P3-1
Stationery Supplies is considering installing an inventory control system in its store in Provo, Utah. The store carries about 1,400 different inventory items and has annual gross sales of about $80,000. The inventory control system would cost $12,500 to install and about $2,000 per year in additional supplies, time, and maintenance. If the savings to the store from the system can be represented as a fixed percentage of annual sales, what would that percentage have to be in order for the system to pay for itself in five years or less?
P3-2
A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The coffeehouse estimates that it costs $45 in paperwork and labor to place an order for the coffee, and holding costs are based on a 20 percent annual interest rate.
a. Determine the optimal order quantity for Colombian coffee. b. What is the time between placement of orders?
c. What is the average annual cost of holding and setup due to this item?
d. If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory.
P3-3
Consider the coffeehouse discussed in Problem 10. Suppose that its setup cost for ordering was really only $ 15. Determine the error made in calculating the annual cost of holding and setup incurred as a result of its using the wrong value of K. ( Note that this implies that its current order policy 15 suboptimal . )
P3-4
The Wod Chemical Company produces a chemical compound that is used as a lawn fertilizer. The compound can be produced at a rate of 10,000 pounds per day. Annual demand for the compound is 0.6 million pounds per year. The fixed cost of setting up for a production run of the chemical is $1,500, and the variable cost of production is $3.50 per pound. The company uses an interest rate of 22 percent to account for the cost of capital, and the costs of storage and handling of the chemical amount to 12 percent of the value. Assume that there are 250 working days in a year. a. What is the optimal size of the production run for this particular compound?
b. What proportion of each production cycle consists of uptime and what proportion consists of downtime?
c. What is the average annual cost of holding and setup attributed to this item? If the compound sells for $3.90 per pound, what is the annual profit the company is realizing from this item?
P3-5
The Crestview Printing Company prints a particularly popular Christmas card once a year and distributes the cards to stationery and gift shops throughout the United States. It costs Crestview 50 cents to print each card, and the company receives 65 cents for each card sold.
Because the cards have the current year printed on them, those cards that are not sold are generally discarded. Based on past experience and forecasts of current buying patterns, the probability distribution of the number of cards to be sold nationwide for the next Christmas season is estimated to be
Quantity Sold 100,000—150,000 150,001—200,000 200,001—250,000 250,001—300,000 300,001—350,000 350,001—400,000 400,001—450,000
Probability
.10 .15 .25 .20 .15 .10 .05
Determine the number of cards that Crestview should print this year.
P3-6
An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on a 28 percent annual interest rate.
The monthly demand for the filter follows a normal distribution with mean 280 and standard deviation 77. Order lead time is assumed to be five months.
Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back-ordered, and the cost assessed for each back-ordered demand is $12.80. Determine the following quantities:
a. The optimal values of the order quantity and the reorder level.
b. The average annual cost of holding, setup, and stock-out associated with this item assuming that an optimal policy is used.
c. Evaluate the cost of uncertainty for this process. That is, compare the average annual cost you obtained in part (b) with the average annual cost that would be incurred if the lead time demand had zero variance.
P3-7
Weiss’s paint store uses a (Q, R) inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Although excess demands are back-ordered, the store owner estimates that unfilled demands cost about $10 each in bookkeeping and loss-of-goodwill costs. Fixed costs of replenishment are $15 per order, and holding costs are
based on a 30 percent annual rate of interest.
a. What are the optimal lot sizes and reorder points for this brand of paint? b. What is the optimal safety stock for this paint?
生产计划与控制作业Problem3
