Krajewski Ch12 Sol Manual

Chapter

12

Inventory Management

DISCUSSION QUESTIONS 1. The short answer is that higher inventories do not provide an advantage in any of the nine competitive priority categories. The important point is that firms must have the “right amount” of inventory to meet their competitive priorities. The only relevant costs considered in this chapter are ordering costs, holding costs, and stockout costs. In the economic order quantity (EOQ) model, costs of placing replenishment orders tradeoff against the costs of holding inventory. Under the assumptions of the EOQ, average inventory is one-half of the order quantity. The number of orders placed per year varies inversely with order quantity. When we consider stockout costs, an additional inventory (safety stock), is held to trade-off costs of poor customer service or costs for expediting shipments from unreliable suppliers. In the lean systems chapter, we see order quantities (lot sizes) that are much smaller than the “ideal” suggested by the EOQ model. As a result, lean systems average inventory is also much lower. Are there some other relevant costs of holding inventory that we have not considered in the EOQ model? If there are, a firm that ignores these costs will make the wrong inventory decisions. These wrong decisions will make the firm less competitive. Let’s examine the relationships between inventory and the nine competitive priorities discussed in the operations strategy chapter. We compare competitors H and L. They are similar in all respects except H maintains much higher inventory than does L. 1) Low-cost operations. Costs include materials, scrap, labor, and equipment capacity that are wasted when products are defective. When a process drifts out of control, competitor H’s large lot sizes tend to result in large quantities of defectives. The EOQ does not consider the cost of defectives, and erroneously assumes that setup costs are constant. Small lots cause frequent setups, but the cost per setup decreases due to the learning curve. Competitor L will enjoy competitive advantages with lower setup, materials, labor, equipment, and inventory holding costs. 2) Top quality. Superior features, durability, safety, and convenience result from improved designs. High inventories force competitor H to choose between scrapping obsolete designs or delaying introduction of product improvements until the old inventory is consumed. In either case, L gains a competitive advantage. 3) Consistent quality. Consistency in conforming to design specifications requires consistency in supplied materials, setups, and processes. Small lots made frequently tend to increase consistency. Again, advantage goes to L. 4) Delivery speed. Large lots take longer to produce than small lots. A customer will wait less time for competitor L to set up and produce orders made in small batches.

Inventory Management • CHAPTER 12 • 307

5) On-time delivery. Contrary to expectations, large inventories do not equate to ontime delivery. It’s more like, lots of inventory equals lots of chaos. Big lots make big scheduling problems. Big lots get dropped, mishandled, and pilfered. Most lean companies experience dramatic improvement in on-time delivery. 6) Development speed. This response is similar to that given for high-performance design. Low inventories result in getting new designs to the market more quickly. 7) Customization. Lean companies usually don’t claim an advantage in customization. However, large inventories provide no advantage with regard to customization either. It remains unlikely that a customized product will be found in inventory, no matter how large. 8) Variety. Mass customizers compete on service or product variety. They will keep products at raw material or component levels until a customer orders a specific configuration. Inventories are at as low a level as possible. 9) Volume flexibility. Lean (low inventory) companies tend to produce the same quantity of every product every day, but they claim considerable volume flexibility from month to month. On the other hand, a large finished goods inventory can be used to absorb volume fluctuations. In summary, a case can be made that several competitive priorities are not considered in the EOQ model. It is sometimes difficult to place a dollar value on these competitive advantages, but the advantages invariably go to the low-inventory, small lot-size firm. So if the EQO is too large, what is the “ideal” lot size? According to the lean philosophy, the “ideal” lot size is one. 2. Reducing cycle inventories has an effect on practically every functional area. Although responses will vary, and sometimes be quite insightful, the following list contains some standard answers: Marketing—Reducing cycle inventories implies that there is less inventory on hand, which could increase stockouts if the inventories are not managed properly. Finance—Smaller-cycle inventories implies that there is less capital tied up in inventory, thereby reducing the pressure for short-term operating capital and allowing for alternative investment options. Operations—Reducing cycle inventories implies that order quantities are to be reduced. Order times and costs must be reduced to facilitate that move. Smaller order quantities enable a shift toward a lean system and enhance a uniform flow of materials through the production process. 3. Organizations will never get to the point where inventories are unneeded. Inventories provide many functions and should be managed, not eliminated. It is impossible to eliminate uncertainties in the provision of products or services. In addition, unless materials can be transported instantaneously, there will always be pipeline inventories. Cycle inventories will exist unless we universally get to the point where production of single units is feasible.

308 • PART 3 • Managing Value Chains

PROBLEMS 1. A part a. Average cycle inventory

=Q 2 = 1000 2 = 500 units = (500 units) ($50+$60) = $55,000

Value of cycle inventory b. Pipeline inventory Value of the pipeline inventory

= dL [(3800 units/year)/(50wks/yr)](6 weeks) = 456 units = (456 units)($50+$30) = $36,480

2. Prince Electronics a. Value of each DC’s pipeline inventory = (75 units/wk)(2 wk)($350/unit) = $52,500 b. Total inventory

= cycle + safety + pipeline = 5[(400/2) + (2*75) + (2*75)] = 2,500 units

3. Lockwood Industries First we rank the items from top to bottom on the basis of their dollar usage. Then we partition them into classes. The analysis was done using OM Explorer Tutor12.2—ABC Analysis. Part # Description 4 7 5 2 6 8 3 1 Total

Qty Used/Year 44,000 70,000 900 120,000 350 200 100 1,200

Value Dollar Usage $1.00 $44,000 $0.30 $21,000 $4.50 $4,050 $0.03 $3,600 $0.90 $315 $1.50 $300 $0.45 $45 $0.01 $12 $73,322

Pct of Total 60.0% 28.6% 5.5% 4.9% 0.4% 0.4% 0.1% 0.0%

Cumulative % Cumulative % of Dollar Value of Items Class 60.0% 12.5% A 88.7% 25.0% A 94.2% 37.5% B 99.1% 50.0% B 99.5% 62.5% C 99.9% 75.0% C 100.0% 87.5% C 100.0% 100.0% C


The dollar usage percentages don’t exactly match the predictions of ABC analysis. For example, Class A items account for 88.7% of the total, rather than 80%. Nonetheless, the important finding is that ABC analysis did find the “significant few.” For the items sampled, particularly close control is needed for items 4 and 7. 4. Terminator Inc. a. Average cycle inventory

Value of cycle inventory

=Q 2 = 250/2 = 125 units = (125 units)($450) = $56,250

⎧ ( 4, 000 units yr ) ⎫ = dL = ⎨ ⎬ ( 3 wk ) 50 wk yr ⎩ ⎭ = 240 units Value of pipeline inventory = (240 units)($150 + $300/2) = $72,000

b. Pipeline inventory

5. Stock-Rite Inc. Computing the annual usage value for each item and rank ordering them highest to lowest, we get: Item D205 U404

Annual Value ($) 9,690 6,075

Cumulative Value ($) 9,690 15,765

A104 L205

3,220 3,035

18,985 22,020

L104 S104 X205 X104

2,005 1,604 1,603 1,500

24,025 25,629 27,232 28,732

A: 55% B: 22%

C: 23%


One classification might be to group the top two items (i.e., 25% of the items) in A class accounting for 55% of the total value. The next two items would be classified as B and the last four as C. The dollar usage percentages don’t exactly match the predictions of ABC analysis. For example, Class A items account for only 55% of the total, rather than 80%. Nonetheless, the important finding is that ABC analysis did find the “significant few.” For the items sampled, particularly close inventory management is needed for items D205 and U404. 6. Yellow Press, Inc. a. Economic order quantity D = 2500 rolls Price = $800 roll H = 15% ( $800 ) = $120 roll-year S = $50 EOQ =

2 DS 2 ( 2500 rolls year )( $50 ) = = 2083.33 = 45.64 or 46 rolls $120 roll-year H

b. Time between orders Q 46 = = 0.0184 year, or every 4.6 days D 2500 if there are 250 working days in a year 7. Babble Inc. a. d = 400 tapes/month D = 4800 tapes/year H = $0.12 S = $12.50 2 DS 2 ( 4,800 )( $12.50 ) EOQ = = = 1, 000, 000 = 1000 tapes H $0.12 b. Time between orders Q 1, 000 = = 0.2083 years or 2.5 months D 4,800 8. Dot Com a. EOQ =

2 ( 32, 000 )( $10 ) 2 DS = = 400 books H $4

b. Optimal number of orders/year c. Optimal interval between orders d. Demand during lead time = dL

= (32,000)/400 = 80 orders = 300/80 = 3.75 days = (5 days)(32,000/300) = 533 books


e. Reorder point = dL + safety stock f. Inventory position = OH + SR – BO

= 533 + 0 = 533 books = 533 + 400 – 0 = 933 books

9. Leaky Pipe Inc. a. EOQ = b. c. d. e. f.

2 ( 30, 000 )( $10 ) 2 DS = = 775 units H $1

Optimal number of orders Optimal interval between orders Demand during lead time = dL Reorder point = dL + safety stock Inventory position = OH + SR – BO

= (30,000)/(775) = 38.7 or 39 = (300)/(39) = 7.69 days = (4 days)(30,000/300) = 400 units = 400 + 0 = 400 units = 400 +775 – 0 = 1175 units

10. Sam’s Cat Hotel a. Economic order quantity d = 90 week D = 4, 680 S = $54 Price = $11.70 H = 27% ( $11.70 ) = $3.159 2 ( 4, 680 )( 54 ) 2 DS = = 160, 000 = 400 bags H 3.159 Time between orders, in weeks Q 400 = = 0.08547 years = 4.44 weeks D 4680 EOQ =

b. Reorder point, R R = demand during protection interval + safety stock Demand during protection interval = dL = 90 * 3 = 270 bags Safety stock = zσ L When the desired cycle-service level is 80%, z = 084 . .

σ L = σ t L = 15 3 = 26 = 25.98 or 26 Safety stock = 0.84 * 26 = 21.82 or about 22 bags R = 270 + 22 = 292 c. Initial inventory position = OH + SR – BO = 320 + 0 – 0 320 – 10 = 310. Because inventory position remains above 292, it is not yet time to place an order.


d. Annual holding cost Q 500 (27% )($11.70) H= 2 2 = $789.75

Annual ordering cost D 4, 680 S= $54 Q 500 = $505.44

At the EOQ, these two costs are equal. When Q = 500 , the annual holding cost is larger than the ordering cost, therefore Q is too large. Total costs are $789.75 + $505.44 = $1,295.19. e. Annual holding cost Q 400 (27% )($11.70) H= 2 2 = $631.80

Annual ordering cost D 4, 680 S= $54 Q 400 = $631.80

Total costs at EOQ: = $1,263.60, which is $31.59 less than when order quantity is 500 bags. 11. Sam’s Cat Hotel, revisited a. If the demand is only 60 bags per week, the correct EOQ is: D = (60 units/wk)(52 wk/yr) = 3,120 bags EOQ =

2 ( 3,120 )( 54 ) 2 DS = = 326.6 or 327 bags H 3.159

If the demand is incorrectly estimated at 90 bags, the EOQ would be incorrectly calculated (from problem 10) as 400 bags: The total cost, working with the actual demand, is: Q D C= H+ S 2 Q C327 =

327 3,120 3.159 + 54 2 327

C327 = $516.50 + $515.23 C327 = $1, 031.73 400 3,120 3.159 + 54 2 400 = $631.80 + $421.20

C400 = C400

C400 = $1, 053 We can see clearly now that the cost penalty of Sam’s difficulty in foreseeing demand for kitty litter is $21.27 ($1,053.00 – $1,031.73).


b. If S = $6, and D = 60 × 52 = 3120 , the correct EOQ is:

EOQ =

2 ( 3,120 )( 6 ) 2 DS = = 108.9 or 109 bags H 3.159

The total cost, working with the actual ordering cost, is Q D H+ S Q 2 109 3,120 = 3.159 + 6 2 109 = $172.17 + $171.74

C= C109 C109

C109 = $343.91 327 3,120 3.159 + 6 2 327 = $516.50 + $57.25

C327 = C327

C327 = $573.74 If the reduced ordering cost continues to be unseen, the cost penalty for not updating the EOQ is (573.74 – 343.91) = $229.83. 12. A Q system (also known as a reorder point system) gizmos d = 300 week σ t = 15 gizmos a. Standard deviation of demand during the protection interval: σ L = σt L

σ L = 15 9 = 45 gizmos b. Average demand during the protection interval: gizmos (9 weeks) = 2700 gizmos dL = 300 week c. Reorder point R = demand during protection interval + safety stock – backorders Safety stock = zσ L When the desired cycle-service level is 99%, z = 2.33. Safety stock = 2.33 * 45 = 104.85 or 105 gizmos R = 2,700 + 105 – 0 = 2,805 13. Petromax Enterprises a. EOQ =

2 ( 50, 000 )( 35 ) 2 DS = = 1,323 units H 2


(

)

b. Safety stock = Zσ L = Z σ t L = (1.29 )(125 ) Reorder point

( 3 ) = 279.29 or 280 units

= average lead time demand + safety stock = (3)(50,000/50) + 278 = 3,278 units

14. A perpetual system (also known as a continuous review system). Find the safety stock reduction when lead time is reduced from five weeks to one week, given: Standard deviation of demand during the (five-week) protection interval is 85 dohickies. Desired cycle service level is 99% (therefore z = 2.33). Safety stock required for five-week protection interval Safety stock = zσ L = 2.33(85) = 198 dohickies Safety stock required for one-week protection interval σ L = σ t L = 85 dohickies

85 = 38 dohickies 5 Safety stock = zσ t = 2.33(38) = 88.54 or 89 dohickies

σt =

15. A two-bin system. “The two-bin system is really a Q system, with the normal level in the second bin being the reorder point R.” Find cycle-service level, given: L = 2 weeks d = 53 whatchamacallits week σ t = 5 whatchamacallits R = 120 whatchamacallits Safety stock = R – dL = 120 – (53*2) = 14 whatchamacallits Safety stock = zσ L = 14 whatchamacallits

σ L = σ t L = 5 2 = 7.07 or 7 whatchamacallits z(7) = 14 z=2 When z = 2, the cycle-service level is 97.72%.

16. Nationwide Auto Parts a. Protection interval (PI) = P + L = 6 +3 = 9 weeks Average demand during PI = 9 (100) = 900 units Standard deviation during PI = 9 • (20) = 60 units b. Target inventory = d(P+L)+zσP+L = 900 + (1.96)(60) = 1,018 c. Order quantity = Target inventory – IP = 1,018 – 350 = 668 units presuming no SR or BO


17. A P system (also known as a periodic review system). Find cycle-service level, given: L = 2 weeks P = 1 week d(P + L) = 218 gadgets σ P + L = 40 gadgets T = 300 gadgets T = Average demand during protection interval + Safety stock T = 218 + z(40) = 300 z = (300 – 218)/40 = 2.05 When z = 2.05, cycle-service level is 97.98 or 98%. 18. A Successful Product Annual Demand, D = (200)(50) = 10,000 units, H = ((0.20)(12.50)) = 2.50 a. Optimal ordering quantity =

(

b. Safety stock = Zσ L = Z σ t L

2 (10, 000 )( 50 ) 2 DS = = 633 units H 2.5

) = (2.33)(16) (4) = 74.56 or 75 units

c. Safety stock will now be % reduction in safety stock d. Safety stock will be % reduction in safety stock

= (2.33)(16) (2) = 52.72 or 53 units = (75 – 53)/75 = 29.33% = (2.33)(8) (4) = 37.28 or 38 units = (75 – 38)/75 = 49.33%

19. Sam’s Cat Hotel with a P system a. Referring to Problem 10, the EOQ is 400 bags. When the demand rate is 15 per day, the average time between orders is (400/15) = 26.67 or about 27 days. The lead time is 3 weeks × 6 days per week = 18 days. If the review period is set equal to the EOQs average time between orders (27 days), then the protection interval (P + L) = (27 + 18) = 45 days. For an 80% cycle-service level z = 084 .

σ P+ L = σ t P + L . 45 = 4108 . σ P + L = 6124 Safety stock = zσ P + L = 0.84(41.08) = 34.51 or 35 bags T = Average demand during the protection interval + Safety stock T = (15*45) + 35 = 710 b. In Problem 10, the Q system required a safety stock of 22 bags to achieve an 80% cycle-service level. Therefore, the P system requires a safety stock that is larger by (35 – 22) 13 bags. c. From Problem 10, inventory position, IP = 310. The amount to reorder is T – IP = 710 – 310 = 400.


20.

Continuous review system. a. Economic order quantity. EOQ =

2 ( 2, 000 )( 40 ) 2 DS = = 894.4 or 894 units H 2

Time between orders (TBO) = Q/D = 894/20,000 = 0.0447 years = 2.32 weeks b. Weekly demand = 20,000/52 = 385 units For a 95% cycle-service level, z = 1.645 . (100) 2 = 232.6 or 233 units Safety stock = zσ L = zσ t L = 1645 Now solve for R, as R = dL + Safety stock = 385(2) + 233 = 1003 units c. i. Annual holding cost of cycle inventory Q 894 H= ( 2 ) = $894.00 2 2 ii. Annual ordering cost D 20,000 S= $40 = $894.85 Q 894 d. With the 15-unit withdrawal, IP drops from 1,040 to 1,025 units. Because this level is above the reorder point (1,025 > 1,003), a new order is not placed. 21. Periodic review system a. From Problem 20, EOQ =

2 ( 20, 000 )( 40 ) 2 DS = = 894.4 or 894 units H 2

Number of orders per year = D Q = 20,000/894 = 22.4 orders per year. EOQ 894 = = 0.0447 years × 52 weeks year = 2.3244 weeks D 20,000 P is rounded to two weeks. P=

b. For a 95% cycle-service level, z = 1.645. Therefore Safety stock = zσ P + L

σ P+ L = σ t P + L σ P + L = 100 2 + 2 = 200 units Safety stock = 1.645(200) = 329 units, T = Average demand during the protection interval + Safety stock T = (385 * 4) + 329 = 1,869 units c. In Problem 20, with a Q system the safety stock is 233 units. Therefore, (329 – 233) = 96 more units of safety stock are needed.


22. Continuous review system a. Economic order quantity 2 DS 2(64)(52)(50) EOQ = = = 160 units H 13

b. Safety stock. When cycle-service level is 88%, z = 1.175. σ L = σ t L = 12 2 = 17 units Safety stock = zσ L = 1.175(17) = 20 units c. Reorder point R = dL + Safety stock = 64(2) + 20 = 148 units d. If Q = 200 and R = 180, average inventory investment is higher than necessary to achieve an 88% cycle-service level. The larger order quantity increases average cycle stock by 20 units, and the higher reorder point increases safety stock by 32 units. 23. Periodic review system a. From problem 22, EOQ = 160 EOQ 160 P= = = 2. 5 weeks d 64 week P is rounded to three weeks. b. For an 88% cycle-service level, z = 1.175. Therefore Safety stock = zσ P + L

σ P+ L = σ t P + L . or 27 units σ P + L = 12 3 + 2 = 268 Safety stock = 1.175(27) = 32 units T = average demand during the protection interval + Safety stock T = (64 * 5) + 32 = 352 units 24. Wood County Hospital a. D = (1000 boxes/wk)(52 wk/yr) = 52,000 boxes H = (0.l5)($35/box)=$5.25/box EOQ =

2 ( 52, 000 )( $15 ) 2 DS = = 545.1 or 545 boxes H $5.25


Q D H+ S 2 Q 900 52, 000 = $5.25 + $15.00 = $3, 229.16 2 900 545 52, 000 = $5.25 + $15.00 = $2,861.82 2 545

C= C900 C545

The savings would be $3,229.16 – $2,861.82 = $367.34. b. When the cycle-service level is 97%, z = 1.88. Therefore, σ L = σt L

σ L = 100 2 = 141.4, or 141 boxes Safety stock = zσ L = 1.88(141) = 265.08, or 265 boxes R = dL + Safety stock = 1000(2) + 265 = 2,265 boxes c. In a periodic review system, find target inventory T, given: P = 2 weeks L = 2 weeks Safety stock = zσ P + L

σ P+ L = σ t P + L σ P + L = 100 2 + 2 = 200 units Safety stock = 1.88(200) = 376 units T = Average demand during the protection interval + Safety stock T = 1000(2 + 2) + 376 T = 4376 units The screen shot below is taken from OM Explorer Solver—Inventory Systems. Notice that the total cost for the Q system is much less than that of the P system. The . reason is that the optimal value of P was not used here. The optimal value is P = 055 weeks.


Results Solver Inventory Systems Continuous Review (Q) System z

Periodic Review (P) System 1.88 Time Between Reviews (P)

2.00 Weeks

; Enter manually Safety Stock Reorder Point Annual Cost

266 Standard Deviation of Demand During Protection Interval 2266 Safety Stock $4,258.32 Average Demand During Protection Interval Target Inventory Level (T) Annual Cost

25.

Golf specialty wholesaler a. Periodic Review System 2 DS 2(2000)(40) EOQ = = = 17888 . or about 179 1-irons H 5 P=

EOQ 179 = = 0.0895 years = 4.475 or 4.0 weeks D 2000

When cycle-service level is 90%, z = 1.28. Weekly demand is (2,000 units/yr)/(50 wk/yr) = 40 units/wk L = 4 weeks T = d ( P + L ) + zσ P + L P + L = 40 ( 8 ) + 1.29 ( 3) 8 = 320 + 10.94 = 331 b. Continuous review system dL = 40 × 4 = 160 SS = zσ L = (1.29)(3) 4 = 7.68 or 8 R = 160 + 8 = 168

200 376

4000 4376 $7,614.00


26. Office Supply Shop The screen shot below is taken from OM Explorer Solver – Demand During Protection Interval Simulator. It shows the results of 500 trials. Demand During Protection Interval Distribution Bin

Back to Inputs

Upper Bound

17 29 41 53 65 77 89 101 113 125

Demand

Frequency

11 23 35 47 59 71 83 95 107 More Total

83 114 151 57 63 14 16 2 0 0 500

Average Demand During Protection Interval

Cumulative Percentage

35

16.6% 39.4% 69.6% 81.0% 93.6% 96.4% 99.6% 100.0% 100.0% 100.0%

Demand During Protection Interval 151

120%

140

Frequency

100

96.4%

93.6%

114

120

99.6%

100.0%

100.0%

100.0%

81.0%

80 60

80%

69.6%

83

57

39.4%

100%

60%

63

40%

40 20

16.6%

14

20%

16 2

0

0

95

107

More

0 11

23

35

47

59

71

83


160

0%

Demand Frequency


a. Given the simulation, the value of R must yield a service level that meets or exceeds the desired value of 95%. That value of R is 71 pens, which will yield a cycle service level of 96.4%. b. The average demand during the protection interval is 35 pens. Since the reorder point is 71, the safety stock must be 71 – 35 = 36 pens. The high level of safety stock is necessary because of the high variance in the demand during protection interval distribution and the high variance in lead time.


27. Grocery store. a. The target level (T) should be 150 tubes of Happy Breath Toothpaste. This result comes from OM Explorer Solver – Demand During Protection Interval Simulator. Demand During Protection Interval Distribution Bin

Back to Inputs

Upper Bound

60 80 100 120 140 160 180 200 220 240

Demand

Frequency

50 70 90 110 130 150 170 190 210 More Total

2 14 71 110 115 113 57 18 0 0 500



132

0.4% 3.2% 17.4% 39.4% 62.4% 85.0% 96.4% 100.0% 100.0% 100.0%

Demand During Protection Interval 120%

120

110

115

113

100.0%

100.0%

80%

80

71

62.4%

60%

57

60 39.4%

40%

40 14

20 0

100%

85.0%

100 Frequency

96.4%

100.0%

2

3.2%

50

70

0.4%

18

17.4%

90

110

130

150

170

190

20% 0

0

210

More


140

0%

Demand Frequency

b.

28.


Using OM Explorer once again, the cycle-service level for T = 150 would be 97.8%. Eliminating the variance in supply lead times will significantly increase the cycle service level of the inventory.

Floral shop a. The EOQ for the continuous review system would be as follows. Q=

2(2550)($30) = 391 $1

The demand during protection interval distribution is shown below.

322 • PART 3 • Managing Value Chains Demand During Protection Interval Distribution Bin

Back to Inputs

Upper Bound

76 112 148 184 220 256 292 328 364 400

Demand

Frequency

58 94 130 166 202 238 274 310 346 More Total

135 159 95 67 34 10 0 0 0 0 500



109

27.0% 58.8% 77.8% 91.2% 98.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Demand During Protection Interval

Frequency

140

120%

159

160

100.0%

98.0%

135

100.0%

100.0%

100.0%

100.0%

91.2% 77.8%

120

80%

95

100

58.8%

60%

80

67

60 40

100%

40% 27.0%

34 10

20 0 58

94

130

166

202

238

20% 0

0

0

0

274

310

346

More


180

0%

Demand Frequency


To attain at least a 90% cycle service level, the florist needs to set the reorder point at 166 baskets.


b. As the output from OM Explorer Solver – Q-System Simulator shows, the average cost per day is $274.74. Probability of Weekly Demand

Probabilty of Lower Range Demand Probability 0.40 0.00 0.30 0.40 0.15 0.70 0.10 0.85 0.05 0.95 1.00

Random Numbers

RN I Demand 0.6586 0.4101 0.8676 0.2831 0.4569 0.8689 0.1591 0.9864 0.4978 0.0223 0.5906 0.8835 0.1373 0.0001 0.7819 0.9917 0.5232 0.7593 0.3090 0.5006 0.4173 0.8148 0.2962 0.3003 0.3560 0.9473 0.7621 0.4240 0.9240 0.3494 0.9098 0.0235 0.2316 0.6310 0.8768 0.8892 0.4683 0.3062 0.3298 0.1754 0.2214 0.8985 0.8108 0.7581 0.7205 0.1673 0.7142 0.8320 0.9648 0.5548

RN II Lead Time 0.8794 0.2609 0.5330 0.8584 0.8724 0.9560 0.2470 0.9519 0.8590 0.7551 0.2691 0.4734 0.4465 0.4061 0.4404 0.8927 0.2572 0.2128 0.8100 0.6821 0.5249 0.4963 0.2767 0.1054 0.7946 0.9374 0.0953 0.2803 0.2087 0.8918 0.0755 0.3544 0.1659 0.8530 0.9013 0.4419 0.6197 0.4341 0.9087 0.7790 0.3099 0.4848 0.2892 0.4780 0.4660 0.4669 0.3310 0.0554 0.1822 0.1393

Probability of Lead Time

Demand (Units) 40 50 60 70 80

Probabilty of Lead Time 0.30 0.40 0.20 0.10 0.00 1.00

Lower Range Lead Time Probability (Periods) 0.00 1 0.30 2 0.70 3 0.90 4 1.00 5

Holding Cost ($/unit/period) $ Order Cost ($/order) $ Stockout Cost ($/unit) $ Order Size Reorder Point Beginning Inventory

1.0 30 10

391 166 300

Simulation of 50 Weeks

Beginning Inventory Week 1 300 2 250 3 200 4 130 5 481 6 431 7 361 8 321 9 241 10 191 11 151 12 101 13 422 14 382 15 342 16 282 17 202 18 543 19 483 20 443 21 393 22 343 23 283 24 243 25 203 26 163 27 93 28 424 29 374 30 304 31 264 32 194 33 154 34 505 35 455 36 385 37 315 38 265 39 225 40 185 41 145 42 105 43 426 44 366 45 306 46 246 47 206 48 146 49 477 50 397 Averages 296.94

Simulated Demand 50 50 70 40 50 70 40 80 50 40 50 70 40 40 60 80 50 60 40 50 50 60 40 40 40 70 60 50 70 40 70 40 40 50 70 70 50 40 40 40 40 70 60 60 60 40 60 60 80 50 53.80

Ending Inventory 250 200 130 90 431 361 321 241 191 151 101 31 382 342 282 202 152 483 443 393 343 283 243 203 163 93 33 374 304 264 194 154 114 455 385 315 265 225 185 145 105 35 366 306 246 206 146 86 397 347 243.14

Stockout Units 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00

Place Order? No No Yes No No No No No No Yes No No No No No No Yes No No No No No No No Yes No No No No No No Yes No No No No No No No Yes No No No No No No Yes No No No

Simulated Lead Time 2 3 1 3 2 3 2 2.29

Days to Receive Order 2 1 0 3 2 1 0 1 0 3 2 1 0 2 1 0 3 2 1 0 2 1 0 -

Holding Cost $ 275 $ 225 $ 165 $ 110 $ 456 $ 396 $ 341 $ 281 $ 216 $ 171 $ 126 $ 66 $ 402 $ 362 $ 312 $ 242 $ 177 $ 513 $ 463 $ 418 $ 368 $ 313 $ 263 $ 223 $ 183 $ 128 $ 63 $ 399 $ 339 $ 284 $ 229 $ 174 $ 134 $ 480 $ 420 $ 350 $ 290 $ 245 $ 205 $ 165 $ 125 $ 70 $ 396 $ 336 $ 276 $ 226 $ 176 $ 116 $ 437 $ 372 $270.04

Ordering Cost 30 30 30 30 30 30 30 $4.20

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

Stockout Cost $0.00

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

Total Cost $ 275 $ 225 $ 195 $ 110 $ 456 $ 396 $ 341 $ 281 $ 216 $ 201 $ 126 $ 66 $ 402 $ 362 $ 312 $ 242 $ 207 $ 513 $ 463 $ 418 $ 368 $ 313 $ 263 $ 223 $ 213 $ 128 $ 63 $ 399 $ 339 $ 284 $ 229 $ 204 $ 134 $ 480 $ 420 $ 350 $ 290 $ 245 $ 205 $ 195 $ 125 $ 70 $ 396 $ 336 $ 276 $ 226 $ 206 $ 116 $ 437 $ 372 $274.24


29. The simulation results with Q = 40 and R = 15 are:

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

a.

b.

Beginning Inventory 19 14 11 7 46 36 27 20 16 14 7 4 38 28 28 23 13 9 TOTAL

Open Orders Received — — — 40 — — — — — — — 40 — — — — — —

Daily Demand 5 3 4 1 10 9 7 4 2 7 3 6 10 0 5 10 4 7

Ending Inventory 14 11 7 46 36 27 20 16 14 7 4 38 28 28 23 13 9 2 343

Inventory Position 14 51 47 46 36 27 20 16 14 47 44 38 28 28 23 13 49 42

The average ending inventory is: 343 = 19.05 or 19 units 18 No stockouts occurred during any of the three cycles.

Amount Ordered 40 — — — — — — — 40 — — — — — — 40 — —


EXPERIENTIAL LEARNING: SWIFT ELECTRONIC SUPPLY, INC. This in-class exercise allows students to test an inventory system of their design against a new demand set. On the day of the simulation, students should come with sufficient copies of Table 12.6. It is best to precede the simulation with a brief overview of the simulation process and the calculation of costs. The instructor may decide to require students to bring a computer to class and use a spreadsheet of their design to accomplish the manual tasks embodied in Table 12.6. Once everyone understands the simulation procedure, the instructor uses the “actual” demands in TN1, one at a time, and proceeding at a pace such that students have a chance to decide whether or not to order that period, how much to order, and calculate relevant costs. The instructor can stop at any point, using TN2 to benchmark students’ results against any of the four provided systems in this manual. A good idea is to stop at the halfway point in the simulation and ask students what their total costs are. The variance is often quite high. The same benchmarking comparisons can be done at the end of the simulation. The instructor can use the students’ results to discuss differences in the systems tried, the importance of using safety stocks, and the value of perfect information. One of the provided systems in this manual utilizes the Wagner-Whitin (WW) approach, which is optimal for perfect forecasts. The variance in student results will be greater if this exercise is used as a prelude to a discussion of formal inventory systems (such as the Q-system or P-system). Alternatively, the exercise can be used after a presentation of the formal systems to give students a practicum for the theory. TN3 shows the cost structure and system parameters for the EOQ-system, Q-system and P-system. All the relevant case information and derived data are on the left side of the sheet, and key computed parameters for three systems are presented on the right side of the sheet. There are some other points that need to be addressed about TN3 through TN7: • • •

“Average Demand/day” and “Standard Deviation” come from a statistical analysis of the historical demand data in Table 12.4. All the ordering quantities are rounded up as integers. Consequently, the associated costs might differ a little from what they actually are. The review time in the EOQ-system is actually up to the student. In TN4 we have used the EOQ divided by average daily demand.


TN4 through TN6 show the application of the provided systems for the demand data in TN1. TN7 shows the results from WW system. In all of our reported results, inventory levels at the start of the day are used to make inventory decisions. This is consistent with the daily purchasing routine at Swift. Economic Order Quantity (EOQ) System

Under this system, students order the EOQ each and every review period, which using the case data would be 3 days, without any forecasts of future demand or consideration of demand variability. TN4 shows the performance of this system. Students may elect to use varying review periods. If so, their results will differ from TN4. Q-system

This system assumes that inventory levels are checked on a daily basis and compared to a “Reorder Point (RP).” If actual inventory level goes below the RP, an order of EOQ is placed; if above, no order will be placed. In the provided results, the RP is calculated by adding safety stock to average demand during the two-day lead time. The safety stock is designed to meet the 95 percent cycle service level. TN5 shows the results of the Q-system. P-system

The inventory level is reviewed every three days, which is determined by dividing EOQ by average demand. The target inventory level is composed of two parts: “average demand during the protection interval,” which is the review period plus the lead time, and the “safety stock.” Every review period (three days in the provided results), an order is placed to bring the inventory position up to the target inventory level. TN6 shows the performance of the P-system. Wager-Whitin (WW) System

The WW system is based on dynamic programming and assumes all demands are known with certainty. Consequently, it provides an absolute lower bound on the solution found by the students. The WW system assumes that stockouts are to be avoided. It is interesting to show the difference in total costs between the WW solution and another system because it demonstrates the cost of uncertainty. The solution using the WW system is shown in TN7. Also note that the lot sizes are shown in the day in which they must arrive. Actual release dates would be two days earlier. This implies that the first order for 1733 would have been placed in day 0, one day before the actual start of the simulation.


TN 1. Actual Data for Simulation


TN 2. Total Costs for Four Systems Day

Demand

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

870 901 960 702 1068 975 977 662 1147 1085 1041 890 1001 960 863 794 1109 948 1040 1008 961 828 764 933 960 988 1028 967 918 965 1068 996 1123 855 1035 1085 824 941 883 828 993 1008 852 725 667 1015 1167 878 824 863 1085 1067 930 1021 828 724 987 737 750 765

EOQ System $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 471.70 724.80 736.80 824.25 1,062.85 1,068.35 1,152.70 1,382.80 2,260.80 2,352.50 2,594.15 2,848.15 2,941.20 3,194.55 3,278.55 3,367.35 3,604.15 4,148.15 4,236.30 4,483.05 4,491.60 4,589.70 4,839.80 4,840.50 4,926.00 5,163.15 5,513.15 5,601.10 5,835.65 6,445.65 6,525.70 6,763.00 7,341.00 7,422.95 7,663.70 7,915.70 8,007.75 8,258.40 8,259.40 8,346.20 8,590.40 8,598.35 8,709.15 8,969.20 8,970.90 9,064.90 9,317.70 9,327.35 9,418.95 9,657.20 9,987.20 10,072.35 10,316.10 10,323.65 10,418.05 10,675.60 10,695.65 10,813.65

Q-System $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 671.70 724.80 860.70 1,147.85 1,186.15 1,327.55 1,611.60 1,641.40 1,755.35 2,024.80 2,044.20 2,151.80 2,416.25 2,441.00 2,746.50 2,804.60 2,946.90 3,238.80 3,282.65 3,421.30 3,721.75 3,775.55 3,917.55 4,210.15 4,251.35 4,380.40 4,663.55 4,698.45 4,816.15 5,084.05 5,095.80 5,401.00 5,454.45 5,589.85 5,884.05 5,931.20 6,070.40 6,368.20 6,416.35 6,550.30 6,841.65 6,896.75 7,054.70 7,361.90 7,410.75 7,551.90 7,851.85 7,908.65 8,047.40 8,332.80 8,371.70 8,495.75 8,778.40 8,824.85 8,958.15 9,254.60 9,313.55 9,470.45

P-System $ 241.50 $ 383.50 $ 548.95 $ 879.30 $ 956.25 $ 1,109.05 $ 1,413.00 $ 1,483.85 $ 1,648.35 $ 1,958.60 $ 2,016.80 $ 2,175.20 $ 2,483.55 $ 2,543.90 $ 2,707.70 $ 3,031.80 $ 3,100.45 $ 3,252.55 $ 3,552.65 $ 3,602.35 $ 3,758.85 $ 4,073.95 $ 4,150.85 $ 4,320.95 $ 4,643.05 $ 4,715.75 $ 4,869.90 $ 5,175.70 $ 5,235.60 $ 5,396.40 $ 5,703.80 $ 5,761.40 $ 5,910.40 $ 6,216.65 $ 6,271.15 $ 6,420.10 $ 6,727.85 $ 6,788.55 $ 6,952.30 $ 7,274.65 $ 7,347.35 $ 7,502.25 $ 7,814.55 $ 7,890.60 $ 8,075.95 $ 8,410.55 $ 8,486.80 $ 8,639.50 $ 8,951.00 $ 9,019.35 $ 9,176.90 $ 9,481.10 $ 9,538.80 $ 9,696.20 $ 10,012.20 $ 10,092.00 $ 10,261.40 $ 10,593.95 $ 10,689.00 $ 10,868.20

WW Solution $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

41.50 324.60 359.70 359.70 690.40 772.35 805.45 805.45 1,059.70 1,059.70 1,354.25 1,404.30 1,404.30 1,687.15 1,726.85 1,726.85 2,026.25 2,078.25 2,078.25 2,367.70 2,409.10 2,409.10 2,703.75 2,751.75 2,751.75 3,051.50 3,099.85 3,099.85 3,401.50 3,454.90 3,454.90 3,753.80 3,796.55 3,796.55 4,092.00 4,133.20 4,133.20 4,418.75 4,460.15 4,460.15 4,753.15 4,795.75 4,795.75 5,079.85 5,130.60 5,130.60 5,458.85 5,543.20 5,586.35 5,586.35 5,886.20 5,932.70 5,932.70 6,210.30 6,246.50 6,246.50 6,559.10 6,634.85 6,673.10 6,673.10


TN 3. Cost Structure and System Parameters

In-case information Cost of DRAM/piece Ordering cost/lot (S) Stockout cost/piece per day Holding Cost (% of Cost of DRAM per day) Beginning balance The cycle inventory service level Lead tme (Days) Data referred Z value at 95% confidence interval Average Demand/day Standard Deviation Holding Cost/day EOQ

$ $ $

$

10.00 200.00 2.00 0.50% 1700 95% 2

1.645 927 126 0.05 2724

EOQ System Average time between orders Order Amount Review time in EOQ system

3 2724 3

Q system Average demand during lead time Safety stock Reorder Point for Q system

1854 294 2148

P system Average demand during the protection interval Safety stock Review Period Targeted Inventory Level

4635 464 3 5099


TN 4. EOQ System Day

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Demand

870 901 960 702 1068 975 977 662 1147 1085 1041 890 1001 960 863 794 1109 948 1040 1008 961 828 764 933 960 988 1028 967 918 965 1068 996 1123 855 1035 1085 824 941 883 828 993 1008 852 725 667 1015 1167 878 824 863 1085 1067 930 1021 828 724 987 737 750 765

Order quantity

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

2724

Average EOQ

2724

Beginning Inventory

1700 830 2724 1764 1062 2724 1749 772 2834 1687 602 2724 1834 833 2724 1861 1067 2724 1776 736 2724 1763 935 2895 1962 1002 2738 1710 743 2724 1759 691 2724 1601 746 2724 1639 815 2724 1841 1013 2744 1736 884 2883 2216 1201 2758 1880 1056 2917 1832 765 2724 1703 875 2875 1888 1151 3125

Ending Actual Ending Inventory with Inventory Back orders

830 -71 1764 1062 -6 1749 772 110 1687 602 -439 1834 833 -127 1861 1067 -42 1776 736 -272 1763 935 171 1962 1002 14 1710 743 -175 1759 691 -305 1601 746 -289 1639 815 -126 1841 1013 20 1736 884 159 2216 1201 34 1880 1056 193 1832 765 -165 1703 875 151 1888 1151 401 2360

830 0 1764 1062 0 1749 772 110 1687 602 0 1834 833 0 1861 1067 0 1776 736 0 1763 935 171 1962 1002 14 1710 743 0 1759 691 0 1601 746 0 1639 815 0 1841 1013 20 1736 884 159 2216 1201 34 1880 1056 193 1832 765 0 1703 875 151 1888 1151 401 2360

Holding Cost

Stockout Cost

Daily total Cost

Order Cost

$ 41.50 $ $ 88.20 $ 53.10 $ $ 87.45 $ 38.60 $ 5.50 $ 84.35 $ 30.10 $ $ 91.70 $ 41.65 $ $ 93.05 $ 53.35 $ $ 88.80 $ 36.80 $ $ 88.15 $ 46.75 $ 8.55 $ 98.10 $ 50.10 $ 0.70 $ 85.50 $ 37.15 $ $ 87.95 $ 34.55 $ $ 80.05 $ 37.30 $ $ 81.95 $ 40.75 $ $ 92.05 $ 50.65 $ 1.00 $ 86.80 $ 44.20 $ 7.95 $ 110.80 $ 60.05 $ 1.70 $ 94.00 $ 52.80 $ 9.65 $ 91.60 $ 38.25 $ $ 85.15 $ 43.75 $ 7.55 $ 94.40 $ 57.55 $ 20.05 $ 118.00

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

142.00 12.00 878.00 254.00 84.00 544.00 350.00 610.00 578.00 252.00 330.00 -

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 -

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 142.00 88.20 253.10 12.00 87.45 238.60 5.50 84.35 230.10 878.00 91.70 241.65 254.00 93.05 253.35 84.00 88.80 236.80 544.00 88.15 246.75 8.55 98.10 250.10 0.70 85.50 237.15 350.00 87.95 234.55 610.00 80.05 237.30 578.00 81.95 240.75 252.00 92.05 250.65 1.00 86.80 244.20 7.95 110.80 260.05 1.70 94.00 252.80 9.65 91.60 238.25 330.00 85.15 243.75 7.55 94.40 257.55 20.05 118.00

927 $ 46.33

$

67.23

$

66.67

$

180.23

Accumulative Costs from Last Day

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 471.70 724.80 736.80 824.25 1,062.85 1,068.35 1,152.70 1,382.80 2,260.80 2,352.50 2,594.15 2,848.15 2,941.20 3,194.55 3,278.55 3,367.35 3,604.15 4,148.15 4,236.30 4,483.05 4,491.60 4,589.70 4,839.80 4,840.50 4,926.00 5,163.15 5,513.15 5,601.10 5,835.65 6,445.65 6,525.70 6,763.00 7,341.00 7,422.95 7,663.70 7,915.70 8,007.75 8,258.40 8,259.40 8,346.20 8,590.40 8,598.35 8,709.15 8,969.20 8,970.90 9,064.90 9,317.70 9,327.35 9,418.95 9,657.20 9,987.20 10,072.35 10,316.10 10,323.65 10,418.05 10,675.60 10,695.65

Accumulative Cost to Date

$ 241.50 $ 383.50 $ 471.70 $ 724.80 $ 736.80 $ 824.25 $ 1,062.85 $ 1,068.35 $ 1,152.70 $ 1,382.80 $ 2,260.80 $ 2,352.50 $ 2,594.15 $ 2,848.15 $ 2,941.20 $ 3,194.55 $ 3,278.55 $ 3,367.35 $ 3,604.15 $ 4,148.15 $ 4,236.30 $ 4,483.05 $ 4,491.60 $ 4,589.70 $ 4,839.80 $ 4,840.50 $ 4,926.00 $ 5,163.15 $ 5,513.15 $ 5,601.10 $ 5,835.65 $ 6,445.65 $ 6,525.70 $ 6,763.00 $ 7,341.00 $ 7,422.95 $ 7,663.70 $ 7,915.70 $ 8,007.75 $ 8,258.40 $ 8,259.40 $ 8,346.20 $ 8,590.40 $ 8,598.35 $ 8,709.15 $ 8,969.20 $ 8,970.90 $ 9,064.90 $ 9,317.70 $ 9,327.35 $ 9,418.95 $ 9,657.20 $ 9,987.20 $ 10,072.35 $ 10,316.10 $ 10,323.65 $ 10,418.05 $ 10,675.60 $ 10,695.65 $ 10,813.65


TN 5. Q-System

Day

Beginning Inventory

Demand

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1700 830 2724 1764 3786 2718 1743 3490 2828 1681 3320 2279 1389 3112 2152 1289 3219 2110 3886 2846 1838 3601 2773 2009 3800 2840 1852 3548 2581 1663 3422 2354 1358 2959 2104 3793 2708 1884 3667 2784 1956 3687 2679 1827 3826 3159 2144 3701 2823 1999 3860 2775 1708 3502 2481 1653 3653 2666 1929 3903

870 901 960 702 1068 975 977 662 1147 1085 1041 890 1001 960 863 794 1109 948 1040 1008 961 828 764 933 960 988 1028 967 918 965 1068 996 1123 855 1035 1085 824 941 883 828 993 1008 852 725 667 1015 1167 878 824 863 1085 1067 930 1021 828 724 987 737 750 765

Average Reorder Point for Q System Order Quantity

Ending Inventory with Back Orders

830 -71 1764 1062 2718 1743 766 2828 1681 596 2279 1389 388 2152 1289 495 2110 1162 2846 1838 877 2773 2009 1076 2840 1852 824 2581 1663 698 2354 1358 235 2104 1069 2708 1884 943 2784 1956 963 2679 1827 1102 3159 2144 977 2823 1999 1136 2775 1708 778 2481 1653 929 2666 1929 1179 3138

2148 2724

Actual Ending Inventory

Inventory Position

Order Quantity

830 0 1764 1062 2718 1743 766 2828 1681 596 2279 1389 388 2152 1289 495 2110 1162 2846 1838 877 2773 2009 1076 2840 1852 824 2581 1663 698 2354 1358 235 2104 1069 2708 1884 943 2784 1956 963 2679 1827 1102 3159 2144 977 2823 1999 1136 2775 1708 778 2481 1653 929 2666 1929 1179 3138

830 2724 1764 3786 2718 1743 3490 2828 1681 3320 2279 1389 3112 2152 1289 3219 2110 3886 2846 1838 3601 2773 2009 3800 2840 1852 3548 2581 1663 3422 2354 1358 2959 2104 3793 2708 1884 3667 2784 1956 3687 2679 1827 3826 3159 2144 3701 2823 1999 3860 2775 1708 3502 2481 1653 3653 2666 1929 3903 3138

2724 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0 2724 0 0

1709.48

2662.88

953.40

Holding Cost

Stockout Cost Ordering Cost

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

$ $ 142.00 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ -

41.50 88.20 53.10 135.90 87.15 38.30 141.40 84.05 29.80 113.95 69.45 19.40 107.60 64.45 24.75 105.50 58.10 142.30 91.90 43.85 138.65 100.45 53.80 142.00 92.60 41.20 129.05 83.15 34.90 117.70 67.90 11.75 105.20 53.45 135.40 94.20 47.15 139.20 97.80 48.15 133.95 91.35 55.10 157.95 107.20 48.85 141.15 99.95 56.80 138.75 85.40 38.90 124.05 82.65 46.45 133.30 96.45 58.95 156.90 85.47

2.37

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 70.00

Daily Total Cost

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 142.00 288.20 53.10 135.90 287.15 38.30 141.40 284.05 29.80 113.95 269.45 19.40 107.60 264.45 24.75 305.50 58.10 142.30 291.90 43.85 138.65 300.45 53.80 142.00 292.60 41.20 129.05 283.15 34.90 117.70 267.90 11.75 305.20 53.45 135.40 294.20 47.15 139.20 297.80 48.15 133.95 291.35 55.10 157.95 307.20 48.85 141.15 299.95 56.80 138.75 285.40 38.90 124.05 282.65 46.45 133.30 296.45 58.95 156.90 157.84



$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 671.70 724.80 860.70 1,147.85 1,186.15 1,327.55 1,611.60 1,641.40 1,755.35 2,024.80 2,044.20 2,151.80 2,416.25 2,441.00 2,746.50 2,804.60 2,946.90 3,238.80 3,282.65 3,421.30 3,721.75 3,775.55 3,917.55 4,210.15 4,251.35 4,380.40 4,663.55 4,698.45 4,816.15 5,084.05 5,095.80 5,401.00 5,454.45 5,589.85 5,884.05 5,931.20 6,070.40 6,368.20 6,416.35 6,550.30 6,841.65 6,896.75 7,054.70 7,361.90 7,410.75 7,551.90 7,851.85 7,908.65 8,047.40 8,332.80 8,371.70 8,495.75 8,778.40 8,824.85 8,958.15 9,254.60 9,313.55

241.50 383.50 671.70 724.80 860.70 1,147.85 1,186.15 1,327.55 1,611.60 1,641.40 1,755.35 2,024.80 2,044.20 2,151.80 2,416.25 2,441.00 2,746.50 2,804.60 2,946.90 3,238.80 3,282.65 3,421.30 3,721.75 3,775.55 3,917.55 4,210.15 4,251.35 4,380.40 4,663.55 4,698.45 4,816.15 5,084.05 5,095.80 5,401.00 5,454.45 5,589.85 5,884.05 5,931.20 6,070.40 6,368.20 6,416.35 6,550.30 6,841.65 6,896.75 7,054.70 7,361.90 7,410.75 7,551.90 7,851.85 7,908.65 8,047.40 8,332.80 8,371.70 8,495.75 8,778.40 8,824.85 8,958.15 9,254.60 9,313.55 9,470.45


TN 6. P-System

Day

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Average Target Inventory Level

Beginning Inventory

Demand

1700 830 4269 3309 2607 4031 3056 2079 4437 3290 2205 4058 3168 2167 4139 3276 2482 3990 3042 2002 4091 3130 2302 4335 3402 2442 4111 3083 2116 4181 3216 2148 4103 2980 2125 4064 2979 2155 4158 3275 2447 4106 3098 2246 4374 3707 2692 3932 3054 2230 4236 3151 2084 4169 3148 2320 4375 3388 2651 4349

870 901 960 702 1068 975 977 662 1147 1085 1041 890 1001 960 863 794 1109 948 1040 1008 961 828 764 933 960 988 1028 967 918 965 1068 996 1123 855 1035 1085 824 941 883 828 993 1008 852 725 667 1015 1167 878 824 863 1085 1067 930 1021 828 724 987 737 750 765

Ending Inventory with Back orders

830 -71 3309 2607 1539 3056 2079 1417 3290 2205 1164 3168 2167 1207 3276 2482 1373 3042 2002 994 3130 2302 1538 3402 2442 1454 3083 2116 1198 3216 2148 1152 2980 2125 1090 2979 2155 1214 3275 2447 1454 3098 2246 1521 3707 2692 1525 3054 2230 1367 3151 2084 1154 3148 2320 1596 3388 2651 1901 3584

Actual Ending Inventory

830 0 3309 2607 1539 3056 2079 1417 3290 2205 1164 3168 2167 1207 3276 2482 1373 3042 2002 994 3130 2302 1538 3402 2442 1454 3083 2116 1198 3216 2148 1152 2980 2125 1090 2979 2155 1214 3275 2447 1454 3098 2246 1521 3707 2692 1525 3054 2230 1367 3151 2084 1154 3148 2320 1596 3388 2651 1901 3584 2219

Inventory Position

Order quantity

830 4269 4269 3309 2607 2492 4031 3056 2079 3020 4437 3290 2205 2894 4058 3168 2167 2932 4139 3276 2482 2617 3990 3042 2002 3097 4091 3130 2302 2797 4335 3402 2442 2657 4111 3083 2116 2983 4181 3216 2148 2951 4103 2980 2125 2974 4064 2979 2155 2944 4158 3275 2447 2652 4106 3098 2246 2853 4374 3707 2692 2407 3932 3054 2230 2869 4236 3151 2084 3015 4169 3148 2320 2779 4375 3388 2651 2448 4349 3584 3196.441 2882.5

5099

Holding Cost

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

41.50 165.45 130.35 76.95 152.80 103.95 70.85 164.50 110.25 58.20 158.40 108.35 60.35 163.80 124.10 68.65 152.10 100.10 49.70 156.50 115.10 76.90 170.10 122.10 72.70 154.15 105.80 59.90 160.80 107.40 57.60 149.00 106.25 54.50 148.95 107.75 60.70 163.75 122.35 72.70 154.90 112.30 76.05 185.35 134.60 76.25 152.70 111.50 68.35 157.55 104.20 57.70 157.40 116.00 79.80 169.40 132.55 95.05 179.20 110.97

Stockout Cost

$ $ 142.00 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ 2.41

Ordering Cost

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 200.00 66.67

Daily total Cost

$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 142.00 165.45 330.35 76.95 152.80 303.95 70.85 164.50 310.25 58.20 158.40 308.35 60.35 163.80 324.10 68.65 152.10 300.10 49.70 156.50 315.10 76.90 170.10 322.10 72.70 154.15 305.80 59.90 160.80 307.40 57.60 149.00 306.25 54.50 148.95 307.75 60.70 163.75 322.35 72.70 154.90 312.30 76.05 185.35 334.60 76.25 152.70 311.50 68.35 157.55 304.20 57.70 157.40 316.00 79.80 169.40 332.55 95.05 179.20 181.17


$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 548.95 879.30 956.25 1,109.05 1,413.00 1,483.85 1,648.35 1,958.60 2,016.80 2,175.20 2,483.55 2,543.90 2,707.70 3,031.80 3,100.45 3,252.55 3,552.65 3,602.35 3,758.85 4,073.95 4,150.85 4,320.95 4,643.05 4,715.75 4,869.90 5,175.70 5,235.60 5,396.40 5,703.80 5,761.40 5,910.40 6,216.65 6,271.15 6,420.10 6,727.85 6,788.55 6,952.30 7,274.65 7,347.35 7,502.25 7,814.55 7,890.60 8,075.95 8,410.55 8,486.80 8,639.50 8,951.00 9,019.35 9,176.90 9,481.10 9,538.80 9,696.20 10,012.20 10,092.00 10,261.40 10,593.95 10,689.00


$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $

241.50 383.50 548.95 879.30 956.25 1,109.05 1,413.00 1,483.85 1,648.35 1,958.60 2,016.80 2,175.20 2,483.55 2,543.90 2,707.70 3,031.80 3,100.45 3,252.55 3,552.65 3,602.35 3,758.85 4,073.95 4,150.85 4,320.95 4,643.05 4,715.75 4,869.90 5,175.70 5,235.60 5,396.40 5,703.80 5,761.40 5,910.40 6,216.65 6,271.15 6,420.10 6,727.85 6,788.55 6,952.30 7,274.65 7,347.35 7,502.25 7,814.55 7,890.60 8,075.95 8,410.55 8,486.80 8,639.50 8,951.00 9,019.35 9,176.90 9,481.10 9,538.80 9,696.20 10,012.20 10,092.00 10,261.40 10,593.95 10,689.00 10,868.20


TN 7. Wagner-Whitin (WW) Solution Period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Average

Demand

Lot Size

870 901 960 702 1068 975 977 662 1147 1085 1041 890 1001 960 863 794 1109 948 1040 1008 961 828 764 933 960 988 1028 967 918 965 1068 996 1123 855 1035 1085 824 941 883 828 993 1008 852 725 667 1015 1167 878 824 863 1085 1067 930 1021 828 724 987 737 750 765

0 1733 0 0 3682 0 0 0 2232 0 2932 0 0 2617 0 0 3097 0 0 2797 0 0 2657 0 0 2983 0 0 2951 0 0 2974 0 0 2944 0 0 2652 0 0 2853 0 0 2407 0 0 3732 0 0 0 3082 0 0 2573 0 0 3239 0 0 0 902.3

Minimum Total Cost

6673.10

End Inventory 1700 830 1662 702 0 2614 1639 662 0 1085 0 1891 1001 0 1657 794 0 1988 1040 0 1789 828 0 1893 960 0 1995 967 0 2033 1068 0 1978 855 0 1909 824 0 1711 828 0 1860 852 0 1682 1015 0 2565 1687 863 0 1997 930 0 1552 724 0 2252 1515 765 0 973.9

End Backorder

Cum. Cost

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

41.5 324.6 359.7 359.7 690.4 772.35 805.45 805.45 1059.7 1059.7 1354.25 1404.3 1404.3 1687.15 1726.85 1726.85 2026.25 2078.25 2078.25 2367.7 2409.1 2409.1 2703.75 2751.75 2751.75 3051.5 3099.85 3099.85 3401.5 3454.9 3454.9 3753.8 3796.55 3796.55 4092 4133.2 4133.2 4418.75 4460.149 4460.149 4753.149 4795.75 4795.75 5079.85 5130.6 5130.6 5458.85 5543.2 5586.35 5586.35 5886.2 5932.7 5932.7 6210.3 6246.5 6246.5 6559.1 6634.85 6673.1 6673.1


CASE: PARTS EMPORIUM * A. Synopsis This case describes the problems facing Sue McCaskey, the new materials manager of a wholesale distributor of auto parts. She seeks ways to cut the bloated inventories while improving customer service. Back orders with excessive lost sales are all too frequent. Inventories were much higher than expected when the new facility was built, even though sales have not increased. Summary data on inventory statistics, such as inventory turns, are not available. McCaskey decides to begin with a sample of two products to uncover the nature of the problems—the EG151 exhaust gasket and the DB032 drive belt. B. Purpose The purpose of this case is to allow the student to put together a plan, using either a continuous review system (Q system) or a periodic review system (P system), for two inventory items. Enough information is available to determine the EOQ and R for a continuous review system (or P and T for a periodic review system). Because stockouts are costly relative to inventory holding costs, a 95% cycle-service level is recommended. Inventory holding costs are 21% of the value of each item (expressed at cost). The ordering costs ($20 for exhaust gaskets and $10 for drive belts) should not be increased to include charges for making customer deliveries. These charges are independent of the inventory replenishment at the warehouse and are reflected in the pricing policy. C. Analysis We now find appropriate policies for a Q system, beginning with the exhaust gasket. Shown here are the calculations of the EOQ and R, followed by a cost comparison between this continuous review system and the one now being used. The difference is what can be realized by a better inventory control system. Reducing lost sales due to back orders is surely the biggest benefit. 1. EG151 Exhaust Gasket a. New plan Begin by estimating annual demand and the variability in the demand during the lead time for this first item. Working with the weekly demands for the first 21 weeks of this year and assuming 52 business weeks per year, we find the EOQ as follows:

Weekly demand average = 102 gaskets/week Annual demand (D) = 102(52) = 5304 gaskets Holding cost = $1.85 per gasket per year (or 0.21 × 0.68 × $12.99) Ordering cost = $20 per order EOQ = 2 ( 5,304 )( $20 ) $1.85 = 339 gaskets Turning to R, the Normal Distribution appendix shows that a 95% cycle-service level corresponds to a z = 1.645. We then find *

This case was prepared by Dr. Rob Bregman, University of Houston, as a basis for classroom discussion.


Standard deviation in weekly demand (σ t ) = 2.86 gaskets, where t = 1σ Standard deviation in demand during lead time (σ L ) = 2.86

2=4

R = Average demand during the lead time + Safety stock = 2(102) + 1.645(4) = 210.6, or 211 gaskets b. Cost comparison After developing their plan, students can compare its annual cost with what would be experienced with current policies. Cost Category Ordering cost Holding cost (cycle inventory) TOTAL

Current Plan $707 139 $846

Proposed Plan $313 314 $627

The total of these two costs for the gasket is reduced by 26 percent (from $846 to $627) per year. The safety stock with the proposed plan may be higher than the current plan, if the reason for the excess back orders is that no safety stock is now being held (inaccurate inventory records or a faulty replenishment system are other explanations). The extra cost of this safety stock is minimal, however. Only four gaskets are being held as safety stock, and their annual holding cost is just another $1.85(4) = $7.40. Surely the lost sales due to back orders are substantial with the current plan and will be much less with the proposed plan. One symptom of such losses is that 11 units are on back order in week 21. A lost sale costs a minimum of $4.16 per gasket (0.32. × $12.99). If 10 percent of annual sales were lost with the current policy, this cost would be $4.16(0.10)(5304) = $2,206 per year. Such a loss would be much reduced with the 95% cycle-service level implemented with the proposed plan. 2. DB032 Drive Belt a. New plan The following demand estimates are based on weeks 13 through 21. Weeks 11 and 12 are excluded from the analysis because the new product’s start-up makes them unrepresentative. We find the EOQ as follows: Weekly demand average = 52 belts/week Annual demand (D) = 52(52) = 2704 belts Holding cost $0.97 per belt per year (or 0.21 × 0.52 × $8.89) Ordering cost $10 per order EOQ = 2 ( 2, 704 )( $10 ) $0.97 = 236 gaskets Turning now to R, where z remains at 1.645, we find: Standard deviation in weekly demand (σ t ) = 1.76 belts, where t = 1 Standard deviation in demand during lead time (σ L ) = 1.76 3 = 3 belts R = Average demand during the lead time + Safety stock = 3(52) + 1.645(3) = 160.9, or 161 belts


b. Cost comparison After developing their plan, students again can compare the cost for the belts with what would be experienced with current policies. Cost Category Ordering cost Holding cost (cycle inventory) TOTAL

Current Plan $ 27 485 $512

Proposed Plan $115 114 $229

With the belt, the total of these two costs is reduced by 55 percent. The safety stock with the proposed plan may be higher with the proposed system, as with the gaskets, but added cost for safety stock is only $0.97(3) = $2.91. The big cost once again is the lost sales due to back orders with the current plan. A lost sale costs a minimum of $4.27 per belt (0.48 × $8.89). If 10 percent of annual sales were lost, the cost with the current policy would be $4.27(0.10)(2704) = $1,155. Such a loss would be much less with the 95% cycle-service level implemented with the proposed plan. D. Recommendations For the gasket, the recommendation is to implement a continuous review system with Q = 339 and R = 211. For the belt, the recommendation is to implement a continuous review system with Q = 236 and R = 161. E. Teaching Strategy This case can be used as a “cold-call” case or as a short case prepared in advance of the class meeting. If used without prior student preparation, it works best as a team assignment. Each team can have a different assignment (P or Q system, gasket or belt). When used as a cold-call case and time is a concern, the instructor should provide the mean and standard deviation of the weekly demand for the two products. Begin with a general discussion of how to do the analysis and then work through the analysis. If done with teams, give each time to follow through. After the teams develop their policies, have them make the cost comparison. It brings back the fundamental notions of cycle inventory and ordering costs that were introduced in this Inventory Management chapter. The discussion at the end can broaden into other issues, such as applying the notion of inventory levers and the use of systems other than a Q system to control inventories. If time permits, the instructor can have the class hand-simulate their policies, using the actual demand data in the first 21 weeks of this year for the gaskets and the last 9 weeks of this year for the belts. Use a form to record the simulation, either as a handout or transparency. The starting conditions on back orders, scheduled receipts, and on-hand inventory can be what is mentioned in the case for week 21. Simulating the new system is similar to what is to be done in Advanced Problem 29 in the chapter.

Krajewski Ch12 Sol Manual

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