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 43AP
Summary Introduction
Interpretation:Number of parts to be acquired in advance of 400-day period is to be calculated.
Concept Introduction:
Central Limit Theorem is defined as when a very large sample is taken for evaluation of random variables, it tends to follow
It states that sampling distribution of any statistic will be normal, when the
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RoyalTech's South Jersey warehouse faces a daily demand that is normally distributed, with mean 1,000 and standard deviation 100 pallets.
RoyalTech's supplier has a lead-time that is normally distributed, with mean 5 days and standard deviation 1 day.
RoyalTech reviews its inventory periodically, that is, every 7 days. (Hint: think about the inventory model appropriate here)
RoyalTech's warehouse runs 365 days a year, and the cost of carrying inventory is 18.25% per year.
The supplier charges RoyalTech $2,000 per pallet, and $5,000 per delivery.
RoyalTech plans to maintain 98% SL.
NORMSINV(0.98) = 2.054. L(2.054) = 0.0073.
Answer the following questions.
1. How much safety stock should Royal Tech carry? [Select]
v pallets.
2. What is RoyalTech's average inventory? [ Select ]
pallets.
3. What is the total relevant cost incurred by RoyalTech per day? $ [ Select]
4. What is the Fill Rate that RoyalTech is able to achieve for this service level? [ Select ]
Your company currently keeps a safety stock of 554 units of a particular product that has a lead time of 10 days. Records indicate that the weekly demand was as follows:
1176
955
780
1052
736
842
748
993
852
738
794
1444
1333
1372
1106
706
923
734
786
729
1357
1165
1277
683
1106
What is the current service level? Input your result as the decimal form and round to 4 decimal places.
You are requested to recommend a safety stock that will ensure an average service level of 97.5%. The lead time is not expected to change. What safety stock would you recommend? (0 decimal places)
A large manufacturer purchases a part from a supplier under a continuous review system. The average demand is 400 units a day with a standard deviation of 50 units a day. It costs $55 to process each order.
The holding cost for a part is $0.2 per month and the company has a policy of maintaining a 96% service level. The company operates 315 days per year. The time from when an order is placed to when it arrives at the company from its vendor is 5 days.
a- What is the reorder point?
b- What order quantity would be appropriate
c- What is the total annual cost for this item?
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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- 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_forwardStroheim’s is a dry goods store located in downtown Milwaukee, Wisconsin. Stroheim’s placesorders weekly with their suppliers for all of their reorders. The lead time for men’s briefs is4 days. Stroheim’s uses a 95 percent service level. Assuming a Type 1 service, what is the orderup to level for the briefs? Assume demands for briefs are uncertain with daily mean demandof 20 and daily standard deviation of 12arrow_forwardA plastic canister manufacturing company maintains an annual safety stock of 500 units of plastic caps. If the company places an annual purchase order for 1,800 units of these caps, its average annual inventory, in units, is between: ( )1,500 and 1,300 ( )3,200 and 3,000 ( )2,400 and 2,200 ( )1,200 and 1,000 ( )1,900 and 1,700arrow_forward
- A newsvendor orders 8000 units. Demand is normally distributed with a mean of9000 and a standard deviation of 2000. What is the stockout probability?arrow_forwardDemand for sandwiches is normally distributed with a mean of 1,280 and a standard deviation of 220. The order quantity is 1,485 units. What is the expected inventory (in units)?arrow_forwardOriental Healthcare is a multi-specialty hospital catering to a variety of illnessesconnected to the heart and respiratory systems. The demand for a class of medicalconsumable is generally random. Recently, an examination of the stores records overa period of 10 weeks revealed the following weekly consumption pattern:Week No. Consumption(Units)1 1202 1093 894 1405 1106 1457 778 1209 13010 80The supplier of the item takes on an average 2 weeks to deliver once the order isplaced. Design an appropriate inventory control policy for a periodic review systemfor a review frequency of 4 weeks for a 99% service levelarrow_forward
- A small grocery store sells fresh produce, which it obtains from a local farmer. During the strawberry season, demand for fresh strawberries can be reasonably approximated using a normal distribution with a mean of 36 quarts per day and a standard deviation of 7 quarts per day. Excess costs run .40 cents per quart. The grocer orders 42 quarts per day.Use Table. What is the implied cost of shortage per quart?arrow_forwardThe injection molding department of a company uses an average of 30 gallons of special lubricanta day. The supply of the lubricant is replenished when the amount on hand is 170 gallons. It takesfour days for an order to be delivered. Safety stock is 50 gallons, which provides a stockout risk of9 percent. What amount of safety stock would provide a stockout risk of 3 percent? Assumenormality.arrow_forward3) A company produces a part that is used in its production process. The company produces the part at a rate of 300 units per day. The daily demand for the product is 180 units. The annual demand for the part is 54,000 units and occurs consistently over the 300 days that the company operates yearly. The company incurs a setup cost of $300 each time the item is produced. The cost of carrying the item in inventory is estimated to be 25 percent of the item's $100 cost. How many units should the company produce each production run to minimize its inventory- associated costs?arrow_forward
- A local store has a customer demand for a product. The daily demand assumed to be normally distributed with an average demand of 25 units with a standard deviation of 5 units. It takes 15 days to receive a new order since the time it is placed and it remains constant. Assuming 80% service level what should be the reorder level? Round-up to the nearest integer.arrow_forward12. A restaurant uses an average of 8 jars of a special sauce every day. When they place an order, the jars arrive to the restaurant in a day (lead time is 1 day). Daily usage of sauce has a standard deviation of 3 jars. They think their demand during the lead time can be modelled with normal distribution. The manager is willing to accept no more than a 10 percent risk of stockout during lead time. Calculate at which level of inventory a new order needs to be placed (i.e. calculate the reorder-point(ROP)).arrow_forwardOne item a computer store sells is supplied by a vendor who handles only that item. Demand forthat item recently changed, and the store manager must determine when to replenish it. The managerwants a probability of at least 96 percent of not having a stockout during lead time. The managerexpects demand to average a dozen units a day and have a standard deviation of two units a day.Lead time is variable, averaging four days with a standard deviation of one day. Assume normalityand that seasonality is not a factor.a. When should the manager reorder to achieve the desired probability?b. Why might the model not be appropriate if seasonality were present?arrow_forward
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