Problems
Use the following information for Problems 1 through 5:
Kathy owns a neighborhood hot dog stand, and wants to determine some good order policies for hot dogs. She estimates her annual demand to be constant and equal to 10,000 hot dogs. Her order cost is $20, the carrying cost rate is 40% per year, the purchase cost is $0.20 per hot dog, and the order lead time is two days.
- What is the optimal order quantity?
- What is the annual order cost
- What is the annual inventory carrying cost and the relevant total annual inventory cost
- How many orders per year will Kathy make? How many days will there be, between orders
- What is the reorder point? What is Kathy’s optimal order policy
- Using the information in Problem 1, if Kathy’s carrying cost rate dropped by half, to 20% per year, how would this impact Problems 1 through 5
- Using the information in Problem 1, if Kathy’s order cost increased to $100, how does this impact Problems 1 through 5
- Find the economic order quantity and the reorder point for the following information: annual demand is 22,500 units; order cost is $70per order; annual inventory carrying cost is $5 per unit; the order lead time is 10 days; and the business operates 300 days per year.
Use the following information for Problems 9 and 10:
Grebby’s Rodeo Tack & Boots sells gear to rodeo industry customers and has been offered discounts for the purchase of some alligator-hide boots from its longtime boot supplier. The pricing alternatives for the alligator boots are: $62 per pairfor 1–299 pair purchased; $57 per pair for 300–599 units purchased; and $54 per pair for 600 or more units purchased.Grebby’s average order cost is $25 per order; the forecasted annual demand for alligator boots is 1,200 pair; and the inventory carrying cost rate is 24% per year.
9. Calculate the EOQ for each of the three purchase prices. Which EOQs are valid
10.Which purchasing alternative should Grebby’s take? What are the total annual inventory costs for the valid alternatives?11.The Big Cheese Pizza Parlor buys lots of pizza boxes. It normally pays $1 per box when ordering from its supplier. Based on its annual forecast for pizza demand, its demand for boxes is estimated to be 10,000 units for the year. It costs $25 to place an order, and its holding cost for boxes is 25% of the cost of a box per year. The supplier tells the Big Cheese Pizza buyer that she can sell the boxes for$0.95 each if the restaurant buys a minimum of 5,000 at a time. Should it take the discount, and what is the total cost?
12.Average demand is 2,500 units per year; order cost is $50 per order; holding cost rate is 20% of the purchase cost per unit per year; and the cost of one unit is $42. What is the total inventory cost per year? If a cost reduction per unit of $1 can be achieved by buying 1,000 ata time, should the buyer take the discount? Justify your answer.
13.The average demand is equal to 10 units per day, the order lead time is 7 days, and the standard deviation of the lead time demand is 4 units. If a 95% service level is desired, what is the reorder point?
14. Roy and Gayle’s Fix-It Shop purchased a new automated inventory control software application, and it wanted to put ROPs on all of it purchased tools and supplies. After forecasting the demand for items for the upcoming year, it was ready to start calculating ROPs.Three of the items are shown here, along with the forecasted annual demands, purchase lead times, lead time demand standard deviation levels, and desired service levels. Calculate the ROPs for the three items and their safety stock levels. Assume the store is open 365 days per year.
Chapter 9
1Boehm Compressors uses a lean production assembly line to make its compressors. In one assembly area, the demand is 100 parts pereighthour day. It uses a container that holds eight parts. It typically takes about six hours to round trip a container from one workcenter to the next and back again. It also desires to hold 15% safety stock of this part in the system.
a. How many containers should Boehm Compressors be using?
b. Calculate the maximum system inventory for this part.
c. If it reduced the number of containers by one, how would this impact the required round-trip time, all else being constant?
Answered
K = D T ( 1 + S )/C ,
Where:
- K= the number of containers;
- D= the demand rate of the assembly line;
- T= the time for a container to make an entire circuit through the system, from being filled, moved, being emptied, and returned to befilled again;
- C= the container size, in number of parts; and
- S= the safety stock factor, from 0 to 100%.
Question 1 (a)
Using the above formula as presented by Wisner (2017), the number of containers will be computed as follows:
Demand rate per hour 100/8 = 12.5 per hour
K = D T ( 1 + S )/C
K= number of containers
D= 12.5
T= 6 hours
S= 15 percent
C= 8
12.5×6(1.15)
86.25
= 86.25/8
=10.78125 = 11 containers
All containers must be whole so, the number of containers will be 11
The maximum inventory
11 × 8 = 88 units.
Question 1 (c)
Reducing the number of containers by 1 to 10 the round-trip time will be
10 = 12.5Tx1.15 14.375
10 = 14.375T/8
T= 5.565 hours
Chapter 10
Given the following information, determine the optimal overbooking policy for Talia’s Beauty Salon. The salon’s capacity is 8 patrons.The historic number of no shows for a typical day along with the probability of occurrence is shown in the table. The average profitability per patron is $100 and the cost of lost goodwill per patron due to overbooking is approximately $50.
Answered
| Patrons | ||||
| No shows | Probability | 8 | 9 | 10 |
| 0 | 0.50 | 8 | 9 | 10 |
| 1 | 0.30 | 7 | 8 | 9 |
| 2 | 0.20 | 6 | 7 | 8 |
Expected Profit with 8 patrons
| No shows | 0 | 1 | 2 |
| Patrons | 8 | 7 | 6 |
| Profit ($) | 800 | 700 | 600 |
| Turnaways | 0 | 0 | 0 |
| Cost | 0 | 0 | 0 |
| Net Profit | 800 | 700 | 600 |
| Probability | 0.50 | 0.30 | 0.20 |
| Expected Profit | 400 | 210 | 120 |
Total Expected Profit $730
Expected Profit with 9 patrons
| No shows | 0 | 1 | 2 |
| Patrons | 9 | 8 | 7 |
| Profit | 900 | 800 | 700 |
| Turnaways | 1 | 0 | 0 |
| Cost | 50 | 0 | 0 |
| Net Profit | 850 | 800 | 700 |
| Probability | 0.5 | 0.3 | 0.2 |
| Expected Profit | 425 | 240 | 140 |
Total Expected Profit $805
Expected Profit with 10 patrons
| No shows | 0 | 1 | 2 |
| Patrons | 10 | 9 | 8 |
| Profit | 1000 | 900 | 800 |
| Turnaways | 2 | 1 | 0 |
| Cost | 100 | 50 | 0 |
| Net Profit | 900 | 850 | 800 |
| Probability | 0.5 | 0.3 | 0.2 |
| Expected Profit | 450 | 255 | 160 |
Total Expected Profit $855
The total expected profits are maximized with 10 patrons (overbooking by 2 patrons).
As such, Talia’s Beauty Salon should apply 2-patrons overbooking policy
