Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 5, Problem 50AP
Summary Introduction
Interpretation:Difference in (Q,R) values compared to normal case are to be discussed.
Concept Introduction: Laplace distribution is a continuous probability distribution in which two independent exponential functions are evaluated. These exponential functions are independent of each other with different parameters
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Ray wishes to determine the optimal order quantity for its best-selling bike in his bike store. Ray pays the supplier a wholesale price of $118 each for this bike. Ray has estimated the average daily demand for this bike is 23 units. The store opens 304 days a year. The cost to carry one bike in the store for a whole year is 8% of the unit bike cost. Ray has estimated that, on average, the order processing cost, i.e., ordering cost, with the bike supplier each time is $152, and it roughly takes 20 working days to receive the order from the supplier. Ray wishes to avoid the stock-out situation with a probability of 95%, and this requires Ray to carry a safety stock of 30 bikes in the store.
What is the optimal order quantity (EOQ value) that Ray should order each time from the bike supplier to minimize his long-run inventory cost?
A retailer uses the order-up-to model to manage inventory of an item in a store. The leadtime for replenishments is four weeks and it can place orders weekly. Weekly demand isPoisson with mean 0.10 unit. Its order-up-to level is five and unfilled demand is backordered. What is the coefficient of variation of its orders?
Show that the optimal run size always exceeds the EOQ.Give an intuitive explanation for this result.
Chapter 5 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 4PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 12PCh. 5.5 - Prob. 16PCh. 5.5 - Prob. 18PCh. 5.6 - Prob. 21PCh. 5.7 - Prob. 24P
Ch. 5.7 - Prob. 25PCh. 5.7 - Prob. 26PCh. 5.7 - Prob. 27PCh. 5 - Prob. 28APCh. 5 - Prob. 31APCh. 5 - Prob. 32APCh. 5 - Prob. 33APCh. 5 - Prob. 37APCh. 5 - Prob. 38APCh. 5 - Prob. 40APCh. 5 - Prob. 41APCh. 5 - Prob. 43APCh. 5 - Prob. 44APCh. 5 - Prob. 45APCh. 5 - Prob. 46APCh. 5 - Prob. 47APCh. 5 - Prob. 48APCh. 5 - Prob. 49APCh. 5 - Prob. 50APCh. 5 - Prob. 51AP
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- HAL Ltd. produces a line of high-capacity disk drives for mainframe computers.The housings for the drives are produced in Hamilton, Ontario, and shipped tothe main plant in Toronto. HAL uses the drive housings at a fairly steady rate of 720per year. Suppose that the housings are shipped in trucks that can hold 40 housingsat one time. It is estimated that the fixed cost of loading the housings onto the truckand unloading them on the other end is $300 for shipments of 120 or fewer housings(i.e., three or fewer truckloads). Each trip made by a single truck costs the company$160 in driver time, gasoline, oil, insurance, and wear and tear on the truck.a. Compute the annual costs of transportation and loading and unloadingthe housings for the following policies: (1) shipping one truck per week,(2) shipping one full truckload as often as needed, and (3) shipping three fulltruckloads as often as needed.b. For what reasons might the policy in part (a) with the highest annual cost bemore…arrow_forwardThe difference(s) between the basic EOQ model and the pro-duction order quantity model is (are) that: a) the production order quantity model does not require theassumption of known, constant demand.b) the EOQ model does not require the assumption ofnegligible lead time.c) the production order quantity model does not require theassumption of instantaneous delivery.d) all of the above.arrow_forwardCOMPUTING REORDER POINTS (ROP) FOR IPHONES WITH AND WITHOUT SAFETY STOCKAn Apple store has a demand (D) for 8,000 iPhones per year. The firm operates a 250-day working year.On average, delivery of an order takes 3 working days, but has been known to take as long as 4 days. Thestore wants to calculate the reorder point without a safety stock and then with a one-day safety stock.APPROACH c First compute the daily demand and then apply Equation (12-6) for the ROP.Then compute the ROP with safety stock.arrow_forward
- Lia ITZY has determined that the annual demand for number 6 screws is 100,000 screws. Lia, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. QUESTION: How many number 6 screws should Lia order at a time if she wishes to minimize total inventory cost?arrow_forwardLia ITZY has determined that the annual demand for number 6 screws is 100,000 screws. Lia, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year. QUESTION: How many orders per year would be placed? What would the annual ordering cost be?arrow_forwardThe materials manager of a tire manfacturer must predict periodically place order for a key chemical one of the raw materials used in manufacturing uses the chemical at a rate of 300lbs each week and the lead time of delivery is 4 days. Assume that the manufacturing operation runs 5 days a week. At what point should the chemical be reorderedd a. when 1200lbs are remaining b. where 0lbs are remaining c. where 375lbs are remaining d. when 240lbs are remarrow_forward
- Daily demand of a chemical at an oil refinery is normally distributed with a mean of 60 litres and a standard deviation of 7. The supplier reliably delivers the chemical by maintaining a constant lead time of 1 week. There are no delivery charges from the supplier. Sales occur throughout the year. An order placement requires one hour of an administrative employee who is paid $20 per hour. Receiving and storing a chemical shipment requires two workers to work for half an hour. Workers are paid $12 per hour each. Chemical’s purchase price is $500 per litre. Annual cost of capital is 5%. Other holding costs are estimated to be $0.5 per litre. Find the order quantity and the reorder point to satisfy a 95% service level during the lead time. (Round answers to 2 decimal places.)arrow_forwardConsider the EOQ model. The optimal order quantity (Q*) is 500. What is the average inventory carried (I*)? Group of answer choices Cannot be determined 3,600 units 500 units 250 units 0 unitsarrow_forwardEOQ Model Suppose during your college life, every year you need $5,000 cash to spend in addition to the studying expenses. Each time in need of cash, you decide to go to the bank for that. And the transportation costs you $5 (assumed amount) of going to the bank and coming back. Assume that the current saving/checking link account has an interest rate of 5%. Please find the optimal solution of the amount of cash each time for the withdraw.arrow_forward
- Using excel. The Metropolitan Bus Company (MBC) purchases diesel fuel from AmericanPetroleum Supply. In addition to the fuel cost, American PetroleumSupply charges MBC $250 per order to cover the expenses of deliveringand transferring the fuel to MBC’s storage tanks. The lead time for anew shipment from American Petroleum is 10 days; the cost of holding agallon of fuel in the storage tanks is $0.04 per month, or $0.48 peryear; and annual fuel usage is 150,000 gallons. MBC buses operate 300days a year.a.What is the optimal order quantity for MBC?b.Howfrequently should MBC order to replenish the gasoline supply?c.TheMBC storage tanks have a capacity of 15,000 gallons. ShouldMBC consider expanding the capacity of its storage tanks?d.What isthe reorder point?arrow_forwardStore manager Rosalía has noted that the daily demand for the exclusive Motomami candles produced and sold in her Fire Doll Artisan Chandlery located in downtown Champaign is 40 candles. Fire Doll Artisan Chandlery remains open 365 days a year. The lead time for producing the candles is 9 days. Based on the batch size of 560 candles, how often (every how many days) does she need to make the candles? (Round this to the nearest whole number).arrow_forwardActa Metals manufactures safes of different sizes and models. One of the models has a demand of 20,000 safes/year. The company can produce at a rate of 4,000 safes a month and it cost $30 to initiate each production run. The actual production cost for each safe is $5.37 and the holding of each unit could be charged a nominal annual interest rate of 15%, if it were to be invested elsewhere. Determine the optimal batch size and the cycle time Determine the maximum on-hand inventory and the average annual holding and setup cost, Determine the production uptime and downtime.arrow_forward
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