Assume the demand data given in the spreadsheet is normally distributed. The acc
ID: 435875 • Letter: A
Question
Assume the demand data given in the spreadsheet is normally distributed. The accounting department estimates the average costs for A, B, and C books to be $5.05, $7.39, and $10.25, respectively, for a single copy. It costs 45% per year, per unit, for annual holding costs. The batch size is 3,500 for an A book, 1,000 for a B book, and 500 for a C book. The administrative cost for ordering a batch of a book has been estimated to be $125.
What is your recommendation for each type of book? Why? How much safety stock should be held, by type of book? What is the total cost of your recommendation? What are the advantages and disadvantages of each option?
Demand Week A Books B Books C Books 1 525.00 154.00 75.00 2 517.00 147.00 151.00 3 562.00 134.00 77.00 4 455.00 145.00 78.00 5 399.00 108.00 79.00 6 526.00 139.00 80.00 7 584.00 203.00 81.00 8 542.00 154.00 231.00 9 511.00 132.00 82.00 10 602.00 168.00 233.00 11 289.00 177.00 159.00 12 602.00 212.00 84.00 13 355.00 172.00 160.00 14 329.00 154.00 237.00 15 535.00 140.00 87.00 16 571.00 154.00 163.00 17 384.00 147.00 164.00 18 641.00 269.00 90.00 19 382.00 220.00 90.00 20 655.00 253.00 241.00 21 581.00 187.00 92.00 22 435.00 243.00 243.00 23 447.00 232.00 169.00 24 399.00 202.00 95.00 25 367.00 206.00 171.00 26 487.00 273.00 96.00 27 579.00 239.00 172.00 28 545.00 203.00 248.00 29 617.00 219.00 99.00 30 364.00 292.00 249.00 31 582.00 251.00 175.00 32 499.00 289.00 102.00 33 568.00 246.00 102.00 34 486.00 238.00 103.00 35 323.00 286.00 254.00 36 623.00 216.00 180.00 37 459.00 248.00 255.00 38 452.00 326.00 256.00 39 728.00 275.00 107.00 40 631.00 336.00 183.00 41 483.00 315.00 259.00 42 619.00 318.00 185.00 43 393.00 289.00 186.00 44 421.00 359.00 111.00 45 636.00 278.00 112.00 46 600.00 347.00 113.00 47 462.00 299.00 264.00 48 683.00 368.00 114.00 49 659.00 271.00 265.00 50 431.00 346.00 117.00 51 501.00 391.00 267.00 52 494.00 308.00 118.00Explanation / Answer
BOOK TYPE A
Yearly Demand = 26,520 units
so D = 26,520
S = ordering cost = $125
H= annual holding cost - 0.45x $5.05 = $2.2725
Calculate EOQ = SQRT of 2*D *S/H
EOQ for A = 1708 units
The aggregate cost for An is given by the following formula:
TC= D/Q*S + Q/2*H
TC = 26,520/1708 * 125 + 1708/2 * 2.2725 = 1940.87 + 1940.72 = $3881.59
To calculate reorder point, R=dL
R = 510 x 5 = 2550 (510 is the normal week after week request computed by means of the spreadsheet and 5 is the lead time in weeks).
To calculate the safety stock for book type A, daily average demand is multiplied by the lead time, 5 weeks in this example. Daily average demand is 73.6 units. Therefore, 73.6 x 35 days will result in a safety stock level of 2, 576. In terms of safety stock, a 50% rule can be applied whereby the lead time is multiple by 50% of the daily demand figure, equaling 1277.5. I would recommend carrying the safety stock of 1277 based on the 50% rule because it will provide adequate stock levels while at the same time limiting inventory carrying costs of 45% in this case. The advantage of carrying the entire safety stock level is that the company is protected against an unexpected decrease in inventory and so orders will be filled. The disadvantage to meeting the safety stock number is the additional holding cost incurred. . Based on these factors, I believe the 50% rule is a good and prudent compromise that allows inventory to be met while keeping costs low.
BOOK TYPE B
The calculations for book type B will be the same as A, but the numbers will change based on the cost of each book and the demand number is lower.
S= $125
D= 12,278 units
H = .45 x $7.39 = $3.325
SQRT of 2*D *S/H
EOQ= 960.81 or961 units
Total cost for book type B:
TC= D/Q*S + Q/2*H
TC = 12,278/961*125 + 961/2*3.325
TC = $1,597 + $1,598 = $3,195
To calculate reorder point, R=dL
R = 236 x 5 = 1,180 (236 is the average weekly demand calculated via the spreadsheet and 5 is the lead time in weeks).
Safety Stock = 33.6 (daily demand) x 35 days = 1177 units
As was the case with book type A, I would recommend the 50% rule and carry half of the 1,177 safety stock figure. The rule in the case of book type B will be more effective because the holding cost for book type B is higher than book type A. Also, by maintaining a safety stock, inventory orders will be met while maintaining low cost figures.
BOOK TYPE C
The counts for book compose C will be the same as An and B, however the numbers will change in light of the cost of each book and the request number is lower.
S= $125
D= 8,104 units
H = .45 x $10.25 = $4.61
SQRT of 2*D *S/H
EOQ= 662.9 or 663 units
Total cost for book type C:
TC= D/Q*S + Q/2*H
TC = 8,104/663*125 +663/2*4.61
TC = $ + $1,527.9 + 1528.2 = $3,056.10
To calculate reorder point, R=dL
R = 156 x 5 = 780 (156 is the normal week after week request ascertained through the spreadsheet and 5 is the lead time in weeks).
Safety Stock = 22.2 (daily demand) x 35 days = 777 units
As was the case with book type A and B, I would recommend the 50% rule and carry half of the 777 safety stock figure. The rule in the case of book type C will be more effective because the holding cost for book type C is higher than book type A and B. Therefore, in this case it may be worth dropping the safety stock because of the higher holding costs, although inventories must still be met.
For each situation (A, B and C) safety stock levels ought to be kept up while in the meantime attempting to limit holding cost. Although holding costs figures are impactful, the risk of not having adequate inventory and being unable to meet demand in a timely fashion can have long-term consequences in terms of customer satisfaction and can ultimately damage the brand. It is important to factor in each variable to determine the appropriate path.
thank you.
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