Practice Problems: Chapter 12, Inventory Management
Problem 1:
ABC Analysis
Stock Number Annual $ Volume Percent of Annual $ Volume
J24 12,500 46.2
R26 9,000 33.3
L02 3,200 11.8
M12 1,550 5.8
P33 620 2.3
T72 65 0.2
S67 53 0.2
Q47 32 0.1
V20 30 0.1
= 100.0
What are the appropriate ABC groups of inventory items?
Problem 2:
Assume you have a product with the following parameters: Annual Demand = 360 units
Holding cost per year = $1.00 per unit Order cost = $100 per order
What is the EOQ for this product?
Problem 4:
Given the data from Problem 3, and assuming a 300-day work year, how many orders should be processed per year? What is the expected time between orders?
Problem 5:
What is the total cost for the inventory policy used in Problem 3?
Problem 6:
Based on the material from Problems 3 – 5, what would cost be if the demand was actually higher than estimated (i.e., 500 units instead of 360 units), but the EOQ established in problem 3 above is used? What will be the actual annual total cost?
Problem 7:
If demand for an item is 3 units per day, and delivery lead-time is 15 days, what should we use for a simple re-order point?
Problem 8:
Assume that our firm produces Type C fire extinguishers. We make 30,000 of these fire
Problem 9:
We use 1,000 electric drills per year in our production process. The ordering cost for these is $100 per order and the carrying cost is assumed to be 40% of the per unit cost. In orders of less than 120, drills cost $78 per unit; for orders of 120 or more the cost drops to $50 per unit.
Should we take advantage of the quantity discount?
Problem 10:
Litely Corp sells 1,350 of its special decorator light switch per year and places orders for 300 of these switches at a time. Assuming no safety stocks, Litely estimates a 50% chance of no shortages in each cycle and the probability of shortages of 5, 10, and 15 units as 0.2, 0.15, and 0.15
respectively. The carrying cost per unit per year is calculated as $5 and the stockout cost is estimated at $6 ($3 lost profit per switch and another $3 loss of goodwill or future sales). What level of safety stock should Litely use for this product? (Consider safety stock of 0, 5, 10, and 15 units.)
Problem 11:
Presume that Litely carries a modern white kitchen ceiling lamp that is quite popular. The
Problem 1:
ABC Groups
Class Items Annual Volume Percent of $ Volume
A J24, R26 21,500 79.5
B L02, M12 4,750 17.6
C P33, T72, S67, Q47, V20 800 2.9
= 100.0
Item P33 is a judgment call. It might be considered a B item by some organizations. However, the modern tendency is to move items to as low a level as possible thereby reducing inventory
management costs.
Problem 2:
Item Class Quantity Policy Number of Items to Count Per Day
A 1,000 Every 5 days 1000/5 = 200/day
B 4,000 Every 40 days 4000/40=100/day
C 8,000 Every 100 days 8000/100=80/day
Problem 3:
The EOQ model assumes any real quantity is feasible. The actual quantity ordered may need to be an integer value and may be affected by packaging or other item characteristics. In the following Problems an EOQ of 268 is assumed.
Problem 4:
Problem 5:
Note that while demand was underestimated by nearly 50%, annual cost increases by only 20% an illustration of the degree to which the EOQ model is relatively insensitive to small errors in estimation of demand.
Problem 7:
ROP = Demand during lead-time = 3 * 15 = 45 units
Problem 8:
Problem 9:
Ordering 100 units at $50 per unit is not possible, the discount does not apply until 120 units are ordered. We need to compare the total costs for the two alternatives, Q($78) and Q = 120. In this situation, the Total Cost equation must include the cost of the item since this is not a constant.
Therefore, we should order 120 each time at a unit cost of $50 and a total cost of $52,033. Notice that Total Holding Cost is not equal to Total Ordering Cost at the lowest cost alternative (Q = 120) since this is not an EOQ.
Problem 10:
Carrying cost equals zero.
Stockout cost:
(There is no shortage if 15 units are maintained)
Therefore: Minimum cost comes from carrying a 10 unit safety stock.
Problem 11: