1. A bakery\'s use of corn sweetener is normally distributed with a mean of 80 g
ID: 448972 • Letter: 1
Question
1. A bakery's use of corn sweetener is normally distributed with a mean of 80 gallons per day and a standard deviation of four gallons per day. Lead time for delivery of the corn sweetener is normal, with a mean of six days and a standard deviation of two days. If the manager wants a service level of 99 percent, what reorder point should be used?
2. A car rental agency uses 96 boxes of staples a year. The boxes cost $4 each. It costs $10 to order staples, and carrying costs are $.80 per box on an annual basis.
Determine:
(A) the order quantity that will minimize the sum of ordering and holding boxes of staples
(B) the annual cost of ordering and carrying the boxes of staples
D = 96 boxes/year
S = $10
H = $.80 per box-year
3. A company can produce a part it uses in an assembly operation at the rate of 50 an hour. The company operates eight hours a day, 300 days a year. Daily usage of the part is 300 parts. The company uses the part every day. The run size is 6,000 parts. The annual holding cost is $2 per unit, and setup cost is $100.
(A) How many runs per year will there be?
(B) While production is occurring, how many parts per day are being added to inventory?
(C) Assuming that production begins when there are no parts on hand, what is the maximum number of parts in inventory?
(D) The machine is dedicated to this product. Every so often, preventive maintenance, which requires six working days, must be performed on it. Does this interrupt production cycles, or is there enough time between cycles to perform the maintenance? Explain.
5. A firm stocks a seasonal item that it buys for $22/unit and sells for $29/unit. During the season, daily demand can be described using a Poisson distribution with a mean of 2.4. Because of the nature of the item, units remaining at the close of business each day must be removed at a cost of $2 each. What is the optimum stocking level, and what is the effective service level?
6. A machine is expected to use approximately three spare parts during its useful life. The spares cost $200 each and have no salvage value or other use. The manager has ordered five spares. Assuming a Poisson usage rate, what range of shortage cost is implied?
9. A manager reorders lubricant when the amount on hand reaches 422 pounds. Average daily usage is 45 pounds, which is normally distributed with a standard deviation of three pounds per day. Lead time is nine days. What is the risk of a stockout?
10. A restaurant prepares Peking duck daily at a cost of $18 per duck. Each duck generates revenue of $47 if sold. Demand for Peking duck can be described by a Poisson distribution with a mean of 4.2 ducks per day. Unsold ducks at the end of each day are converted to duck soup at an additional cost of $5 over and above the resulting value as soup. How many ducks should be prepared each day?
11. A service garage uses 120 boxes of cleaning cloths a year. The boxes cost $6 each. Ordering cost is $3 and holding cost is 10 percent of purchase cost per unit on an annual basis.
Determine:
(A) the economic order quantity
(B) the total cost of carrying the cloths (excluding purchase price)
(C) the average inventory
D = 120 boxes per year
S = $3
H = .10($6) = $.60 per box-year
12. A shop owner uses a reorder point approach to restocking a certain raw material. Lead time is six days. Usage of the material during lead time is normally distributed with a mean of 42 pounds and a standard deviation of four pounds. When should the raw material be reordered if the acceptable risk of a stockout is 3 percent?
13. A shop that makes candles offers a scented candle, which has a monthly demand of 360 boxes. Candles can be produced at a rate of 36 boxes per day. The shop operates 20 days a month. Assume that demand is uniform throughout the month. Setup cost is $60 for a run, and holding cost is $2 per box on a monthly basis.
Determine the following:
(A) the economic run size
(B) the maximum inventory
(C) the number of days in a run
The daily usage rate (u) is 18 boxes. The daily production rate (p) is 36 boxes.
Explanation / Answer
1. Reorder point = dbar*LT +z*sqrt(LT*sigmad^2+ dbar^2*sigmaLT^2)
Z=2.33
LT= 6 days
Dbar= 80
Sigmad= 4
sigmaLT= 2
Reorder point = 80*6 + 2.33*sqrt(6*4^2 +80^2*2^2)
= 853 gallons
2.
a) Qopt. = sqrt(2*D*S/H)
= sqrt(2*96*10/0.8)
= 49.98 or 49
b) TC = 49/2* 0.8 + 96/49*10
= $39.19
Note: Please be specific to the question that need to be answered.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.