systems frequently consider the relationships among a beginning inventory,a production quantity, a demand or sales, and an ending inventory. For a givenproduction period j, letsj-1 = ending inventory from the previous period (beginning inventory for period j)xj = production quantity in period jdj = demand in period jsj = ending inventory for period ja. Write the mathematical relationship or model that shows ending inventory as a functionof beginning inventory, production, and demand.b. What constraint should be added if production capacity for period j is given by Cj?c. What constraint should be added if inventory requirements for period j mandate anending inventory of at least Ij?
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Use the Quantity Discount Excel template to find your answer.
Chapter 12 Solutions
Practical Management Science
Ch. 12.4 - Prob. 1PCh. 12.4 - Prob. 2PCh. 12.4 - Prob. 3PCh. 12.4 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.4 - Prob. 9PCh. 12.4 - Prob. 10P
Ch. 12.4 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12 - Prob. 27PCh. 12 - Prob. 28PCh. 12 - Prob. 29PCh. 12 - Prob. 30PCh. 12 - Prob. 31PCh. 12 - Prob. 32PCh. 12 - Prob. 33PCh. 12 - Prob. 34PCh. 12 - Prob. 35PCh. 12 - Prob. 36PCh. 12 - Prob. 38PCh. 12 - Prob. 39PCh. 12 - Prob. 40PCh. 12 - Prob. 42PCh. 12 - Prob. 43PCh. 12 - Prob. 44PCh. 12 - Prob. 45PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 53PCh. 12 - Prob. 54PCh. 12 - In terms of K, D, and h, what is the average...Ch. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61PCh. 12 - Prob. 62PCh. 12 - Prob. 63PCh. 12 - Prob. 64PCh. 12 - Prob. 65PCh. 12 - Prob. 66PCh. 12 - Prob. 67PCh. 12 - Prob. 68PCh. 12 - Prob. 69PCh. 12 - Prob. 70PCh. 12 - Prob. 71PCh. 12 - Prob. 1.1CCh. 12 - Prob. 1.2CCh. 12 - Prob. 1.3C
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- A company is presently ordering on the basis of an EOQ. The demand is10,000 units a year, the unit cost is $10, the ordering cost is $30, and the cost of carrying inventory is 20%. The supplier offers a discount of 3% on orders of1000 units or more. What will be the saving (loss) of accepting the discount? Please state all the formulas and concepts used behind the solution.arrow_forwardThe best quantity to order One of the formulas for inventorymanagement says that the average weekly cost of ordering, payingfor, and holding merchandise iswhere q is the quantity you order when things run low (shoes,TVs, brooms, or whatever the item might be); k is the cost ofplacing an order (the same, no matter how often you order); c isthe cost of one item (a constant); m is the number of items soldeach week (a constant); and h is the weekly holding cost per item(a constant that takes into account things such as space, utilities,insurance, and security). Find dA>dq and d2A>dq2.arrow_forwardYou would like to use the fixed-time period inventory model to compute the desired order quantity for a company. You know that vendor lead time is 10 days and the number of days between reviews is 15. Which of the following is the standard deviation of demand over the review and lead time period if the standard deviation of daily demand is 10? -25 -40 -50 -73 -100arrow_forward
- Red Corporation uses the reorder point modelto plan its purchases. It sellsitssole productat the following daily amounts:Minimum=30,000; Average=40,000;Maximum=60,000. Its supplier takes 3 dayson average and 4 days maximum to deliverthe order. The-reorder point would be A. 240,000B. 160,000C. 120,000D. 90,000arrow_forwardRed Corporation uses the reorder point model to plan its purchases. It sells its sole product at the following daily amounts: Minimum=30,000; Average=40,000; Maximum=60,000. Its supplier takes 3 days on average and 4 days maximum to deliver the order. The-reorder point would be: A. 240,000B. 160,000C. 120,000D. 90,000arrow_forwardKickBites Manufacturing has a demand for 1,000 pumps each year. The cost of a pump is $50. It cost KickBites Manufacturing $40 to place an order, and the carrying cost is 25% of the unit cost. If pumps are ordered in quantities of between 200 and 250, KickBites Manufacturing can get a discount on the cost of the pumps. Should the company order 200 pumps or 250 pumps at a time and take the 3% discount? [Provide your answers in two decimal points]arrow_forward
- An electronics retailer wants to develop an inventory policy to achieve 99% chance of not getting stockouts for a chip. The daily demand for the chip is estimated to be Normal with mean 200 and standard deviation of 20. They count the chip inventory every 2 weeks to place an order, and it takes 11 days for the ordered chips to be delivered. The retailer operates 7 days a week, 365 days a year. They are going to implement an order-up-to model. A) What base stock level should they choose? B) What is the number of chips they would have on order (on average)? C) When they checked their inventory of chips to place a new order, they found that they ran out of stock completely. In addition, they have 10 chips on way to be delivered, while there are five customers who paid for 20 chips in total and are waiting to receive their chips. How many chips should the retailer order?arrow_forwardThe owner and manager of a hardware store reevaluates his inventory policy for hammers. sells an average of 50 hammers a month, so you have placed purchase orders for 50 hammers with a distributor at a cost of $20 each at the end of each month. But the owner does not place all the store orders and find that this takes much of your time. He estimates that the value of his time spent ordering hammers is $75. a) What must be the unit cost of maintaining hammers for the current policy of the hardware store to be Optimal according to the EOQ model? b) If the distributor delivers an order for hammers in 5 business days (out of an average of 25 per month), what should be the reorder point, according to the EOQ model?arrow_forwardA coffee shop consumes 350 lbs of coffee per week at a steady rate. The coffee shop buys coffee from a supplier at the cost of $10 per lb, and ordering cost of $5 per order. The supplier takes 8 days to deliver an order (assume that 1 week = 7 days). What should be the reorder point (in pounds) for the coffee shop (i.e., at what level of inventory it should place an order with the supplier).arrow_forward
- Which one of the following variables is not explicitly considered in the computation of the Economic Order Quantity? a. Per unit per year cost of storage and storage insurance for the inventories purchased b. Annual quantity forecasted by the firm that will satisfy the demand of the customers c. Any deductions from the selling price granted by the suppliers to the buyers due to certain quantities reached d. Ordering or transaction cost that must be constant regardless of quantity orderedarrow_forwardA manufacturing company uses 25,000 components at an even rate during a year. Eachorder placed with the supplier of the components is for 2,000 components, which is theeconomic order quantity. The company holds a buffer inventory of 500 components. Theannual cost of holding one component in inventory is $2.What is the total annual cost of holding inventory of the component?arrow_forwardI run a Ford car dealership, and I experience known and constant demand for cars. I sell 10,000 cars annually. The cost of ordering is $1,108, and the annual cost of holding a car on the lot is $500. What is the economic ordering quantity (EOQ)? Round to the nearest whole number (so if your answer is 443.363, round to 443)arrow_forward
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