1. The Hastings Company is a nation-wide wholesaler for small electronic devices. One of its most popular items is a new GPS unit called the WAM1-1000. Hastings has gathered the foilvv 1 information and has asked you to develop a continuous review inventory control system for this item:
Order quantity for each order placed with manufacturer = 10,000 units
Average demand = 1,000 units/week
Standard deviation of weekly demand = 200 units
Average lead time = 5 weeks
Standard deviation of lead time: 1.5 weeks
Cycle-service level = 90% (z for 90% = 1.28)
a. What is the standard deviation of demand during lead time?
b. What is the safety stock level that should be carried for the WAMI-1000?
c. What is the reorder point for the WAMI-1000?
d. If Hastings decides to increase its cycle-service level to from 90% to 95% ( z for 95% = 1.65), how does this change the actions that should take?
2. A production manager uses the economic lot size approach to determine the batch size for a product with an annual demand of 20,000 units per year. The setup cost for each batch is $50 and once the setup is complete, the product may be produced at the rate of 800 units per day. There is a holding cost of $2 per unit per year and the plant operates on a 250-day production year. If the machine used to produce this product is needed for another item and it takes one day to set up regardless so product, how many production days are available for production of the new item? What is the to cost?
3. As an inventory manager, you must decide on the order quantity for an item. Us annual demand is 1,000 units. Ordering costs are $50 each time an order is placed, and the holding cost is 25 percent of the per-unit price. Your supplier provided the following price schedule. (4 Grades)
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Quantity
|
Price per Unit
|
|
1-199
|
$10.00
|
|
200-499
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$ 9.80
|
|
500 or more
|
$ 9.60
|
What ordering-quantity policy do you recommend?
4 Given the following information set up the problem in a transportation table and solve for the minimum-cost plan:
|
PERIOD
|
|
1
|
2
|
3
|
|
Demand
|
550
|
700
|
75
|
|
Capacity
|
|
|
|
|
Regular
|
500
|
500
|
50
|
|
Overtime
|
50
|
50
|
50
|
|
Subcontract
|
120
|
120
|
10
|
|
Beginning inventory
|
100
|
|
|
|
Costs
|
|
|
|
|
Regular time
|
$ 60 per unit
|
|
|
|
Overtime
|
$ 80 per unit
|
|
|
|
Subcontract
|
$ 90 per unit
|
|
|
|
Inventory carrying cost
|
$ 1 per unit
|
|
|
|
Month Back-order cost per month
|
$ 3 per unit
|
|
|
5. Demand for rug-cleaning Machines at Clyde's U-Rent-It is shown in the following. Machines are rented by the day only. Profit on the rug cleaners is $10 per day. Clyde has four rug-cleaning Machines.
|
Demand
|
Freq.
|
|
0
|
.30
|
|
1
|
.20
|
|
2
|
.20
|
|
3
|
.15
|
|
4
|
.10
|
|
5
|
.05
|
|
|
1.00
|
a. Assuming that Clyde's stocking decision is optimal, what is the implied range of excess cost per machine?
b. Your answer from part a has been presented to Clyde, who protests that the amount is too low. Does this suggest an increase or a decrease in the number of rug machines he stocks? Explain.
c. Suppose now that the $10 mentioned as profit is instead the excess cost per day for each machine and that the shortage cost is unknown.
Assuming that the optimal number of machines is four, what is the implied range of shortage cost per machine?
6. Eagle Fabrication has the following aggregate demand requirement and other data for the upcoming four quarters.
|
Quarter
|
Demand
|
|
Previous quarter's output
|
1500 units
|
|
1
|
1300
|
|
Beginning inventory
|
200 units
|
|
2
|
1400
|
|
Stock out cost
|
$ 50 per unit
|
|
3
|
1500
|
|
Inventory holding cost
|
$ 10 per unit at end of quarter
|
|
4
|
1300
|
|
Hiring workers
|
$ 4 per unit
|
|
|
|
|
Firing workers
|
$ 8 per unit
|
|
|
|
|
Unit cost
|
$ 30 per unit
|
|
|
|
|
Overtime
|
$ 10 extra per unit
|
Which of the following production plans is better: Plan A-chase demand by hiring and firing; or Plan B-produce at a constant rate of 1200 and obtain the remainder from overtime?