(See student companion site for Excel template.)
• Problem 1 • Solution
Tacky Souvenirs sells lovely handmade tablecloths at its island (a) First, calculate the annual demand and the annual holding
store. These tablecloths cost Taclcy $15 each. Customers want cost.
to buy the tablecloths at a rate of 240 per week. The company
operates 52 weeks per year. Tacky, the owner, estimates his Annual demand = (52 weeks X 240 units per week)
ordering cost at $50. Annual holding costs are 20 percent of the = 12,480 units
unit cost. Lead time is 2 weeks. Using the information given,
(a) Calculate the economic order quantity. Annual holding cost = (0.20 X $15)
(b) Calculate the total annual costs using Üie EOQ. = $3.00 per unit per year
(c) Determine the reorder point.
Now calculate the economic order quantity as shown in the
• Before You Begin: spreadsheet.
To calculate the economic order quantity, you use the formula
2 X 12480 X $50
= 644.98, or 645 tablecloths
$3
Q
Examine the spreadsheet to see how you can solve EOQ prob-
Remember that the demand information and the holding cost lems using a spreadsheet. Note that you can use weeldy demand
must be for the same time frame. That is, i f you use annual since the lead time is given i n weeldy increments. Just make
demand, you must use an annual holding cost. Once you have cal- sure that the average demand time frame matches the time
culated the EOQ, you calculate total annual costs with the formula frame used with lead time,
(b) The total costs are
rc -H
12480 \ / 645
rc ——$50 + $3 $1934.94
To find the reorder point, use the formula: R = dL. Remember 645 / V2
that demand must be in the same time frame as is given for lead
(c) The reorder point is
time. For example, if lead time is given as three weeks, then use
weeldy demand. If lead time is given in days, use daily demand.
R = 240 units X 2 weeks = 480 units
, SOLVED PROBLEMS » 467
A B C
1
2 Tacky Souvenirs
3
4 Problem Inputs
5 Weekly Demand 240
6 Operating Weeks per year 52 / B7: =B5*B6 |
7 Annual Demand (units) 12480
8
9 Ordering Cost $50.00
10
11 Annual Holding Cost (%) 20.0%
12 Unit Cost $15.00 / 813: = 8 1 2 * 8 1 1 [|^
13 Annual Holding Cost ($/unit) $3.00
14
15 Lead Time (weeks) 2
16
17 Calculations and Solution / B18 =SQRT((2*87*89)/813) ||
18 EOQ (exact calculation) 644.98062 / B19 =R0UND(818,0)1
19 EOQ (rounded to nearest integer) 645 / B20 =(87/819)*B9
20 Annual Ordering Costs $967.44 / 821 =(819/2)*813
21 Annual Holding Costs $967.50 / 822 = 8 2 0 + 8 2 1 1
Total Annual Costs $1,934.94 V 823 = 8 5 * 8 1 5 |r_
22
23 Reorder Point (units) 480
• Problem 2 2DS
Q =
Jack's Packs manufactures backpacks made from microfabrics.
The cutting department prepares the material for use by the H 1-
backpack stitching department. The cutting department can cut
enough material to make 200 backpacks per day. The backpack Remember that the ratio d/p does not have to be daily demand
stitching department produces 90 backpacks per day. Annual divided by daily production. You need only use figures for
demand for the product is 22,500 units. The company operates the same time frame. The ratio of annual demand divided by
250 days per year. Estimated setup cost is $60. Annual holding annual production is equivalent to the daily demand divided
cost is $6 per backpack. by daily production. You also should check to be sure that the
demand rate is smaller than the production rate. Otherwise,
(a) Calculate the economic production quantity for the cutting you can never produce enough to satisfy demand. V^^hen calcu-
department. lating total costs, make sure that you determine the maximum
(b) Calculate the total annual costs for the EPQ. inventory level when assessing holding costs.
o Before You Begin: • Solution
For this problem, calculate the EPQ. We use a modified ver- (a) First, calculate the EPQ as follows:
sion of the EOQ formula since we have relaxed the assumption
regarding all of the items being delivered at one time. W^ith the 2 X 22,500 X $60
EPQ model, units are produced daily. Some are used immedi- 904.53, or 905 backpacks
90
ately to satisfy demand, while the other units are put into inven- $6 1 ~
tory. The appropriate formula is 200
,468 « CHAPTER 12 INVENTORY MANAGEMENT POLICIES
(b) To calculate total costs, determine the maximum inventory Now that you have determined the maximum inventory level
level as follows: calculate total costs:
90 22,500 ^ \ /498
JMOX = 9 0 5 1 497.75, or 498 backpacks rc
200 $2985.71
• Problem 3 2 X 625 X $ 1 0
Ye Olde Shoe Repaire has customers requesting leather soles 91.9, or 92 pairs
$1.48
throughout the year. The owner, Warren, buys these soles from
Since this order quantity does not match the unit price used
The Leather Company (TLC) at a price of $8 per pair. In an
to calculate the EOQ, this answer is infeasible. This means
effort to improve profitability by seUing in greater quantities, if we place an order for 92 pairs, we are charged $7.60 per
the sales rep for TLC has made the following offer to Ye Olde pair rather than the $7.40 we used i n calculating the EOQ.
Shoe Repaire: I f Warren orders from 1 to 50 pairs at a time, the (b) Since the first Q is infeasible, we calculate the EOQ for the
cost per pair is $8.00. I f the order is between 5 1 and 100 pairs next higher price. Make sure to calculate the new annual
at a time, the cost is $7.60. On orders for more than 100 pairs holding cost, 2 0 percent of $7.60, or $1.52.
at a time, the cost per pair Is $7.40. The owner estimates annual
demand to be 625 pairs of soles. Holding costs are 2 0 percent 2 X 625 X $ 1 0
of unit price. The cost to place an order is $10. Determine the Q = = 90.68, or 9 1 pairs
$1.52
most cost-effective ordering poUcy for Ye Olde Shoe Repaire.
I f we place an order for 9 1 pairs, we wül be charged $7.60
• Before You Begin: per pair, which is the price we used to calculate this EOQ.
This is a quantity discount problem with proportional holding Therefore, this is a feasible order quantity. We are ready to
costs. You begin by calculating the EOQ for the least expensive calculate the total annual cost for this policy:
unit price. Check to see i f this quantity is feasible. Feasibility
occurs when you can order the EOQ quantity and pay the unit 625 91
rc $10 4- —$1.52 + ($7.60 X 625)
price that was used in your calculation. For example, if the EOQ 91
turns out to be 92 pairs of leather soles and you used a unit price
$4887.84
of $7.40 per pair, you need to check to see whether or not you
will be charged $7.40 per pair if you place an order for 92 pairs.
Since the feasible solution was not at the lowest price,
I f the initial price assumption does not match what you would
we must now compute the total cost of any cheaper price,
actually pay, then the quantity is infeasible. Once you find a
assuming that we order just enough to quahfy for the
feasible quantity, calculate the total annual costs for that policy, cheaper price. This means we need to order 101 pairs to
including the annual material costs. You must also calculate the qualify for the $7.40 price. The total cost of tills policy is
total costs associated with ordering just enough units to qualify
for any cheaper prices available. For example, i f the feasible
625 101
quantity occurs with a cost of $7.60 per pair and you know rc $10 -I- $1.48 4- ( $ 7 . 4 0 X 6 2 5 )
101
that i f you buy 100 pairs at a time you qualify for a imit price
of $7.40, you calculate the total annual cost assuming that you $4761.62
would order just enough (100 pairs) to qualify for the lower unit
price. You must do this for all prices lower than the price of the Since the total annual cost of ordering 101 pairs at a time is
feasible EOQ. Your best policy is based on the total annual costs. less expensive. Ye Olde Shoe Repaire should order 101 pairs
each time leather soles are needed.
• Solution
(a) First, we need to calculate the EOQ at the lowest price
offered. The annual holding cost is 2 0 percent of the unit
cost, or $1.48—that is, $7.40 times 2 0 percent.
• Problem 4 (a) Determine the appropriate z value.
Frank's Ribs loiows that the demand during lead time for his world- (b) Calculate how much safety stock Frank should hold.
famous ribs is described by a normal distribution with a mean of
1000 pounds and a standard deviation of 100 pounds. FranIc is
willing to accept a stockout risk of approximately 2 percent.
, DISCUSSION QUESTIONS • 469
• Before You Begin: service level, 0.9800, and the z value of 0, 0.5000. Looldng
In this problem, you need to find out how much safety stock at the entry for z = 2.05, you should see 0.4798, which is as
should be held. First, use Appendix B to determine the z value close to 0.4800 as we can get. Therefore, the appropriate z
for the desired safety stock level. Then, using the formula value is 2.05.
SS = zffrfi., calculate the required safety stock. (b) To determine the amount of safety stock Frank should hold,
multiply the z value by the standard deviation:
• Solution SS = 2.05 X 100 pounds = 205 pounds
(a) Go to Appendix B. You need to find the z value associated
with 0.4800, which is the difference between the desired Frank should hold 205 pounds of ribs in safety stock.
• Problem 5 • Solution
Peter sells programs at State University's home football games. Based on the information given, we developed a payoff table to
Peter must buy the programs before the game in multiples of 100 determine the expected profit for each possible order quantity.
(2000,2100,2200, etc.). Peter has determined that the probability of Net profit for each combination or order quantity and demand are
selling different quantities of programs at a given game is as follows: calculated as shown. The order quantity with the highest expected
profit is 2200 programs. Peter should order 2200 prograins.
Demand for Programs Probabih'ty of Demand
Probability of Occurrence
2000 0.10
0.10 0.20 0.40 0.20 0.10
2100 0.20
2200 0.40 Actual
2300 0.20 customer
2400 0.10 demand
(programs) 2000 2100 2200 2300 2400
Peter plans to sell the programs for $4 each. He pays $2.50 for
Number of
each program and there is no salvage value. Determine how
Programs Expected
many programs Peter should buy to maximize his profit.
Ordered Profit
2000 $3000 $3000 $3000 $3000 $3000 $3000
• Before You Begin:
2100 $2750 $3150 $3150 $3150 $3150 $3110
For tills problem, we are only able to make a single purchase.
2200 $2500 $2900 $3300 $3300 $3300 $3140
Determine which order quantity has tlie highest expected pay-
2300 $2250 $2650 $3050 $3450 $3450 $3010
off. Develop a payoff table to show the expected value from each
2400 $2000 $2400 $2800 $3200 $3600 $2800
order quantity.
DIscysslon Qyestlons
1. Visit a local business and identify the different types of 10. Describe what is included in shortage costs.
inventory used. 11. Explain the assumptions of the EOQ model.
2. After visiting a local business, explain the different func- 12. Describe techniques for determining order quantities other
tions of its inventory. than tiie EOQ or EPQ.
3. Explain the objectives of inventory management at the local 13. Describe how changes in the demand, ordering cost,
business. or holding cost affect the EOQ.
4. Describe how the objectives of inventory management can 14. Explain how a company can justify smaller order quantities.
be measured. 15. Explain what safety stock is for.
5. Explain the different methods for measuring customer 16. Explain how safety stock affects the reorder point.
semce. 17. Describe the type of products that require a single-period
6. Compare the two techniques, inventoiy turnover and weeks model.
of supply. 18. Explain the basic concept of ABC analysis.
7. Describe the relevant costs associated with inventory 19. Explain the concept of perpetual review.
pohcies. 20. Explain how two-bin systems work.
8. Explain what is included in the annual holding cost.
9. Describe what is included in ordering or setup costs.
