A car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is willing to backlog some demand but estimates that if he is short one car for one year, he will lose $20,000 worth of future profits. Each time the dealer places an order for cars, the ordering cost is $10,000. Determine the dealer’s optimal ordering policy. What is the maximum shortage that will occur? Assume it costs $5000 to store a car for a year

A car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is willing to backlog some demand but estimates that if he is short one car for one year, he will lose $20,000 worth of future profits. Each time the dealer places an order for cars, the ordering cost is $10,000. Determine the dealer’s optimal ordering policy. What is the maximum shortage that will occur? Assume it costs $5000 to store a car for a year

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.4: Simulation With Built-in Excel Tools

Problem 13P

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In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)
Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
ABC firm uses roughly 3,400 pounds of chemical dye a year. Currently, the firm purchases 300 pounds per order and pays P120.00 per pound. The supplier has just announced that orders of 1,000 pounds or more will be filled at a price of P80.00 per pound. The manufacturing firm incurs a cost of P4,000.00 each time it submits an order and assigns an annual holding cost of 17% of the purchase price per pound. a. Determine the order size that will minimize the total cost.b. If the supplier offered the discount at 1,500 pounds instead of 1,000 pounds, what order size would minimize total cost?
A Mercedes dealer must pay $20,000 for each carpurchased. The annual holding cost is estimated to be 25%of the dollar value of inventory. The dealer sells an averageof 500 cars per year. He believes that demand is backloggedbut estimates that if he is short one car for one year he willlose $20,000 worth of future profits. Each time the dealerplaces an order for cars, ordering cost amounts to $10,000.Determine the Mercedes dealer’s optimal ordering policy.What is the maximum shortage that will occur?
A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for 2.00 to the grocer, and the grape pies are sold for 4.00. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 2100 cups of sugar and 3000 cups of flour. Each apple pie requires 1 1/2 cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make and apple pie in 6 minutes and a grape pie in 3 minutes.…
A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $10.00 to the grocer, and the grape pies are sold for $8.00. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 1,500 cups of sugar and 2,400 cups of flour. Each apple pie requires 1½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in 6 minutes and a grape pie in 3 minutes. They plan to work no more than 60 hours. (Round your answers to nearest whole number.) b. Determine the amounts of sugar, flour, and time that will be unused. (Leave no cells blank -…
One of the products stocked at Weiss’s paint store, mentioned in Problem 14, is a certain type of highly volatile paint thinner that, due to chemical changes in the product,has a shelf life of exactly one year. Al Weiss purchases the paint thinner for $20 a galloncan and sells it for $50 a can. The supplier buys back cans not sold during the yearfor $8 for reprocessing. The demand for this thinner generally varies from 20 to 70cans a year. Al assumes a holding cost for unsold cans at a 30 percent annual interestrate.a. Assuming that all values of the demand from 20 to 70 are equally likely, what is theoptimal number of cans of paint thinner for Al to buy each year?b. More accurate analysis of the demand shows that a normal distribution gives abetter fit of the data. The distribution mean is identical to that used in part (a), andthe standard deviation estimator turns out to be 7. What policy do you nowobtain?
A hot dog vendor at Wrigley Field sells hot dogs for$1.50 each. He buys them for $1.20 each. All the hot dogshe fails to sell at Wrigley Field during the afternoon can besold that evening at Comiskey Park for $1 each. The dailydemand for hot dogs at Wrigley Field is normally distributedwith a mean of 40 and a standard deviation of 10.a If the vendor buys hot dogs once a day, how manyshould he buy?b If he buys 52 hot dogs, what is the probability that hewill meet all of the day’s demand for hot dogs at Wrigley?
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Rocky Mountain Tire Centre sells 20,000 tires of a particular type per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20. per tire if fewer than 500 tires are ordered, $18. Per tire if more than 500 but fewer than 1,000 tires are ordered and $17. per tire if 1,000 or more tires are ordered. Quantity Unit Price 1-499 $20. 500-999 $18. 1000 & over $17 Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. What value of Z should be applied? How many drives should be carried as safety stock?
A tire store orders its stock for a popular winter tire once every year. The cost of a tire for the store is $120. The store sells a tire for $140 at the regular price. The regular demand per year is 1,000 tires, which is normally distributed with a standard deviation of 70 tires. Customers do not prefer to buy from an older stock; hence the store does not keep the tires for the next year. The store is able to sell the excess stock at a reduced price of $80 per tire. How many tires the store should order each year?
Long last Appliance Store has a demand of 1300 units per month for one of its fast selling portable smoothie machine (model G), it incurs a fixed order placement, transportation and receiving cost of $3000 each time an order is delivered. Each machine cost the company $550 and the company has a holding cost of 12%. The company has two other models of the smoothie machine which are also popular with consumers. Evaluate the company’s inventory management policy if lots for each model are ordered and delivered independently by determining the following: The optimal order size The cycle inventory The number of orders per year The annual ordering and holding cost The total cost of the inventory Briefly state rationale for the approach used for (a-e)