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132
 
CHAPTER 10 
PURCHASING AND SUPPLY SCHEDULING DECISIONS 
 
1 
(a) The following requirements schedules will lead to the proper timing and quantities for 
the purchase orders. 
 
Desk style A 
Week
1 2 3 4 5 6 7 8
Sales forecast 150 150 200 200 150 200 200 150
Receipts 200 300 300 300 300
Qty on hand 0 50 200 0 100 250 50 150 0
Releases to prod. 300 300 300 300
 
Desk style B 
Week
1 2 3 4 5 6 7 8
Sales forecast 60 60 60 80 80 100 80 60
Receipts 100 100 100 100 100
Qty on hand 80 20 60 0 20 40 40 60 0
Releases to prod. 100 100 100 100 100
 
Desk style C 
Week
1 2 3 4 5 6 7 8
Sales forecast 100 120 100 80 80 60 60 80
Receipts 100 100 100 100 100
Qty on hand 200 100 80 80 0 20 60 0 60
Releases to prod. 100 100 100 100 100
 
Summing the releases for these three desk release schedules gives a production 
requirements schedule for desks in general and sheets of plywood in particular. That 
is, 
 
Week
1 2 3 4 5 6 7 8
Desk requirement 500 100 400 500 200 400 100 0
Plywood sheetsa 1500 300 1200 1500 600 1200 300 0
a Desk requirements times 3 
 
Now, find the purchase order releases for the plywood sheets. 
 
Week
1 2 3 4 5 6 7 8
Sales forecast 1500 300 1200 1500 600 1200 300 0
Receipts 600 1000 1000 1000 1000
Qty on hand 2400 900 1200 1000 500 900 700 400 400
Releases to prod. 1000 1000 1000 1000
 
 
 133
 Therefore, purchase orders should be placed in weeks 1, 2, 3, and 4 for 1000 sheets 
each. 
 
(b) Using Equation 10-2 in the text, the probability of not having the plywood sheets at 
the time needed would be: 
 
 P P
C Pr
c
c c
= −
+
= −
+
=1 1 5
01 5
0 02
.
. 
 
 From Appendix A, z@1-.02 = 2.05. Therefore, the lead-time should be: 
 
 T LT z sLT
* . ( ) .= + × = + =14 2 05 2 181 days 
 
 Another ½ week should be added to the current lead-time of 2 weeks. 
 
2 
(a) Using Equation 10-2, the probability of not having the item when needed for 
production is: 
 
 P P
C Pr
c
c c
= −
+
= −
× +
=1 1 150
0 2 35 365 150
0 0001
( . / )
. 
 
 The time to place an order ahead of need is: 
 days 28)4(6.314* =+=×+= LTszLTT 
 
 where z@1-.0001 = 3.6 from Appendix A. 
 
(b) Use part period cost balancing. The unit carrying cost is (0.2/52)×35 = 0.134. Then, 
 
 (Q=250) Week 4 
 0.134×[500 + 200]/2 = 46.9 
 
 (Q=1350) Weeks 4 + 5 
 0.134×[(1350 + 1050)/2 + (1050 + 200)/2] = 244.6 
 
 The carrying cost closest to the order cost of $50 is Q = 250. Order this amount. 
 
3 
Using the requirements planning procedure, we can develop a schedule of material flows 
through the network over the next 10 weeks. 
 
Whse 1 1 2 3 4 5 6 7 8 9 10
Requirements 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200
Schd receipts 7500 7500
On-hand qty 1700 500 6800 5600 4400 3200 2000 800 7100 5900 4700
Releases 7500 7500
 
 134
Whse 1 1 2 3 4 5 6 7 8 9 10
Requirements 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200
Schd receipts 7500 7500
On-hand qty 1700 500 6800 5600 4400 3200 2000 800 7100 5900 4700
Releases 7500 7500
Whse 2 1 2 3 4 5 6 7 8 9 10
Requirements 2300 2300 2300 2300 2300 2300 2300 2300 2300 2300
Schd receipts 7500 7500 7500
On-hand qty 3300 1000 6200 3900 1600 6800 4500 2200 7400 5100 2800
Releases 7500 7500 7500
Whse 3 1 2 3 4 5 6 7 8 9 10
Requirements 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700
Schd receipts 7500 7500 7500 7500
On-hand qty 3400 700 5500 2800 100 4900 2200 7000 4300 1600 6400
Releases 7500 7500 7500 7500
Regnl whse A 1 2 3 4 5 6 7 8 9 10
Requirements 22500 0 0 15000 0 15000 7500 0 7500 0
Schd receipts 15000 15000
On-hand qty
52300 29800 29800 29800 14800 14800 14800 7300 7300 1300 1300
Releases to
plant 15000 15000
Whse 4 1 2 3 4 5 6 7 8 9 10
Requirements 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100
Schd receipts 7500 7500 7500 7500 7500
On-hand qty 5700 1600 5000 900 4300 200 3600 7000 2900 6300 2200
Releases 7500 7500 7500 7500 7500
Whse 5 1 2 3 4 5 6 7 8 9 10
Requirements 1700 1700 1700 1700 1700 1700 1700 1700 1700 1700
Schd receipts 7500 7500
On-hand qty 2300 600 6400 4700 3000 1300 7100 5400 3700 2000 300
Releases 7500 7500
Whse 6 1 2 3 4 5 6 7 8 9 10
Requirements 900 900 900 900 900 900 900 900 900 900
Schd receipts 7500 7500
On-hand qty 1200 300 6900 6000 5100 4200 3300 2400 1500 600 7200
Releases 7500 7500
Regnl whse B 1 2 3 4 5 6 7 8 9 10
Requirements 22500 0 7500 0 15000 7500 0 7500 7500 0
Schd receipts 15000 15000 15000
On-hand qty
31700 9200 24200 16700 16700 1700 9200 1700 9200 9200 9200
Releases to
plant 15000 15000
 
 135
Plant 1 2 3 4 5 6 7 8 9 10
Requirements 0 0 0 30000 0 0 30000 0 0 0
Schd receipts 40000 20000
On-hand qty 0 0 0 0 10000 10000 10000 0 0 0 0
Releases-matls 40000 20000 
 
Summing the releases to the plant shows that the plant should place 30,000 cases into 
production in weeks 4 and 7. 
 Because demand is shown to be constant, the average inventory must be one-half the 
order quantity. For the six field warehouses and a shipping quantity of 7500, the average 
long run inventory would be (7500/2)×6 = 22,500 cases. For the regional warehouses, 
the average inventory would be (15,000/2)×2 = 15,000 cases. For the plant, the average 
inventory would be 20,000/2 = 10,000 cases. The total system average inventory would 
be 22,500 + 15,000 + 10,000 = 47,500 cases. 
 
4 
(a) The leverage principle shows the relative change that must be made in cost, price, or 
sales volume to affect a given change in the profit level. Usually it is used in 
reference to the cost of goods sold to show the impact that small changes in the cost 
of goods will have on profits and the important role that purchasing plays in the 
profitability of the firm. The following simple profit and loss statements will show 
how much change is needed in various activities to increase profits by 10 percent. 
 
Sales Price L&S OH COG
Current (+4%) (1%) (-3%) (-6%) (-2%)
Sales $55.0 $57.2 $55.5 $55.0 $55.0 $55.0
Cost of goods 27.5 28.6 27.5 27.5 27.5 27.0
Labor & salaries 15.0 15.6 15.0 14.5 15.0 15.0
Overhead 8.0 8.0 8.0 8.0 7.5 8.0
Profit $ 4.5 $ 5.0 $ 5.0 $ 5.0 $ 5.0 $ 5.0
 
 Due to the magnitude of cost of goods sold, it requires less than a two percent 
change in COG to increase profits by 10 percent. 
 
(b) The current ROA as: 
 
 Profit margin = (4.5/55)×100 = 8.2 percent 
 Investment turnover = 55/20 = 2.75 
 ROA = 2.75×8.2 = 22.6 percent 
 
Reducing cost of goods by 7 percent will increase profits to 55 − 27.5×0.93 − 15 − 8 
= $6.43 and the profit margin now is 6.43×100/55 = 11.7 percent. Inventory at 20 
percent of total assets is $4 million. If the cost of goods is reduced by 7 percent, 
inventory value will decline to $4×0.93 = $3.72. Total assets will be 3.72 + 16 = 
$19.72 million. The investment turnover is 55/19.72 = 2.789. The ROA now will be 
11.7×2.789 = 32.63 percent. 
 
 
 
 136
5 
(a) A mixed purchasing strategy will generally be beneficial when prices show a definite 
seasonality, they are predictable, and inventory costs associated with forward buying 
are not excessive. In the problem, we should consider forward buying in the first half 
of the year and hand-to-mouth buying in the last half. To test the various strategies, 
compare (1) hand-to-mouth buying, (2) forward buying every 2 months, (3) forward 
buying every 3 months, and (4) forward buying for the first 6 months. The results are 
summarized in Table 10-1. 
 The inventory for the hand-to-mouth buying strategy can be approximated as 
50,000/2 = 25,000. The carrying cost would be 0.30×4.98×25,000 = $37,350 per 
year. 
 The carrying cost for the two month forward buying strategy is: 
 
 0.30×4.88×[(0.5×100,000/2) + (0.5×50,000/2)] = $54,900 
 
 For the 3-month forwardbuying strategy: 
 
 0.3×4.56×[(0.5×300,000/2) + (0.5×50,000/2)] = $119,700 
 
 From the total costs in Table 10-1, the best strategy is to forward buy the first six-
month's requirements in January and hand-to-mouth buy for the last six months. 
 
(b) Some possible disadvantages are: 
 
 • Prices may fall rather than rise in the first six months 
 • There may not be adequate storage space to accommodate such a large purchase. 
 • The materials may be perishable and not easily stored. 
 • Uncertainties in the requirements and carrying costs may void the strategy. 
 
 137
 
TABLE 10-1 A Comparison of Various Forward Buying Strategies with Hand-to-Mouth Buying 
 Hand-to-mouth buy 2-month forward buy 3-month forward buy 6-month forward buy 
 Price, 
$/unit 
Quantity, 
units 
 
Total 
Price, 
$/unit 
Quantity, 
units 
 
Total 
Price, 
$/unit 
Quantity, 
units 
 
Total 
Price, 
$/unit 
Quantity, 
units 
 
Total 
Jan 4.00 50,000 $200,000 4.00 100,000 $400,000 4.00 150,000 $600,000 4.00 300,000 $1,200,000 
Feb 4.30 50,000 215,000 
Mar 4.70 50,000 235,000 4.70 100,000 470,000 
Apr 5.00 50,000 250,000 5.00 150,000 750,000 
May 5.25 50,000 262,000 5.25 100,000 525,000 
Jun 5.75 50,000 287,500 
Jly 6.00 50,000 300,000 6.00 50,000 300,000 6.00 50,000 300,000 6.00 50,000 300,000 
Aug 5.60 50,000 280,000 5.60 50,000 280,000 5.60 50,000 280,000 5.60 50,000 280,000 
Sep 5.40 50,000 270,000 5.40 50,000 270,000 5.40 50,000 270,000 5.40 50,000 270,000 
Oct 5.00 50,000 250,000 5.00 50,000 250,000 5.00 50,000 250,000 5.00 50,000 250,000 
Nov 4.50 50,000 225,000 4.50 50,000 225,000 4.50 50,000 225,000 4.50 50,000 225,000 
Dec 4.25 50,000 212,000 4.25 50,000 212,000 4.25 50,000 212,500 4.25 50,000 212,500 
 Subtotals $2,987,500 $2,932,500 $2,887,500 $2,737,500 
 Inventory costs 37,350 54,900 72,150 119,700 
 Totals $3,024,850 $2,987,400 $2,959,650 $2,857,200 
 
 Average price/unit $4.98 $4.88 $4.81 $4.56 
 
 138
6 
(a) On the average, a total expenditure of 1.10×25,000 = $27,500 should be made for 
copper each month. 
 
(b) For the next 4 months, the dollar averaging purchases would be: 
 
 
 The average per-lb. cost would be $110,000/100,970 = $1.089. The inventory 
carrying cost over 4 months would be 0.20×1.089×(4/12) ×12,622 = $916. 
 If hand-to-mouth were used, we would have: 
 
(1) (2) (3)=(1)×(2) (4)=(2)/2
Price, No. of Total Average
Month $/lb. lb. cost,$ inventory, lb.
1 1.32 25,000 33,000 12,500
2 1.05 25,000 26,250 12,500
3 1.10 25,000 27,500 12,500
4 0.95 25,000 23,750 12,500a
100,000 $110,500 12,500
a 50,000/4 = 12,500
 
 The average per-lb. cost would be $110,500/100,000 = $1.105. The inventory 
carrying cost over 4 months would be 0.20×1.105×(4/12) ×12,500 = $921. 
 If 100,000 lbs. of copper were purchased, the two strategies can be compared as 
follows. 
 
 Purchase Inventory Total 
Strategy cost cost cost 
Dollar averaging $108,900 + 916 = $109,816 
Hand-to-mouth 110,500 + 921 = 111,421 
 
 Dollar averaging buying would be preferred. 
 
7 
For an inclusive quantity discount price incentive plan, we first compute the economic 
order quantities for each range of price. Using 
 
 Q DS IC* /= 2 
 
we compute 
(1) (2) (3)=(1)×(2) (4)=(2)/2
Price, No. of Total Average
Month $/lb. lb. cost,$ inventory, lb.
1 1.32 20,833 27,500 10,417
2 1.05 26,190 27,500 13,095
3 1.10 25,000 27,500 12,500
4 0.95 28,947 27,500 14,474
100,970 $110,000 12,622a
 a50,486/4 = 12,622 
 
 139
 
 Q1 2 500 15 0 20 49 95 38 75
* ( )( ) / ( . )( . ) .= = cases 
 
 Q2 2 500 15 0 20 44 95 40 85
* ( )( ) / ( . )( . ) .= = cases 
 
Since Q2
* is outside of the second price bracket, Q1
* is the only relevant quantity. Now 
we check the total cost at Q1
* and at the minimum quantities within the price break. We 
solve: 
 
 TC PD DS Q IC Qi i i i i= + +/ / 2 
 
At Q = 38.75 
 
 TC = 49.95×500 + 500×15/38.75 + 0.2×49.95×38.75/2 
 = $25,362 
 
At Q = 50 
 
 TC = 44.95×500 + 500×15/50 + 0.2×44.95×50/2 
 = $22,850 
 
At Q = 80 
 
 TC = 39.95×500 + 500×15/80 + 0.2×39.95×80/2 
 = $20,388 
 
Floor polish should be purchased in quantities of 80 cases. 
 
8 
This noninclusive price discount problem requires solving the following relevant total 
cost equation for various order quantities until the minimum cost is found. 
 
 TC PD DS Q IC Qi i i i i= + +/ / 2 
 
The computations can be shown in the table below given that D = 1,400, S = 75, and I = 
0.25. 
 
 140
 
Q Price P×D +D×S/Q +I×C×Q/2 = Total cost
20 795 1,113,000.00 5,250.00 1,987.50 $1,120,237.50
50 795 1,113,000.00 2,100.00 4,968.75 1,120,068.75
100 795 1,113,000.00 1,050.00 9,937.50 1,123,987.50
200 795 1,113,000.00 525.00 19,875.00 1,133,400.00
300 200×795+100×750 1,092,000.00 350.00 29,250.00 1,121,600.00
300
400 200×795+200×750 1,081,500.00 262.50 38,625.00 1,120,387.50
400
500 200×795+200×750 1,068,200.00 210.00 47,687.50 1,116,097.50
+100×725
500
550 200×795+200×750 1,063,363.64 190.91 52,218.75 1,115,773.27⇐⇐⇐⇐
+150×725
550
600 200×795+200×750 1,059,333.33 175.00 56,750.00 1,116,258.33
+200×725
600
 
The optimal purchase quantity is 550 motors. 
 
9 
(a) This problem is a good application of the transportation method of linear 
programming. We begin by determining the costs for the current sourcing 
arrangement. 
 
Source Destination Price Transport Volume Cost
Dayton Cincinnati 3.40 0.05 5,000 $17,250
Dayton Baltimore 3.40 0.15 1,000 3,550
Kansas City Dallas 3.45 0.08 2,500 8,825
Minneapolis Los Angeles 3.25 0.24 1,200 4,188
Total $33,813
 
 To optimize, we establish the following transportation cost matrix and solve it using 
any appropriate method, such as the TRANLP module in LOGWARE. 
 
 Cincin-
nati 
 
Dallas 
Los 
Angeles 
 
Baltimore 
 
Capacity 
 
Minneapolis 
3.40 
 
3.44 3.49 
 1200 
3.46 
1200 
 
Kansas City 
3.55 
 
3.53 3.65 3.63 
4800 
 
Dayton 
3.45 
 5000 
3.52 
 2500 
3.67 3.55 
 1000 
 
9999 
Requirements 5000 2500 1200 1000 
 
The total cost for this solution is $33,788, or a savings of $25 over the current sourcing. 
 
 
 141
(b) Because Minneapolis is at capacity, this supplier should be examined further. If 
unlimited capacity were available at Minneapolis, all requirements would be met by 
this supplier for a total cost of $33,248, or a savings of $565 for this material. 
 
(c) The above analysis does indicate that too many suppliers are being used. Only two 
are needed if Minneapolis continues to supply at the current level. If Minneapolis can 
be expanded, it becomes the only supplier. Of course, whether the company would 
risk a single supplier for this material must be left unanswered. 
 
10 
(a) The deal-buying equation (Equation 10-5) can be applied to this problem. First, find 
the optimal order quantity before the discount. 
 
 Q DS
IC
* ( , )( )
. ( )
= = =
2 2 120 000 40
0 30 100
566 units 
 
 Next, find the adjusted order quantity after the discount has been applied. 
 
 $
( )
( , )
( )( . )
( )
( )
,
*
Q dD
p d I
pQ
p d
=
−
+
−
=
−
+
−
=
10 120 000
100 5 0 30
100 566
100 5
42 700 units 
 
 A large order size of 42,700 units should be placed. 
 
(b) The time that an order of this size will be held before it isdepleted is given by: 
 
 
$ ,
,
.Q
D
= =
42 700
120 000
0 356 years, or 18.5 weeks 
 
 142
 INDUSTRIAL DISTRIBUTORS, INC. 
Teaching Note 
 
Strategy 
The purpose of the Industrial Distributors case study is to illustrate the computation of 
purchase quantities under inclusive and noninclusive price discounts and transport rate-
weight breaks. The INPOL module of LOGWARE is helpful in conducting the analysis. 
As a teaching strategy, it may be worthwhile to begin any class discussion with the cost 
tradeoffs that are present in such a problem as this. This will help to establish the nature 
of the total cost equation that needs to be solved in this problem. 
 
Answers to Questions 
(1) What size of replenishment orders, to the nearest 50 units, should Walter place, given 
the manufacturer's noninclusive price policy? 
 
When price discounts are offered, purchase quantities are not simply determined by a 
single formula. Due to discontinuities in the total cost curve as a function of order 
quantity, the optimal order quantity is found by computing total costs for different 
quantity values. In this case of both price and transport rate breaks plus warehousing 
costs that can be affected by the order size, the following annual total cost formula is to 
be solved. 
 
 TC PD RD SD
Q
ICQ W Q = + + + + ( - )
2
300 
 
where 
 
 TC = total cost for quantity Q, $ 
 PD = purchase cost for price P, $ 
 RD = transport costs at rate R, $ 
 SD/Q = ordering cost at quantity Q, $ 
 ICQ/2 = carrying cost at quantity Q, $ 
W(Q-300) = public warehousing cost if Q is greater than 300 units, $ 
 W = public warehousing rate, $ per unit per year 
 D = annual demand, units 
 P = price for orders of size Q, $ per unit 
 R = transport per unit for shipments of size Q, $ per unit 
 S = order processing cost, $ per order 
 I = annual carrying cost, % 
 C = product value, $ per unit 
 Q = size of purchase order, units 
 
Under noninclusive price discounts, price is an average, determined by the number of 
units in each break. For example, if 250 units are to be ordered, the average price per 
unit would be computed as: 
 
 
 143
P250
100 100 50
250
00 = ( $700) + ( $680) + ( $670)× × × = $686. 
 
A table of annual costs can now be developed, as shown in Table 1. To the nearest 50 
units, the optimal purchase quantity should be 250 units. 
 
(2) If the manufacturer's pricing policy were one where the prices in each quantity break 
included all units purchased, should Walter change his replenishment order size? 
 
The average price per unit is more easily determined in this case than the previous one. 
Since all units are included in the price break back to the first unit, the average price is 
simply the price associated with a given purchase quantity. 
 Finding the optimal purchase quantity is simply a matter of determining the total cost 
for the quantities, found by the economic order quantity formula, assuming these 
quantities are feasible, and for the quantities at the transport rate-weight break. The 
comparison is made among the total costs of these alternatives. These costs are shown in 
Table 2. 
 The order quantities, as determined by the economic order quantity formula for the 
base price of $700, would be: 
 
 Q DS
IC
* = = ( )( )
. ( + . )
 = . , or 19 units2 2 1500 25
0 3 700 7 2
18 8 
 
where C is the $700 price per unit at Baltimore plus the $45 transport cost from 
Baltimore, as determined by an LTL shipment (19 units × 250 lb. = 4,750 lb.) at $18 
× 2.5 cwt. = $45 per unit. The Q values for the other prices in the schedule lie outside the 
feasible range of the price used to compute Q. 
 The optimal strategy is to purchase 201 units per order, which is one unit into the last 
price break. Yes, Walter should alter his buying strategy. 
 
TABLE 1 Annual Costs by Quantity Purchased for Noninclusive Price Discounts 
 
Quantity 
Average 
price 
Purchase 
cost 
Transport 
cost 
Ordering 
cost 
Carrying 
cost 
Warehouse 
cost 
 
Total cost 
19 $700.00 $1,050,000 $67,500 $2,049 $2,045 $0 $1,121,594 
50 700.00 1,050,000 67,500 750 5,588 0 1,123,838 
100 700.00 1,050,000 67,500 371 11,287 0 1,129,158 
150 693.33 1,039,995 67,500 250 16,613 0 1,124,363 
160 692.50 1,038,750 45,000 234 17,340 0 1,101,324 
200 690.00 1,035,000 45,000 187 21,707 0 1,101,818 
250 686.00 1,029,000 45,000 150 26,850 0 1,101,000⇐Opt. 
300 683.33 1,063,286 45,000 125 32,100 0 1,102,225 
400 680.00 1,020,000 45,000 94 42,600 1,000 1,108,694 
a EOQ at a price of ($700 + 45) per unit.
b First price break. 
c Transport rate break. 
d Second price break. 
 
TABLE 2 Annual Costs by Quantity Purchased for Inclusive Price Discounts 
 
 144
 
Quantity 
Average 
price 
Purchase 
cost 
Transport 
cost 
Ordering 
cost 
Carrying 
cost 
Warehouse 
cost 
 
Total cost 
19 $700.00 $1,050,000 $67,500 $2,049 $2,045 $0 $1,121,594 
19 680.00 Infeasible 
19 670.00 Infeasible 
101 680.00 1,020,000 67,500 371 10,984 0 1,098,855 
160 680.00 1,020,000 45,000 234 17,040 0 1,082,274 
201 670.00 1,005,000 45,000 187 21,105 0 1,032,732⇐Opt. 
a Feasible EOQ at a price of ($700 + 45) per unit. 
b Infeasible EOQ at a price of ($680 + 45) per unit. 
c Infeasible EOQ at a price of ($670 + 30) per unit. 
d First price break. 
e Transport rate break. 
 f Second price break.