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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 8Sales forecast 150 150 200 200 150 200 200 150Receipts 200 300 300 300 300Qty on hand 0 50 200 0 100 250 50 150 0Releases to prod. 300 300 300 300 Desk style B

Week1 2 3 4 5 6 7 8

Sales forecast 60 60 60 80 80 100 80 60Receipts 100 100 100 100 100Qty on hand 80 20 60 0 20 40 40 60 0Releases to prod. 100 100 100 100 100 Desk style C

Week1 2 3 4 5 6 7 8

Sales forecast 100 120 100 80 80 60 60 80Receipts 100 100 100 100 100Qty on hand 200 100 80 80 0 20 60 0 60Releases 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 8Desk requirement 500 100 400 500 200 400 100 0Plywood sheetsa 1500 300 1200 1500 600 1200 300 0a Desk requirements times 3 Now, find the purchase order releases for the plywood sheets.

Week1 2 3 4 5 6 7 8

Sales forecast 1500 300 1200 1500 600 1200 300 0Receipts 600 1000 1000 1000 1000Qty on hand 2400 900 1200 1000 500 900 700 400 400Releases to prod. 1000 1000 1000 1000

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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 PC Pr

c

c c

= −+

= −+

=1 1 501 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 PC Pr

c

c c

= −+

= −× +

=1 1 1500 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 10Requirements 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200Schd receipts 7500 7500On-hand qty 1700 500 6800 5600 4400 3200 2000 800 7100 5900 4700Releases 7500 7500

134

Whse 1 1 2 3 4 5 6 7 8 9 10Requirements 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200Schd receipts 7500 7500On-hand qty 1700 500 6800 5600 4400 3200 2000 800 7100 5900 4700Releases 7500 7500

Whse 2 1 2 3 4 5 6 7 8 9 10Requirements 2300 2300 2300 2300 2300 2300 2300 2300 2300 2300Schd receipts 7500 7500 7500On-hand qty 3300 1000 6200 3900 1600 6800 4500 2200 7400 5100 2800Releases 7500 7500 7500

Whse 3 1 2 3 4 5 6 7 8 9 10Requirements 2700 2700 2700 2700 2700 2700 2700 2700 2700 2700Schd receipts 7500 7500 7500 7500On-hand qty 3400 700 5500 2800 100 4900 2200 7000 4300 1600 6400Releases 7500 7500 7500 7500

Regnl whse A 1 2 3 4 5 6 7 8 9 10Requirements 22500 0 0 15000 0 15000 7500 0 7500 0Schd receipts 15000 15000On-hand qty

52300 29800 29800 29800 14800 14800 14800 7300 7300 1300 1300Releases to

plant 15000 15000

Whse 4 1 2 3 4 5 6 7 8 9 10Requirements 4100 4100 4100 4100 4100 4100 4100 4100 4100 4100Schd receipts 7500 7500 7500 7500 7500On-hand qty 5700 1600 5000 900 4300 200 3600 7000 2900 6300 2200Releases 7500 7500 7500 7500 7500

Whse 5 1 2 3 4 5 6 7 8 9 10Requirements 1700 1700 1700 1700 1700 1700 1700 1700 1700 1700Schd receipts 7500 7500On-hand qty 2300 600 6400 4700 3000 1300 7100 5400 3700 2000 300Releases 7500 7500

Whse 6 1 2 3 4 5 6 7 8 9 10Requirements 900 900 900 900 900 900 900 900 900 900Schd receipts 7500 7500On-hand qty 1200 300 6900 6000 5100 4200 3300 2400 1500 600 7200Releases 7500 7500

Regnl whse B 1 2 3 4 5 6 7 8 9 10Requirements 22500 0 7500 0 15000 7500 0 7500 7500 0Schd receipts 15000 15000 15000On-hand qty

31700 9200 24200 16700 16700 1700 9200 1700 9200 9200 9200Releases to

plant 15000 15000

135

Plant 1 2 3 4 5 6 7 8 9 10Requirements 0 0 0 30000 0 0 30000 0 0 0Schd receipts 40000 20000On-hand qty 0 0 0 0 10000 10000 10000 0 0 0 0Releases-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 COGCurrent (+4%) (1%) (-3%) (-6%) (-2%)

Sales $55.0 $57.2 $55.5 $55.0 $55.0 $55.0Cost of goods 27.5 28.6 27.5 27.5 27.5 27.0Labor & salaries 15.0 15.6 15.0 14.5 15.0 15.0Overhead 8.0 8.0 8.0 8.0 7.5 8.0Profit $ 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 forward buying 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)/2Price, No. of Total Average

Month $/lb. lb. cost,$ inventory, lb.1 1.32 25,000 33,000 12,5002 1.05 25,000 26,250 12,5003 1.10 25,000 27,500 12,5004 0.95 25,000 23,750 12,500a

100,000 $110,500 12,500a 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)/2Price, No. of Total Average

Month $/lb. lb. cost,$ inventory, lb.1 1.32 20,833 27,500 10,4172 1.05 26,190 27,500 13,0953 1.10 25,000 27,500 12,5004 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 cost20 795 1,113,000.00 5,250.00 1,987.50 $1,120,237.5050 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 1,123,987.50200 795 1,113,000.00 525.00 19,875.00 1,133,400.00300 200×795+100×750 1,092,000.00 350.00 29,250.00 1,121,600.00

300400 200×795+200×750 1,081,500.00 262.50 38,625.00 1,120,387.50

400500 200×795+200×750 1,068,200.00 210.00 47,687.50 1,116,097.50

+100×725500

550 200×795+200×750 1,063,363.64 190.91 52,218.75 1,115,773.27⇐⇐⇐⇐+150×725

550600 200×795+200×750 1,059,333.33 175.00 56,750.00 1,116,258.33

+200×725600

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 CostDayton Cincinnati 3.40 0.05 5,000 $17,250Dayton Baltimore 3.40 0.15 1,000 3,550Kansas City Dallas 3.45 0.08 2,500 8,825Minneapolis 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 DSIC

* ( , )( ). ( )

= = =2 2 120 000 400 30 100

566 units

Next, find the adjusted order quantity after the discount has been applied.

$( )

( , )( )( . )

( )( )

,*

Q dDp d I

pQp d

=−

+−

=−

+−

=10 120 000100 5 0 30

100 566100 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 is depleted is given by:

$ ,

,.Q

D= =42 700

120 0000 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 SDQ

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

P250100 100 50

25000 = ( $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 DSIC

* = = ( )( ). ( + . )

= . , or 19 units2 2 1500 250 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.