INVENTORY MANAGEMENT

1. Number 2 pencils at the campus bookstore are
sold at a fairly steady rate of 60 per week. The pencils cost the bookstore 2
kuru? each and sell for 15 kuru? each. It costs the bookstore 12 YTL to
initiate an order, and holding costs are based on an annual interest rate of 25
percent. Determine the optimal number of pencils for the bookstore to purchase
and the time between placement of orders. What are the yearly holding and setup
costs for this item?

2. A
local company produces a programmable EPROM for several industrial clients. It
has experienced a relatively flat demand of 2500 units per year for the
product. The EPROM is produced at a rate of 10000 units per year. The
accounting department has estimated that it costs 50 YTL to initiate a
production run, each unit costs the company 2 YTL to manufacture, and the cost
of holding is based on a 30 percent annual interest rate. Determine the optimal
size of a production run. Find the time between initiation of production runs,
the time devoted to production, and the downtime each production cycle. What is
the maximum level of the on-hand inventory of the EPROMs?
D,.
3. A
large producer of household products purchases a glyceride used in one of its
deodorant soaps from outside of the company. It uses the glyceride at a fairly
steady rate of 40 pounds
per month, and the company uses a 23 percent annual interest rate to compute
holding costs. The chemical can be purchased from two suppliers, A and B. A
offers the following all-units discount schedule:

Order Size

Price per Pound

0?Q<500 1.30 YTL 500?Q<1000 1.20 YTL 1000?Q 1.10 YTL whereas B offers the following incremental discount schedule: 1.25 YTL per pound for all orders less than or equal to 700 pounds, and 1.05 YTL per pound for all incremental amounts over 700 pounds. Assume that the cost of order processing for each case is 150 YTL. Which supplier should be used? 4.In a continuous review system, the demand rate for gizmos is normally distributed, with an average of 300 units per week. The lead time is 9 weeks. The standard deviation of weekly demand is 15 units. a) What is the standard deviation of demand during the 9-week lead time? b) What is the average demand during the 9-week lead time? c) What reorder point results in a cycle-service level of 99 percent? 5.Dorothys pastries are freshly baked and sold at several specialty shops. When they are a day old, they must be sold at reduced prices. Daily demand is distributed as follows: Demand Probability 50 0.25 150 0.50 200 0.25 Each pastry sells for 1.00 YTL and costs 0.60 YTL to make. Each one not sold at the end of the day can be sold the next day for 0.30 YTL as a day-old merchandise. How many pastries should be baked each day? 6.The buyer for Needless Markup, a famous high end department store, must decide on the quantity of a high-priced womens handbag to produce in Italy for the following Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a discount firm for $20.00. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only. a)Suppose that the sales of the bags are equally likely to be anywhere from 50 to 250 handbags during the season. Based on this, how many bags should the buyer purchase? (Hint: This means that the correct distribution of demand is uniform. You may solve this problem assuming either a discrete or a continuous uniform distribution.) b)A detailed analysis of past data shows that the number of bags sold is better described by a normal distribution, with mean 150 and standard deviation 20. Now what is the optimal number of bags to be purchased? 7.Nationwide Auto Parts uses a periodic review inventory control system for one of its stock items. The review interval is six weeks, and the lead time for receiving the materials ordered from its wholesaler is three weeks. Weekly demand is normally distributed, with mean of 100 units and a standard deviation 20 units. a) What are the average and the standard deviation of demand during the protection interval? b) What should be the target inventory level if the firm desires 97.5 percent stock-out protection? c) If 350 units were in stock at the time of a certain periodic review, how many units should be ordered? 8.In a periodic review system, the lead time for gadgets is 2 weeks and the review period is 1 week. Demand during the protection interval averages 218 units, with a standard deviation of 40 units. What is the cycle-service level when the target inventory level is set at 300 units? INVENTORY MANAGEMENT1. Number 2 pencils at the campus bookstore are sold at a fairly steady rate of 60 per week. The pencils cost the bookstore 2 kuru? each and sell for 15 kuru? each. It costs the bookstore 12 YTL to initiate an order, and holding costs are based on an annual interest rate of 25 percent. Determine the optimal number of pencils for the bookstore to purchase and the time between placement of orders. What are the yearly holding and setup costs for this item? 2. A local company produces a programmable EPROM for several industrial clients. It has experienced a relatively flat demand of 2500 units per year for the product. The EPROM is produced at a rate of 10000 units per year. The accounting department has estimated that it costs 50 YTL to initiate a production run, each unit costs the company 2 YTL to manufacture, and the cost of holding is based on a 30 percent annual interest rate. Determine the optimal size of a production run. Find the time between initiation of production runs, the time devoted to production, and the downtime each production cycle. What is the maximum level of the on-hand inventory of the EPROMs? D,. 3. A large producer of household products purchases a glyceride used in one of its deodorant soaps from outside of the company. It uses the glyceride at a fairly steady rate of 40 pounds per month, and the company uses a 23 percent annual interest rate to compute holding costs. The chemical can be purchased from two suppliers, A and B. A offers the following all-units discount schedule:Order SizePrice per Pound 0?Q<5001.30 YTL 500?Q<10001.20 YTL1000?Q1.10 YTLwhereas B offers the following incremental discount schedule: 1.25 YTL per pound for all orders less than or equal to 700 pounds, and 1.05 YTL per pound for all incremental amounts over 700 pounds. Assume that the cost of order processing for each case is 150 YTL. Which supplier should be used? 4.In a continuous review system, the demand rate for gizmos is normally distributed, with an average of 300 units per week. The lead time is 9 weeks. The standard deviation of weekly demand is 15 units. a) What is the standard deviation of demand during the 9-week lead time?b) What is the average demand during the 9-week lead time?c) What reorder point results in a cycle-service level of 99 percent? 5.Dorothys pastries are freshly baked and sold at several specialty shops. When they are a day old, they must be sold at reduced prices. Daily demand is distributed as follows: DemandProbability500.251500.502000.25Each pastry sells for 1.00 YTL and costs 0.60 YTL to make. Each one not sold at the end of the day can be sold the next day for 0.30 YTL as a day-old merchandise. How many pastries should be baked each day? 6.The buyer for Needless Markup, a famous high end department store, must decide on the quantity of a high-priced womens handbag to produce in Italy for the following Christmas season. The unit cost of the handbag to the store is $28.50 and the handbag will sell for $150.00. Any handbags not sold by the end of the season are purchased by a discount firm for $20.00. In addition, the store accountants estimate that there is a cost of $0.40 for each dollar tied up in inventory, as this dollar invested elsewhere could have yielded a gross profit. Assume that this cost is attached to unsold bags only. a)Suppose that the sales of the bags are equally likely to be anywhere from 50 to 250 handbags during the season. Based on this, how many bags should the buyer purchase? (Hint: This means that the correct distribution of demand is uniform. You may solve this problem assuming either a discrete or a continuous uniform distribution.)b)A detailed analysis of past data shows that the number of bags sold is better described by a normal distribution, with mean 150 and standard deviation 20. Now what is the optimal number of bags to be purchased? 7.Nationwide Auto Parts uses a periodic review inventory control system for one of its stock items. The review interval is six weeks, and the lead time for receiving the materials ordered from its wholesaler is three weeks. Weekly demand is normally distributed, with mean of 100 units and a standard deviation 20 units. a) What are the average and the standard deviation of demand during the protection interval?b) What should be the target inventory level if the firm desires 97.5 percent stock-out protection?c) If 350 units were in stock at the time of a certain periodic review, how many units should be ordered?8.In a periodic review system, the lead time for gadgets is 2 weeks and the review period is 1 week. Demand during the protection interval averages 218 units, with a standard deviation of 40 units. What is the cycle-service level when the target inventory level is set at 300 units?