Document Sample

Chapter 12: Determining Optimal Level of Product Availability Exercise Solutions 1. * C 50 0.2941 u CSL C C 50 120 u o Optimal lot-size = O NORMINV(CSL , , ) = NORMINV(0.2941,100,40) = 78.34 * * Given that p = $200, s = $30, c = $150: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $2,657 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 7.41 Expected understock = ( – O)[1 – NORMDIST((O – )/, 0, 1, 1)] + NORMDIST((O – )/, 0, 1, 0) = 29.07 EXCEL worksheet 12-1 illustrates these computations 2. With revised forecasting: * C u 50 0.2941 CSL Cu Co 50 120 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.2941,100,15) = 91.88 Given that p = $200, s = $30, c = $150: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $4,121 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) 1 = 2.78 Expected understock = ( – O)[1 – NORMDIST((O – )/, 0, 1, 1)] + NORMDIST((O – )/, 0, 1, 0) = 10.9 EXCEL worksheet 12-2 illustrates these computations 3. Mean demand during lead time =DL= (2000)(2) = 4000 Standard deviation of demand during lead time = L = D L = 500 2 = 707 Safety inventory = ROP – DL = 6000 – 4000 = 2000 CSL = NORMDIST (6000, 4000, 707, 1) = 0.9977 Cost of overstocking = (0.25)(40) = $10 HQ 10 10000 Justifying cost of understocking: Cu = $411 (1 CSL) D year (1 0.9977) 2000 52 Optimal CSL = C u 80 0.8889 Cu Co 80 10 Optimal safety stock = (NORMSINV (0.8889)) (707) = 863 units EXCEL worksheet 12-3 illustrates these computations 4. Using the current policy: * C 30 0.75 u CSL C C 30 10 u o Optimal lot-size = O NORMINV(CSL , , ) = NORMINV(0.75,20000,10000) = 26,745 * * Given that p = $60, s = $20, c = $30: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) 2 + O (p – c) [1 – NORMDIST(O, , , 1)] = $472,889 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 8,236 Using South America option: * C u 30 0.857 CSL C C u o 30 5 NORMINV(CSL , , ) = NORMINV(0.857,20000,10000) * * Optimal lot-size = O = 30,676 Given that p = $60, s = $25, c = $30: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $521,024 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 11,407 So, it is evident that using South America option results in increased expected profits, but also increases the production capacity requirements needed at Champion. EXCEL worksheet 12-4 illustrates these computations 5. Current sourcing (one line): Reguplo: * C u 100 0.8333 CSL Cu Co 100 20 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.8333,10000,1000) = = 10,967 Given that p = $200, s = $80, c = $100: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) 3 – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $970,018 Each of the other models: * C u 110 0.7857 CSL Cu Co 110 30 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.7857,1000,700) = = 1,554 Given that p = $220, s = $80, c = $110: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $81,421 Total expected profits = $970,018 + 3($81,421) = $1,214,280 Tailored sourcing policy: The computations are exactly the same with revised data for Reguplo (c = $90) and for each of the other three models ( c= $120) Total expected profits = $1,281,670 Thus, it is benefical to utilize the tailored sourcing option due to increased expected profits. This option increases the optimal production lot size for Reguplo and decreases the lot sizes for each of the other three options. EXCEL worksheet 12-5 illustrates these computations 6. IBM: * C u 35 0.7447 CSL C C u o 35 12 NORMINV(CSL , , ) = NORMINV(0.7447,5000,2000) = 6,316 * * Optimal lot-size = O Given that p = $50, s = $3, c = $15: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) 4 + O (p – c) [1 – NORMDIST(O, , , 1)] = $144,796 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 1,622 Similarly, the other three are evaluated and the results are summarized below: Outputs AT&T HP Cisco Optimal cycle service level 0.7447 0.7447 0.7447 Optimal production size 8,645 5,316 5,447 Expected profits $207,245 $109,796 $106,776 Expected overstock 2,028 1,622 1,785 Total production lot size = 6316 + 8,645 + 5,316 + 5,447 = 25,723 Total expected profits = $144,796 + $207,245 + $109,796 + $106,776 = $568,612 Total expected overstock = 1,622 + 2,028 + 1,622 + 1,785 = 7,057 (= amount donated to charity on average) EXCEL worksheet 12-6 illustrates these computations 7. With aggregation: Anticipated demand = 5,000 + 7,000 + 4,000 + 4,000 = 20,000 Standard deviation = 20002 25002 20002 22002 4369 * C u 32 0.8889 CSL C Cu o 32 4 NORMINV(CSL , , ) = NORMINV(0.8889,20000,4369) * * Optimal lot-size = O = 25,333 Given that p = $50, s = $14, c = $18: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $610,210 5 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 5,568 As can be seen from the results above, postponement increases the expected profit and decreases the amount of overstock. EXCEL worksheet 12-7 illustrates these computations 8. (a) Cost of overstocking, CO = $ 0.50 Cost of understocking, CU = $ 1.00 Mean demand 50,000 Standard deviation of demand = 15,000 Optimal CSL = C u 1 0.67 Cu Co 1 0.5 Optimal order quantity = (NORMSINV (0.67))(15,000) + 50,000 = 56,461 (b) Cost of overstocking, CO = $ 0.50 Cost of understocking, CU = $ 5.00 Mean demand 50,000 Standard deviation of demand = 15,000 Optimal CSL = C u 5 0.91 C C u o 5 0.5 Optimal order quantity = (NORMSINV (0.91))(15,000) + 50,000 = 70,028 EXCEL worksheet 12-8 illustrates these computations 6 9. (a) Mean demand = 5,000 Standard deviation of demand = 2,000 Cost of overstocking, CO $ 40.00 Order size = 6,000 CSL (implied by the order size) = NORMDIST (6000-5000/2000) = 0.691 Implied cost of understocking, CU = (CO)(CSL)/(1-CSL) = (40)(0.691)/(1-0.691) = $89.64 (b) Mean demand = 5,000 Standard deviation of demand = 2,000 Cost of overstocking, CO $ 40.00 Order size = 8,000 CSL (implied by the order size) = NORMDIST (8000-5000/2000) = 0.933 Implied cost of understocking, CU = (CO)(CSL)/(1-CSL) = (40)(0.933)/(1-0.933) = $558.74 EXCEL worksheet 12-9 illustrates these computations 10. Current policy: * C u 45 0.6923 CSL Cu Co 45 20 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.6923,4000,1750) = 4879 Given that p = $125, s = $60, c = $80: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) 7 + O (p – c) [1 – NORMDIST(O, , , 1)] = $140,001 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 1,224 Southern Hemisphere option: * C u 45 0.90 CSL C Cu o 45 5 NORMINV(CSL , , ) = NORMINV(0.9,4000,1750) = 6243 * * Optimal lot-size = O Given that p = $125, s = $75, c = $80: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $164,644 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 2,326 EXCEL worksheet 12-10 illustrates these computations 11. (a) Mean demand during lead time =DL= (40)(1) = 40 Standard deviation of demand during lead time = L = D L = 5 1 = 5 Safety inventory = ROP – DL = 45 – 40 = 5 CSL = NORMDIST (45, 40, 5, 1) = 0.8413 Cost of holding one unit for one year = (0.25)(4) = $1 HQ 1 200 Justifying cost of understocking: Cu = $0.086 (1 CSL) D year (1 0.8413) 40 365 8 (b) HQ(CSL) 1 200 0.8413 Justifying cost of understocking: Cu = $0.073 (1 CSL) D year (1 0.8413) 40 365 (c) HQ 1 200 Desired CSL = 1 = 1 = 0.9909 Cu D year 1.5 40 365 Desired safety stock = (NORMSINV(0.9909))(5) = 11.8 Desired reorder point = 40 + 11.8 = 51.8 EXCEL worksheet 12-11 illustrates these computations 12. Without postponement: For each box: * C u 10 0.7692 CSL Cu Co 10 3 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.7692,20000,8000) = 25,891 Given that p = $20, s = $7, c = $10: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $168,362 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 6,965 Total expected profits = 4(168,362) = $673,446 Total expected overstock = 4(6,965) = 27,860 Total production quantity = 4(25,891) = 103,564 9 With postponement: Anticipated demand = 20,000 + 20,000 + 20,000 + 20,000 = 80,000 Standard deviation = 80002 80002 80002 80002 16000 * C 8 0.6154 u CSL C C 85 u o Optimal lot-size = O NORMINV(CSL , , ) = NORMINV(0.6154,80000,16000) * * = 84,694 Given that p = $20, s = $7, c = $12: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $560,515 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 9,003 Indifferent: At a unit cost of $10.7 the two options, i.e., postponement and no postponement would be indifferent. This unit cost is obtained by using the solver option in EXCEL by considering cell 21 as the changing cell while cell 35 is utilized as the target cell with a value of $673,446. EXCEL worksheet 12-12 illustrates these computations 13. The with and without postponement calculations are similar to problem 12 (EXCEL worksheet 12-13 illustrates these computations), but what is new in this problem is the tailored postponement which is discussed below: Tailored postponement: Popular style without postponement: C 15 CSL u 15 7 0.6818 * Cu Co Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.6818,30000,5000) = 32,364 Given that p = $35, s = $13, c = $20: 10 Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $410,757 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 3,396 Other three styles with postponement: Aggregated expected demand = 8,000 + 8,000 + 8,000 = 24,000 Standard deviation = 40002 40002 40002 6928 * C u 14 0.6182 CSL Cu Co 14 8 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.6182,24000,6928) = 26,083 Given that p = $35, s = $13, c = $21.4: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $268,281 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 18,083 Total expected profit = $410,757 + $268,281 = $679,038 Total expected overstock = 3,396 + 18,083 = 21,479 EXCEL worksheet 12-13 illustrates these computations 14. Without discount: * C u 65 0.6842 CSL Cu Co 65 30 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.6842,20000,8000) 11 = 23,836 Given that p = $95, s = $0, c = $30: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $1,029,731 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 5,470 With discount: Optimal lot-size = O* 25,000 Given that p = $95, s = $0, c = $28: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $1,076,941 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 6,295 Expected profits increase with discount. EXCEL worksheet 12-14 illustrates these computations 15. Without discount: * C u 7 0.7 CSL Cu Co 73 Optimal lot-size = O* NORMINV(CSL* , , ) = NORMINV(0.7,70000,25000) = 83,110 Given that p = $10, s = $0, c = $3: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) 12 + O (p – c) [1 – NORMDIST(O, , , 1)] = $403,077 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 17,869 With discount: Optimal lot-size = O* 100,000 Given that p = $10, s = $0, c = $2.75: Expected profits = (p – s) NORMDIST((O – )/, 0, 1, 1) – (p – s) NORMDIST((O – )/, 0, 1, 0) – O (c – s) NORMDIST(O, , , 1) + O (p – c) [1 – NORMDIST(O, , , 1)] = $410,974 Expected overstock = (O – )NORMDIST((O – )/, 0, 1, 1) + NORMDIST((O – )/, 0, 1, 0) = 31,403 Expected profits increase with discount. EXCEL worksheet 12-15 illustrates these computations 16. a. the manufacturer should order : 40-Gb 20-Gb 6-Gb 26,772 47,419 84,054 b. The expected profits for the units are: 40-Gb 20-Gb 6-Gb $1,664,888 $2,048,931 $2,080,846 c. If the available capacity is limited to 140,000 units the manufacturer should order: 40-Gb 20-Gb 6-Gb 26,772 41,300 72,028 13 Formatted: Right: -2.12" expected profits would be: 40-Gb 20-Gb 6-Gb $1,790,125 $2,072,482 $2,002,170 Formatted: Justified EXCEL worksheet 12-16 illustrates these computations. Formatted: Justified 14

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 60 |

posted: | 8/7/2012 |

language: | Latin |

pages: | 14 |

OTHER DOCS BY 2mz1O10

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.